Class 11 • Physics

Thermodynamics & KTG

Chapter-11

1000 Questions

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163 Easy835 Medium2 Hard

Practice Questions

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Options:

107

MediumJEE Mains2026

10 kg of ice at -10^{\circ} \mathrm{C} is added to 100 kg of water to lower its temperature from 25 { }^{\circ} \mathrm{C}. Consider no heat exchange to surroundings. The decrement to the temperature of water is \_\_\_\_ { }^{\circ} \mathrm{C}. (specific heat of ice =2100 \mathrm{~J} / \mathrm{Kg} .{ }^{\circ} \mathrm{C}, specific heat of water =4200 \mathrm{~J} / \mathrm{Kg} .{ }^{\circ} \mathrm{C}, latent heat of fusion of ice =3.36 \times 10^5 \mathrm{~J} / \mathrm{Kg} )

Options:

A) 15

B) 10

C) 6.67

D) 11.6

108

MediumJEE Mains2026

In the following p-V diagram the equation of state along the curved path is given by (V-2)^2=4 a p where a is a constant. The total work done in the closed path is

Options:

A) +\frac{1}{3 a}

B) -\frac{1}{a}

C) \frac{1}{2 a}

D) -\frac{1}{3 a}

109

EasyJEE Mains2026

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P_1 to P_2 is \alpha Joule ( P_1=21.7 \mathrm{~Pa} and \left.P_2=30 \mathrm{~Pa}, \mathrm{C}_v=21 \mathrm{~J} / \mathrm{K} . \mathrm{mol}, R=8.3 \mathrm{~J} / \mathrm{mol} . \mathrm{K}\right). The value of \alpha is \_\_\_\_ .

Options:

A) 21

B) 28

C) 24

D) 15

110

MediumJEE Mains2026

Density of water at 4^{\circ} \mathrm{C} and 20^{\circ} \mathrm{C} are 1000 \mathrm{~kg} / \mathrm{m}^3 and 998 \mathrm{~kg} / \mathrm{m}^3 respectively. The increase in internal energy of 4 kg of water when it is heated from 4^{\circ} \mathrm{C} to 20^{\circ} \mathrm{C} is \_\_\_\_ J. (specific heat capacity of water =4.2 \mathrm{~J} / \mathrm{kg}. and 1 atmospheric pressure =10^5 \mathrm{~Pa} )

Options:

A) 268799.2

B) 315826.2

C) 234699.2

D) 258700.8

111

MediumJEE Mains2026

One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature 27^{\circ} \mathrm{C} and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27^{\circ} \mathrm{C} doing the same amount of work W, then its final temperature will be (close to) \_\_\_\_ { }^{\circ} \mathrm{C}. $ \left(\log _e 2=0.693\right)

Options:

A) -56

B) -117

C) -30

D) -189

112

MediumJEE Mains2026

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 \mathrm{~cm}^2 and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by 4^{\circ} \mathrm{C}, then the piston will move \_\_\_\_ cm. (atmospheric pressure =10^5 \mathrm{~Pa} )

Options:

A) 1.55

B) 14.5

C) 15.5

D) 1.45

113

MediumJEE Mains2026

An air bubble of volume 2.9 \mathrm{~cm}^3 rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17^{\circ} \mathrm{C}. The volume of the bubble when it reaches the surface, where the water temperature is 27^{\circ} \mathrm{C}, is \_\_\_\_ \mathrm{cm}^3. ( \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, density of water =10^3 \mathrm{~kg} / \mathrm{m}^3, and 1 atm pressure is 10^5 \mathrm{~Pa} )

Options:

A) 2.0

B) 4.2

C) 3.0

D) 4.5

114

MediumJEE Mains2026

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is 32 \times 10^{18} / \mathrm{s} then collision frequency in gas A is \_\_\_\_ /s.

Options:

A) 8 \times 10^{18}

B) 2 \times 10^{18}

C) 32 \times 10^{18}

D) 4 \times 10^{18}

115

MediumJEE Mains2026

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100^{\circ} \mathrm{C} and 40^{\circ} \mathrm{C} respectively. Given the thermal conductivity of \operatorname{rod} x is three times of that of \operatorname{rod} y, the temperature at junction points B and E are (close to):

Options:

A) 60^{\circ} \mathrm{C} and 45^{\circ} \mathrm{C} respectively

B) 80^{\circ} \mathrm{C} and 70^{\circ} \mathrm{C} respectively

C) 89^{\circ} \mathrm{C} and 73^{\circ} \mathrm{C} respectively

D) 80^{\circ} \mathrm{C} and 60^{\circ} \mathrm{C} respectively

116

MediumJEE Mains2026

The volume of an ideal gas increases 8 times and temperature becomes (1 / 4)^{\text {th }} of initial temperature during a reversible change. If there is no exchange of heat in this process (\Delta \mathrm{Q}=0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

Options:

A) \mathrm{NH}_3

B) \mathrm{O}_2

C) \mathrm{CO}_2

D) He

117

EasyJEE Mains2026

The r.m.s. speed of oxygen molecules at 47 °C is equal to that of the hydrogen molecules kept at _________ °C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)

Options:

A) -100

B) -253

C) -20

D) -235

118

EasyJEE Mains2026

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27^{\circ} \mathrm{C} to 87^{\circ} \mathrm{C}. The rate of consumption of the gas is \_\_\_\_ \mathrm{g} / \mathrm{s}. (Take heat of combustion of gas =5.0 \times 10^4 \mathrm{~J} / \mathrm{g} ) specific heat capacity of water =4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}

Options:

A) 4.2

B) 2.1

C) 0.21

D) 0.42

119

EasyJEE Mains2025

A monoatomic gas having \gamma = \frac{5}{3} is stored in a thermally insulated container and the gas is suddenly compressed to \left( \frac{1}{8} \right)^{\text{th}} of its initial volume. The ratio of final pressure and initial pressure is: (\gamma is the ratio of specific heats of the gas at constant pressure and at constant volume)

Options:

A) 16

B) 32

C) 28

D) 40

120

EasyJEE Mains2025

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take g = 10 m/s 2 , specific heat of water = 4200 J/(kg K))

Options:

A) 0.36 K

B) 0.23 K

C) 0.48 K

D) 0.14 K

121

EasyJEE Mains2025

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Options:

A) 1 : \sqrt{10}

B) 10 : 1

C) 1 : 10

D) 1 : 1

122

EasyJEE Mains2025

Match List - I with List - II . List - I List - II (A) Isothermal (I) ΔW (work done) = 0 (B) Adiabatic (II) ΔQ (supplied heat) = 0 (C) Isobaric (III) ΔU (change in internal energy) ≠ 0 (D) Isochoric (IV) ΔU = 0 Choose the correct answer from the options given below :

Options:

A) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

B) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

C) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

D) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

123

EasyJEE Mains2025

Match the List I with List II List - I List - II (A) Triatomic rigid gas (I) \frac{C_p}{C_v}=\frac{5}{3} (B) Diatomic non-rigid gas (II) \frac{C_p}{C_v}=\frac{7}{5} (C) Monoatomic gas (III) \frac{C_p}{C_v}=\frac{4}{3} (D) Diatomic rigid gas (IV) \frac{C_p}{C_v}=\frac{9}{7} Choose the correct answer from the options given below:

Options:

A) A-III, B-IV, C-I, D-II

B) A-II, B-IV, C-I, D-III

C) A-IV, B-II, C-III, D-I

D) A-III, B-II, C-IV, D-I

124

MediumJEE Mains2025

Consider a rectangular sheet of solid material of length l=9 \mathrm{~cm} and width \mathrm{d}=4 \mathrm{~cm}. The coefficient of linear expansion is \alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1} at room temperature and one atmospheric pressure. The mass of sheet m=0.1 \mathrm{~kg} and the specific heat capacity C_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}. If the amount of heat supplied to the material is 8.1 \times 10^2 \mathrm{~J} then change in area of the rectangular sheet is :

Options:

A) 2.0 \times 10^{-6} \mathrm{~m}^2

B) 6.0 \times 10^{-7} \mathrm{~m}^2

C) 3.0 \times 10^{-7} \mathrm{~m}^2

D) 4.0 \times 10^{-7} \mathrm{~m}^2

125

MediumJEE Mains2025

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K . If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa ).

Options:

A) 24

B) 4.4

C) 18

D) 6

126

EasyJEE Mains2025

Match List - I with List - II. List - I List - II (A) Isobaric (I) \Delta Q=\Delta W (B) Isochoric (II) \Delta Q=\Delta U (C) Adiabatic (III) \Delta Q= zero (D) Isothermal (IV) \Delta Q=\Delta U+P\Delta V \Delta Q= Heat supplied \Delta W= Work done by the system \Delta \mathrm{U}= Change in internal energy \mathrm{P}= Pressure of the system \Delta \mathrm{V}= Change in volume of the system Choose the correct answer from the options given below :

Options:

A) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

B) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

C) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

D) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)

127

MediumJEE Mains2025

Consider the sound wave travelling in ideal gases of \mathrm{He}, \mathrm{CH}_4, and \mathrm{CO}_2. All the gases have the same ratio \frac{P}{\rho}, where P is the pressure and \rho is the density. The ratio of the speed of sound through the gases \mathrm{V}_{\mathrm{He}}: \mathrm{V}_{\mathrm{CH}_4}: \mathrm{V}_{\mathrm{CO}_2} is given by

Options:

A) \sqrt{\frac{7}{5}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}

B) \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{4}{3}}

C) \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{7}{5}}

D) \sqrt{\frac{4}{3}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{7}{5}}

128

MediumJEE Mains2025

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 \times 10^{-7} \mathrm{~m} and 600 \mathrm{~m} / \mathrm{s}, respectively. Find the frequency of its collisions.

Options:

A) 5 \times 10^8 / \mathrm{s}

B) 9 \times 10^5 / \mathrm{s}

C) 2 \times 10^{10} / \mathrm{s}

D) 2 \times 10^9 / \mathrm{s}

129

MediumJEE Mains2025

An ideal gas exists in a state with pressure P_0, volume V_0. It is isothermally expanded to 4 times of its initial volume \left(\mathrm{V}_0\right), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

Options:

A) \mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.75)

B) \mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.75)

C) \mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.25)

D) \mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.25)

130

EasyJEE Mains2025

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4 \% when heated by 1^{\circ} \mathrm{C}. Its initial temperature must be:

Options:

A) 2500 K

B) 25^{\circ} \mathrm{C}

C) 250^{\circ} \mathrm{C}

D) 250 K

131

MediumJEE Mains2025

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 \mathrm{~cm}^3 and temperature 27^{\circ} \mathrm{C}. The change in temperature when the gas is adiabatically compressed to 200 \mathrm{~cm}^3 is: (Take \gamma=1.5 ; \gamma is the ratio of specific heats at constant pressure and at constant volume)

Options:

A) 300 K

B) 600 K

C) 327 K

D) 522 K

132

MediumJEE Mains2025

During the melting of a slab of ice at 273 K at atmospheric pressure :

Options:

A) Internal energy of ice-water system remains unchanged.

B) Positive work is done by the ice-water system on the atmosphere.

C) Positive work is done on the ice-water system by the atmosphere.

D) Internal energy of the ice-water system decreases.

133

MediumJEE Mains2025

A piston of mass M is hung from a massless spring whose restoring force law goes as F=-k x^3, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height \mathrm{L}_0 to \mathrm{L}_1, the total energy delivered by the filament is:(Assume spring to be in its natural length before heating)

Options:

A) n R T \ln \left(\frac{L_1}{L_0}\right)+M g\left(L_1-L_0\right)+\frac{3 k}{4}\left(L_1{ }^4-L_0{ }^4\right)

B) n R T \ln \left(\frac{L_1}{L_0}\right)+M g\left(L_1-L_0\right)+\frac{k}{4}\left(L_1^4-L_0{ }^4\right)

C) n R T \ln \left(\frac{L_1^2}{L_0^2}\right)+\frac{M g}{2}\left(L_1-L_0\right)+\frac{k}{4}\left(L_1^4-L_0{ }^4\right)

D) 3 n R T \ln \left(\frac{L_1}{L_0}\right)+2 M g\left(L_1-L_0\right)+\frac{k}{3}\left(L_1{ }^3-L_0{ }^3\right)

134

EasyJEE Mains2025

\text { Match List - I with List - II. } \begin{array}{lll} & \text { List - I } & {List - II }\\ \text { } \\ \text { (A) } & \text { Heat capacity of body } & \text { (I) } \mathrm{J} \mathrm{~kg}^{-1} \\ \text { (B) } & \text { Specific heat capacity of body } & \text { (II) } \mathrm{J} \mathrm{~K}^{-1} \\ \text { (C) } & \text { Latent heat } & \text { (III) } \mathrm{J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1} \\ \text { (D) } & \text { Thermal conductivity } & \text { (IV) } \mathrm{J} \mathrm{~m}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1} \end{array} \text { Choose the correct answer from the options given below : }

Options:

A) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

B) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

C) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

D) (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

135

MediumJEE Mains2025

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from \mathrm{T}_1 to \mathrm{T}_2 is proportional to \left(\mathrm{T}_2-\mathrm{T}_1\right). Choose the correct answer from the options given below :

Options:

A) (B), (D) only

B) (B), (E) only

C) (A), (C), (E) only

D) (A), (C), (D) only

136

EasyJEE Mains2025

In an adiabatic process, which of the following statements is true?

Options:

A) The internal energy of the gas decreases as the temperature increases

B) The molar heat capacity is zero

C) Work done by the gas equals the increase in internal energy

D) The molar heat capacity is infinite

137

MediumJEE Mains2025

The equation for real gas is given by \left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where \mathrm{P}, \mathrm{V}, \mathrm{T} and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \mathrm{ab}^{-2} is equivalent to that of :

Options:

A) Compressibility

B) Planck's constant

C) Energy density

D) Strain

138

EasyJEE Mains2025

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

Options:

A) low thermal conductivity and high electrical conductivity

B) low thermal conductivity and low electrical conductivity

C) high thermal conductivity and high electrical conductivity

D) high thermal conductivity and low electrical conductivity

139

MediumJEE Mains2025

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Reason (R) : In isothermal process, PV = constant, while in adiabatic process PV^{\gamma} = constant. Here \gamma is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below:

Options:

A) (A) is true but (R) is false

B) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

C) (A) is false but (R) is true

D) Both (A) and (R) are true and (R) is the correct explanation of (A)

140

MediumJEE Mains2025

A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

Options:

A) \frac{13}{5}t

B) \frac{10}{13}t

C) \frac{5}{13}t

D) \frac{13}{10}t

141

MediumJEE Mains2025

A poly-atomic molecule \left(C_V=3 R, C_P=4 R\right., where R is gas constant) goes from phase space point \mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right) to point \mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right) to point \mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right. \mathrm{Pa}, \mathrm{V}_C=8 \times 10^{-6} \mathrm{~m}^3 ). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is :

Options:

A) 500 \mathrm{R}(\ln 3+\ln 4)

B) 450 \mathrm{R}(\ln 4-\ln 3)

C) 500 \mathrm{R} \ln 2

D) 400 \mathrm{R} \ln 4

142

EasyJEE Mains2025

The work done in an adiabatic change in an ideal gas depends upon only :

Options:

A) change in its pressure

B) change in its temperature

C) change in its specific heat

D) change in its volume

143

EasyJEE Mains2025

The ratio of vapour densities of two gases at the same temperature is \frac{4}{25} , then the ratio of r.m.s. velocities will be :

Options:

A) \frac{5}{2}

B) \frac{25}{4}

C) \frac{4}{25}

D) \frac{2}{5}

144

MediumJEE Mains2025

The kinetic energy of translation of the molecules in 50 g of \text{CO}_2 gas at 17°C is :

Options:

A) 4205.5 J

B) 3582.7 J

C) 3986.3 J

D) 4102.8 J

145

EasyJEE Mains2025

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Options:

146

MediumJEE Mains2025

A Carnot engine (\mathrm{E}) is working between two temperatures 473 K and 273 K . In a new system two engines - engine E_1 works between 473 K to 373 K and engine E_2 works between 373 K to 273 K . If \eta_{12}, \eta_1 and \eta_2 are the efficiencies of the engines E, E_1 and E_2, respectively, then

Options:

A) \eta_{12}=\eta_1 \eta_2

B) \eta_{12}=\eta_1+\eta_2

C) \eta_{12} \geq \eta_1+\eta_2

D) \eta_{12}<\eta_1+\eta_2

147

EasyJEE Mains2025

The temperature of a body in air falls from 40^{\circ} \mathrm{C} to 24^{\circ} \mathrm{C} in 4 minutes. The temperature of the air is 16^{\circ} \mathrm{C}. The temperature of the body in the next 4 minutes will be :

Options:

A) \frac{28}{3}{ }^{\circ} \mathrm{C}

B) \frac{56}{3}{ }^{\circ} \mathrm{C}

C) \frac{42}{3}{ }^{\circ} \mathrm{C}

D) \frac{14}{3}{ }^{\circ} \mathrm{C}

148

MediumJEE Mains2025

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

Options:

A) zero

B) 40\pi

C) 5\pi

D) 10\pi

149

MediumJEE Mains2025

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Both (\mathbf{A}) and (\mathbf{R}) are true and (\mathbf{R}) is the correct explanation of (\mathbf{A})

B) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

C) (A) is false but (R) is true

D) (A) is true but (\mathbf{R}) is false

150

EasyJEE Mains2025

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

Options:

151

MediumJEE Mains2025

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

Options:

A) A, C Only

B) A, D, E Only

C) E Only

D) A, B, C, D Only

152

EasyJEE Mains2025

Water of mass m gram is slowly heated to increase the temperature from T_1 to T_\gamma. The change in entropy of the water, given specific heat of water is 1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, is :

Options:

A) \mathrm{m}\left(\mathrm{T}_2-\mathrm{T}_1\right)

B) zero

C) \mathrm{m} \ln \left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)

D) \mathrm{m} \ln \left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)

153

EasyJEE Mains2025

Using the given P-V diagram, the work done by an ideal gas along the path A B C D is :

Options:

A) 3 \mathrm{P}_0 \mathrm{~V}_0

B) -3 \mathrm{P}_0 \mathrm{~V}_0

C) -4 \mathrm{P}_0 \mathrm{~V}_0

D) 4 \mathrm{P}_0 \mathrm{~V}_0

154

EasyJEE Mains2025

Match the List - I with List - II List - I List - II (A) Pressure varies inversely with volume of an ideal gas. (I) Adiabatic process (B) Heat absorbed goes partly to increase internal energy and partly to do work. (II) Isochoric process (C) Heat is neither absorbed nor released by a system. (III) Isothermal process (D) No work is done on or by a gas. (IV) Isobaric process Choose the correct answer from the options given below:

Options:

A) A-I, B-III, C-II, D-IV

B) A-I, B-IV, C-II, D-III

C) A-III, B-I, C-IV, D-II

D) A-III, B-IV, C-I, D-II

155

EasyJEE Mains2025

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is _______ grams. (Latent heat of fusion of lead =2.5 \times 10^4 \mathrm{JKg}^{-1} and specific heat capacity of lead =125 \mathrm{JKg}^{-1} \left.\mathrm{K}^{-1}\right)

Options:

A) 20

B) 15

C) 5

D) 10

156

EasyJEE Mains2025

Given are statements for certain thermodynamic variables, (A) Internal energy, volume (\mathrm{V}) and mass (\mathrm{M}) are extensive variables. (B) Pressure (P), temperature ( T ) and density ( \rho ) are intensive variables. (C) Volume (V), temperature (T) and density ( \rho ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :

Options:

A) (C) and (D) Only

B) (A) and (B) Only

C) (D) and (A) Only

D) (B) and (C) Only

157

MediumJEE Mains2025

For a diatomic gas, if \gamma_1=\left(\frac{C p}{C v}\right) for rigid molecules and \gamma_2=\left(\frac{C p}{C v}\right) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)

Options:

A) \gamma_2<\gamma_1

B) \gamma_2>\gamma_1

C) \gamma_2=\gamma_1

D) 2 \gamma_2=\gamma_1

158

MediumJEE Mains2025

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

Options:

A) 64 E

B) 16 E

C) E

D) 256 E

159

MediumJEE Mains2025

An amount of ice of mass 10^{-3} \mathrm{~kg} and temperature -10^{\circ} \mathrm{C} is transformed to vapour of temperature 110^{\circ} \mathrm{C} by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice =2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, specific heat of water =4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, specific heat of steam =1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, Latent heat of ice =3.35 \times 10^5 \mathrm{Jkg}^{-1} and Latent heat of steam =2.25 \times 10^6 \mathrm{Jkg}^{-1} )

Options:

A) 3022 J

B) 3043 J

C) 3003 J

D) 3024 J

160

MediumJEE Mains2024

A real gas within a closed chamber at $27^{\circ} \mathrm{C} undergoes the cyclic process as shown in figure. The gas obeys P V^3=R T equation for the path A to B. The net work done in the complete cycle is (assuming R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$):

Options:

A) -20$J

B) 205J

C) 225J

D) 20J

161

EasyJEE Mains2024

The temperature of a gas is $-78^{\circ} \mathrm{C} and the average translational kinetic energy of its molecules is \mathrm{K}. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 \mathrm{~K}$ is :

Options:

A) -78^{\circ} \mathrm{C}

B) 127^{\circ} \mathrm{C}

C) -39^{\circ} \mathrm{C}

D) 117^{\circ} \mathrm{C}

162

MediumJEE Mains2024

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :

Options:

A) \frac{4}{5}

B) \frac{8}{5 \sqrt{5}}

C) \frac{2}{\sqrt{5}}

D) \frac{16}{25}

163

MediumJEE Mains2024

A sample of 1 mole gas at temperature $T is adiabatically expanded to double its volume. If adiab constant for the gas is \gamma=\frac{3}{2}$, then the work done by the gas in the process is :

Options:

A) \mathrm{R} \mathrm{T}[2+\sqrt{2}]

B) \mathrm{RT}[2-\sqrt{2}]

C) \frac{\mathrm{R}}{\mathrm{T}}[2-\sqrt{2}]

D) \frac{T}{R}[2+\sqrt{2}]

164

EasyJEE Mains2024

A diatomic gas $(\gamma=1.4) does 100 \mathrm{~J}$ of work in an isobaric expansion. The heat given to the gas is :

Options:

A) 150 J

B) 490 J

C) 350 J

D) 250 J

165

EasyJEE Mains2024

Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Statement I is false but Statement II is true

B) Both Statement I and Statement II are true

C) Statement I is true but Statement II is false

D) Both Statement I and Statement II are false

166

EasyJEE Mains2024

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $(27^{\circ} \mathrm{C})$. The ratio of specific heat of gases at constant volume respectively is:

Options:

A) \frac{3}{2}

B) \frac{3}{5}

C) \frac{7}{5}

D) \frac{5}{3}

167

MediumJEE Mains2024

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d} and the ratio \frac{V_b}{V_c}$ is:

Options:

A) \frac{V_a}{V_d} \neq \frac{V_b}{V_c}

B) \frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^{-1}

C) \frac{V_a}{V_d}=\frac{V_b}{V_c}

D) \frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^2

168

EasyJEE Mains2024

Given below are two statements: Statement (I) : Dimensions of specific heat is $[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]. Statement (II) : Dimensions of gas constant is [\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}]$. In the light of the above statements, choose the most appropriate answer from the options given below.

Options:

A) Statement (I) is incorrect but statement (II) is correct

B) Both statement (I) and statement (II) are incorrect

C) Both statement (I) and statement (II) are correct

D) Statement (I) is correct but statement (II) is incorrect

169

MediumJEE Mains2024

Energy of 10 non rigid diatomic molecules at temperature $\mathrm{T}$ is :

Options:

A) 35 RT

B) \frac{7}{2}$ RT

C) 70 K B T

D) 35 K B T

170

EasyJEE Mains2024

A total of $48 \mathrm{~J} heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2^{\circ} \mathrm{C}. The work done by the gas is: Given, \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.

Options:

A) 23.1 J

B) 48 J

C) 24.9 J

D) 72.9 J

171

MediumJEE Mains2024

The specific heat at constant pressure of a real gas obeying $P V^2=R T$ equation is:

Options:

A) R

B) C_V+R

C) C_V+\frac{R}{2 V}

D) \frac{R}{3}+C_V

172

EasyJEE Mains2024

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

Options:

A) \frac{1}{2 \sqrt{2}}

B) \frac{1}{4}

C) \frac{2 \sqrt{2}}{1}

D) \frac{1}{32}

173

MediumJEE Mains2024

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$ for the gas is :

Options:

A) \frac{5}{3}

B) \frac{3}{2}

C) \frac{7}{5}

D) \frac{9}{7}

174

EasyJEE Mains2024

If $\mathrm{n} is the number density and \mathrm{d}$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

Options:

A) \frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}

B) \frac{1}{\sqrt{2} n^2 \pi^2 d^2}

C) \frac{1}{\sqrt{2 n \pi d^2}}

D) \sqrt{2} \mathrm{n} \pi \mathrm{d}^2

175

EasyJEE Mains2024

The heat absorbed by a system in going through the given cyclic process is :

Options:

A) 61.6 J

B) 431.2 J

C) 19.6 J

D) 616 J

176

EasyJEE Mains2024

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} \mathrm{C} is \mathrm{Z}, then the collision frequency of the same system at 127^{\circ} \mathrm{C}$ is :

Options:

A) \frac{\sqrt{3}}{2} \mathrm{Z}

B) \frac{2}{\sqrt{3}} \mathrm{Z}

C) \frac{3}{4} \mathrm{Z}

D) \frac{4}{3} \mathrm{Z}

177

MediumJEE Mains2024

A sample of gas at temperature $T is adiabatically expanded to double its volume. Adiabatic constant for the gas is \gamma=3 / 2. The work done by the gas in the process is: (\mu=1 \text { mole })

Options:

A) R T[2 \sqrt{2}-1]

B) R T[2-\sqrt{2}]

C) R T[1-2 \sqrt{2}]

D) R T[\sqrt{2}-2]

178

EasyJEE Mains2024

The translational degrees of freedom $\left(f_t\right) and rotational degrees of freedom \left(f_r\right) of \mathrm{CH}_4$ molecule are:

Options:

A) f_t=2 and f_r=2

B) f_t=3 and f_r=3

C) f_t=3 and 4f_r=2$$

D) f_t=2 and f_r=3

179

MediumJEE Mains2024

P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct :

Options:

A) \rho_1>\rho_2

B) \rho_2<\rho_3

C) \rho_1=\rho_2=\rho_3

D) \rho_1<\rho_2

180

EasyJEE Mains2024

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega and 10 \Omega respectively. After inserting in a hot bath of temperature 400^{\circ} \mathrm{C}$, the resistance of platinum wire is :

Options:

A) 10 $\Omega

B) 16 $\Omega

C) 8 $\Omega

D) 2 $\Omega

181

EasyJEE Mains2024

On celcius scale the temperature of body increases by $40^{\circ} \mathrm{C}$. The increase in temperature on Fahrenheit scale is :

Options:

A) 75^{\circ} \mathrm{F}

B) 70^{\circ} \mathrm{F}

C) 72^{\circ} \mathrm{F}

D) 68^{\circ} \mathrm{F}

182

EasyJEE Mains2024

A diatomic gas (\gamma=1.4) does 200 \mathrm{~J} of work when it is expanded isobarically. The heat given to the gas in the process is :

Options:

A) 800 \mathrm{~J}

B) 600 \mathrm{~J}

C) 700 \mathrm{~J}

D) 850 \mathrm{~J}

183

EasyJEE Mains2024

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 \mathrm{~km} / \mathrm{s}, the root mean square velocity of oxygen at the same condition in \mathrm{km} / \mathrm{s} is :

Options:

A) 1.0

B) 1.5

C) 2.0

D) 0.5

184

EasyJEE Mains2024

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

Options:

A) \frac{3}{2} \mathrm{R}

B) \frac{7}{4} \mathrm{R}

C) \frac{5}{2} \mathrm{R}

D) \frac{9}{4} \mathrm{R}

185

MediumJEE Mains2024

The pressure and volume of an ideal gas are related as \mathrm{PV}^{\frac{3}{2}}=\mathrm{K} (Constant). The work done when the gas is taken from state A\left(P_1, V_1, T_1\right) to state B\left(P_2, V_2, T_2\right) is :

Options:

A) 2\left(\mathrm{P}_2 \sqrt{\mathrm{V}_2}-\mathrm{P}_1 \sqrt{\mathrm{V}_1}\right)

B) 2\left(\sqrt{\mathrm{P}_1} \mathrm{~V}_1-\sqrt{\mathrm{P}_2} \mathrm{~V}_2\right)

C) 2\left(\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1\right)

D) 2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right)

186

EasyJEE Mains2024

The speed of sound in oxygen at S.T.P. will be approximately: (given, $R=8.3 \mathrm{~JK}^{-1}, \gamma=1.4$)

Options:

A) 341 m/s

B) 333 m/s

C) 325 m/s

D) 315 m/s

187

MediumJEE Mains2024

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

Options:

A) 29 RT

B) 27 RT

C) 20 RT

D) 21 RT

188

MediumJEE Mains2024

The given figure represents two isobaric processes for the same mass of an ideal gas, then

Options:

A) P_2>P_1

B) P_1>P_2

C) P_1=P_2

D) P_2 \geq P_1

189

EasyJEE Mains2024

The parameter that remains the same for molecules of all gases at a given temperature is :

Options:

A) kinetic energy

B) mass

C) momentum

D) speed

190

EasyJEE Mains2024

A block of ice at $-10^{\circ} \mathrm{C} is slowly heated and converted to steam at 100^{\circ} \mathrm{C}$. Which of the following curves represent the phenomenon qualitatively:

Options:

191

MediumJEE Mains2024

If three moles of monoatomic gas $\left(\gamma=\frac{5}{3}\right) is mixed with two moles of a diatomic gas \left(\gamma=\frac{7}{5}\right), the value of adiabatic exponent \gamma$ for the mixture is

Options:

A) 1.35

B) 1.52

C) 1.40

D) 1.75

192

HardJEE Mains2024

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $\mathrm{C}_{\mathrm{A}} and \mathrm{C}_{\mathrm{B}}. The molar heat capacity at constant pressure and constant volume are represented by \mathrm{C_P} and \mathrm{C_V}$, respectively. Choose the correct statement.

Options:

A) \mathrm{C_P>C_B>C_A>C_V}

B) \mathrm{C}_{\mathrm{P}}>\mathrm{C}_{\mathrm{V}}>\mathrm{C}_{\mathrm{A}}=\mathrm{C}_{\mathrm{B}}

C) \mathrm{C}_{\mathrm{A}}=0 and \mathrm{C}_{\mathrm{B}}=\infty

D) \mathrm{C_A=\infty, C_B=0}

193

EasyJEE Mains2024

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} \mathrm{C}$ ?

Options:

A) 20 K

B) 80 K

C) 4 K

D) -73$ K

194

EasyJEE Mains2024

The temperature of a gas having $2.0 \times 10^{25} molecules per cubic meter at 1.38 \mathrm{~atm} (Given, \mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$) is :

Options:

A) 500 K

B) 300 K

C) 200 K

D) 100 K

195

MediumJEE Mains2024

N moles of a polyatomic gas (f=6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N$ is :

Options:

A) 6

B) 2

C) 4

D) 3

196

MediumJEE Mains2024

A thermodynamic system is taken from an original state $\mathrm{A} to an intermediate state B by a linear process as shown in the figure. It's volume is then reduced to the original value from \mathrm{B} to \mathrm{C} by an isobaric process. The total work done by the gas from A to B and B to C$ would be :

Options:

A) 800 J

B) 2200 J

C) 33800 J

D) 1200 J

197

EasyJEE Mains2024

Two vessels $A and B are of the same size and are at same temperature. A contains 1 \mathrm{~g} of hydrogen and B contains 1 \mathrm{~g} of oxygen. \mathrm{P}_{\mathrm{A}} and \mathrm{P}_{\mathrm{B}} are the pressures of the gases in \mathrm{A} and \mathrm{B} respectively, then \frac{P_A}{P_B}$ is:

Options:

A) 4

B) 32

C) 8

D) 16

198

EasyJEE Mains2024

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{\mathrm{Cp}}{\mathrm{Cv}}$ for the gas is :

Options:

A) \frac{7}{5}

B) \frac{3}{2}

C) \frac{9}{7}

D) \frac{5}{3}

199

EasyJEE Mains2024

The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where \mathrm{P}, \mathrm{V} and \mathrm{T} are pressure, volume and temperature respectively and \mathrm{R} is the universal gas constant. The dimensions of \frac{\mathrm{a}}{\mathrm{b}^2}$ is similar to that of :

Options:

A) P

B) RT

C) PV

D) R

200

EasyJEE Mains2024

The total kinetic energy of 1 mole of oxygen at $27^{\circ} \mathrm{C} is : [Use universal gas constant (R)=8.31 \mathrm{~J} /$ mole K]

Options:

A) 6232.5 J

B) 5670.5 J

C) 6845.5 J

D) 5942.0 J

201

EasyJEE Mains2024

0.08 \mathrm{~kg} air is heated at constant volume through 5^{\circ} \mathrm{C}. The specific heat of air at constant volume is 0.17 \mathrm{~kcal} / \mathrm{kg}^{\circ} \mathrm{C} and \mathrm{J}=4.18 joule/\mathrm{~cal}$. The change in its internal energy is approximately.

Options:

A) 318 J

B) 298 J

C) 284 J

D) 142 J

202

MediumJEE Mains2024

The average kinetic energy of a monatomic molecule is $0.414 \mathrm{~eV} at temperature : (Use K_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{mol}-\mathrm{K}$)

Options:

A) 3000 K

B) 3200 K

C) 1600 K

D) 1500 K

203

EasyJEE Mains2023

A thermodynamic system is taken through cyclic process. The total work done in the process is :

Options:

A) 100 \mathrm{~J}

B) Zero

C) 300 \mathrm{~J}

D) 200 \mathrm{~J}

204

EasyJEE Mains2023

A flask contains Hydrogen and Argon in the ratio 2: 1 by mass. The temperature of the mixture is 30^{\circ} \mathrm{C}. The ratio of average kinetic energy per molecule of the two gases ( \mathrm{K} argon/K hydrogen) is : (Given: Atomic Weight of \mathrm{Ar}=39.9 )

Options:

A) \frac{39.9}{2}

B) 2

C) 39.9

D) 1

205

EasyJEE Mains2023

The initial pressure and volume of an ideal gas are P$_0 and V_0. The final pressure of the gas when the gas is suddenly compressed to volume \frac{V_0}{4} will be : (Given \gamma$ = ratio of specific heats at constant pressure and at constant volume)

Options:

A) P$_0(4)^{\frac{1}{\gamma}}

B) P$_0

C) 4P$_0

D) P$_0(4)^{\gamma}

206

EasyJEE Mains2023

The mean free path of molecules of a certain gas at STP is $1500 \mathrm{~d}, where \mathrm{d} is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 \mathrm{~K}$ is approximately:

Options:

A) 750 \mathrm{~d}

B) 1500 \mathrm{~d}

C) \mathrm{2049~ d}

D) 1098 \mathrm{~d}

207

MediumJEE Mains2023

The rms speed of oxygen molecule in a vessel at particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v, where v is the average speed of the molecule. The value of x will be: \left(\right. Take \left.\pi=\frac{22}{7}\right)

Options:

A) 4

B) 8

C) 28

D) 27

208

EasyJEE Mains2023

An engine operating between the boiling and freezing points of water will have A. efficiency more than 27%. B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures. C. efficiency equal to $27 \% D. efficiency less than 27 \%$ Choose the correct answer from the options given below:

Options:

A) B and C only

B) B and D only

C) B, C and D only

D) A and B only

209

EasyJEE Mains2023

If the r. m.s speed of chlorine molecule is $490 \mathrm{~m} / \mathrm{s} at 27^{\circ} \mathrm{C}, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon =39.9 \mathrm{u}, molecular mass of chlorine =70.9 \mathrm{u}$ )

Options:

A) 451.7 \mathrm{~m} / \mathrm{s}

B) 751.7 \mathrm{~m} / \mathrm{s}

C) 551.7 \mathrm{~m} / \mathrm{s}

D) 651.7 \mathrm{~m} / \mathrm{s}

210

EasyJEE Mains2023

The Thermodynamic process, in which internal energy of the system remains constant is

Options:

A) Isobaric

B) Isochoric

C) Adiabatic

D) Isothermal

211

EasyJEE Mains2023

The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C} is approximately : (Given mass of a nitrogen molecule =4.6 \times 10^{-26} \mathrm{~kg} and take Boltzmann constant \mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{JK}^{-1}$ )

Options:

A) 91 m/s

B) 1260 m/s

C) 27.4 m/s

D) 523 m/s

212

MediumJEE Mains2023

1 \mathrm{~kg} of water at 100^{\circ} \mathrm{C} is converted into steam at 100^{\circ} \mathrm{C} by boiling at atmospheric pressure. The volume of water changes from 1.00 \times 10^{-3} \mathrm{~m}^{3} as a liquid to 1.671 \mathrm{~m}^{3} as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisaiton =2257 \mathrm{~kJ} / \mathrm{kg}, Atmospheric pressure = \left.1 \times 10^{5} \mathrm{~Pa}\right)

Options:

A) + 2090 kJ

B) -$ 2426 kJ

C) + 2476 kJ

D) -$ 2090 kJ

213

EasyJEE Mains2023

On a temperature scale '$\mathrm{X}', the boiling point of water is 65^{\circ} \mathrm{X} and the freezing point is -15^{\circ} \mathrm{X}. Assume that the \mathrm{X} scale is linear. The equivalent temperature corresponding to -95^{\circ} \mathrm{X}$ on the Farenheit scale would be:

Options:

A) -148^{\circ} \mathrm{F}

B) -48^{\circ} \mathrm{F}

C) -63^{\circ} \mathrm{F}

D) -112^{\circ} \mathrm{F}

214

EasyJEE Mains2023

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{\mathrm{rms}}\right)$ and choose the correct answer from the options given below:

Options:

A) \mathrm{v}_{\mathrm{rms}}( mono )=\mathrm{v}_{\mathrm{rms}}( dia )=\mathrm{v}_{\mathrm{rms}}( poly )

B) \mathrm{v}_{\mathrm{rms}} (mono) > \mathrm{v}_{\mathrm{rms}}( dia ) > \mathrm{v}_{\mathrm{rms}}$ (poly)

C) \mathrm{v}_{\mathrm{rms}} (dia) < \mathrm{v}_{\mathrm{rms}} (poly) < \mathrm{v}_{\text {rms }}$ (mono)

D) \mathrm{v}_{\mathrm{rms}} (mono) < \mathrm{v}_{\mathrm{rms}} (dia) < \mathrm{v}_{\mathrm{rms}}$ (poly)

215

EasyJEE Mains2023

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

Options:

A) 4RT

B) 16RT

C) 8RT

D) 11RT

216

EasyJEE Mains2023

A gas is compressed adiabatically, which one of the following statement is NOT true.

Options:

A) There is no heat supplied to the system

B) The temperature of the gas increases.

C) There is no change in the internal energy

D) The change in the internal energy is equal to the work done on the gas.

217

MediumJEE Mains2023

Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to $\frac{1}{8} of its original volume while the gas in B is compressed adiabatically to \frac{1}{8}$ of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Options:

A) \frac{1}{8}

B) 8$^\frac{3}{2}

C) 4

D) 8

218

EasyJEE Mains2023

Match List I with List II : List I List II (A) 3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases (C) 3 Translational, 2 rotational and 1 vibrational degrees of freedom (III) Rigid diatomic gases (D) 3 Translational, 3 rotational and more than one vibrational degrees of freedom (IV) Nonrigid diatomic gases Choose the correct answer from the options given below:

Options:

A) (A)-(I), (B)-(III), (C)-(IV), (D)-(II)

B) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

C) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)

D) (A)-(I), (B)-(IV), (C)-(III), (D)-(II)

219

EasyJEE Mains2023

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ} \mathrm{C}$ is

Options:

A) 627^{\circ} \mathrm{C}

B) 927^{\circ} \mathrm{C}

C) 327^{\circ} \mathrm{C}

D) 1227^{\circ} \mathrm{C}

220

EasyJEE Mains2023

Work done by a Carnot engine operating between temperatures $127^{\circ} \mathrm{C} and 27^{\circ} \mathrm{C} is 2 \mathrm{~kJ}$. The amount of heat transferred to the engine by the reservoir is :

Options:

A) 8 kJ

B) 2 kJ

C) 4 kJ

D) 2.67 kJ

221

MediumJEE Mains2023

Given below are two statements: Statement I: If heat is added to a system, its temperature must increase. Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below

Options:

A) Both Statement I and Statement II are true

B) Statement I is false but Statement II is true

C) Statement I is true but Statement II is false

D) Both Statement I and Statement II are false

222

EasyJEE Mains2023

The temperature of an ideal gas is increased from $200 \mathrm{~K} to 800 \mathrm{~K}. If r.m.s. speed of gas at 200 \mathrm{~K} is v_{0}. Then, r.m.s. speed of the gas at 800 \mathrm{~K}$ will be:

Options:

A) v_{0}

B) 2 v_{0}

C) 4 v_{0}

D) \frac{v_{0}}{4}

223

EasyJEE Mains2023

A body cools in 7 minutes from $60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C}. The temperature of the surrounding is 10^{\circ} \mathrm{C}$. The temperature of the body after the next 7 minutes will be:

Options:

A) 34^{\circ} \mathrm{C}

B) 28^{\circ} \mathrm{C}

C) 32^{\circ} \mathrm{C}

D) 30^{\circ} \mathrm{C}

224

EasyJEE Mains2023

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

Options:

A) 1: 1

B) 1: 2

C) 1: 4

D) 4: 1

225

EasyJEE Mains2023

A source supplies heat to a system at the rate of $1000 \mathrm{~W}. If the system performs work at a rate of 200 \mathrm{~W}$. The rate at which internal energy of the system increases is

Options:

A) 600 W

B) 1200 W

C) 500 W

D) 800 W

226

EasyJEE Mains2023

The number of air molecules per cm$^3 increased from 3\times10^{19} to 12\times10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:

Options:

A) 1.25

B) 0.25

C) 0.50

D) 0.75

227

EasyJEE Mains2023

A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}. When the temperature of cold reservoir raised by x, its efficiency decreases to \frac{1}{6}. The value of x, if the temperature of hot reservoir is 99^\circ$C, will be :

Options:

A) 66 K

B) 62 K

C) 16.5 K

D) 33 K

228

EasyJEE Mains2023

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point '$\mathrm{K}$' is :

Options:

A) -273^{\circ} \mathrm{C}

B) -373^{\circ} \mathrm{C}

C) -100^{\circ} \mathrm{C}

D) -40^{\circ} \mathrm{C}

229

MediumJEE Mains2023

A sample of gas at temperature $T is adiabatically expanded to double its volume. The work done by the gas in the process is \left(\mathrm{given}, \gamma=\frac{3}{2}\right)$ :

Options:

A) W=T R[\sqrt{2}-2]

B) W=\frac{T}{R}[\sqrt{2}-2]

C) W=\frac{R}{T}[2-\sqrt{2}]

D) W=R T[2-\sqrt{2}]

230

MediumJEE Mains2023

\left(P+\frac{a}{V^{2}}\right)(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of \frac{b^{2}}{a}$, will be:

Options:

A) Energy density

B) Bulk modulus

C) Modulus of rigidity

D) Compressibility

231

EasyJEE Mains2023

The average kinetic energy of a molecule of the gas is

Options:

A) proportional to volume

B) dependent on the nature of the gas

C) proportional to absolute temperature

D) proportional to pressure

232

MediumJEE Mains2023

Heat energy of 735 \mathrm{~J} is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :

Options:

A) 572 \mathrm{~J}

B) 441 \mathrm{~J}

C) 525 \mathrm{~J}

D) 735 \mathrm{~J}

233

EasyJEE Mains2023

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is \frac{16}{81}. Then the ratio of \frac{\mathrm{Cp}}{\mathrm{Cv}} will be.

Options:

A) \frac{3}{1}

B) \frac{4}{3}

C) \frac{1}{2}

D) \frac{3}{2}

234

MediumJEE Mains2023

The pressure of a gas changes linearly with volume from $\mathrm{A} to \mathrm{B}$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

Options:

A) 6 J

B) 4.5 J

C) zero

D) -$4.5 J

235

EasyJEE Mains2023

The correct relation between $\gamma = {{{c_p}} \over {{c_v}}}$ and temperature T is :

Options:

A) \gamma \propto T

B) \gamma \propto {1 \over {\sqrt T }}

C) \gamma \propto {1 \over T}

D) \gamma \propto T^\circ

236

EasyJEE Mains2023

Given below are two statements: one is labelled as Assertion \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A : Efficiency of a reversible heat engine will be highest at -273^{\circ} \mathrm{C} temperature of cold reservoir. Reason R : The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as \eta=\left(1-\frac{T_{2}}{T_{1}}\right) In the light of the above statements, choose the correct answer from the options given below

Options:

A) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}

B) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}

C) A is false but \mathbf{R} is true

D) A is true but \mathbf{R} is false

237

EasyJEE Mains2023

A flask contains hydrogen and oxygen in the ratio of 2: 1 by mass at temperature 27^{\circ} \mathrm{C}. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

Options:

A) 1 : 1

B) 4 : 1

C) 1 : 4

D) 2 : 1

238

MediumJEE Mains2023

The pressure $(\mathrm{P}) and temperature (\mathrm{T}) relationship of an ideal gas obeys the equation \mathrm{PT}^{2}=$ constant. The volume expansion coefficient of the gas will be :

Options:

A) 3 T^{2}

B) \frac{3}{T^2}

C) \frac{3}{T^3}

D) \frac{3}{T}

239

EasyJEE Mains2023

Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal energy of the gas will not change. D. The gas will do positive work. E. The gas will do negative work. Choose the correct answer from the options given below :

Options:

A) B and D only

B) C and E only

C) A and E only

D) C and D only

240

MediumJEE Mains2023

Heat energy of 184 kJ is given to ice of mass 600 g at $-12^\circ \mathrm{C}. Specific heat of ice is \mathrm{2222.3~J~kg^{-1^\circ}~C^{-1}} and latent heat of ice in 336 \mathrm{kJ/kg^{-1}} A. Final temperature of system will be 0^\circC. B. Final temperature of the system will be greater than 0^\circ$C. C. The final system will have a mixture of ice and water in the ratio of 5 : 1. D. The final system will have a mixture of ice and water in the ratio of 1 : 5. E. The final system will have water only. Choose the correct answer from the options given below :

Options:

A) A and E only

B) B and D only

C) A and C only

D) A and D only

241

MediumJEE Mains2023

At 300 K, the rms speed of oxygen molecules is $\sqrt {{{\alpha + 5} \over \alpha }} times to that of its average speed in the gas. Then, the value of \alpha will be (used \pi = {{22} \over 7}$)

Options:

A) 27

B) 28

C) 24

D) 32

242

EasyJEE Mains2023

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If $d Q and d W represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics d Q=d U-d W$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:

Options:

A) Both A and R are correct but R is not the correct explanation of A

B) Both A and R are correct and R is the correct explanation of A

C) A is correct but R is not correct

D) A is not correct but R is correct

243

EasyJEE Mains2023

Match List I with List II List I List II A. Isothermal Process I. Work done by the gas decreases internal energy B. Adiabatic Process II. No change in internal energy C. Isochoric Process III. The heat absorbed goes partly to increase internal energy and partly to do work D. Isobaric Process IV. No work is done on or by the gas Choose the correct answer from the options given below :

Options:

A) A-I, B-II, C-IV, D-III

B) A-II, B-I, C-III, D-IV

C) A-II, B-I, C-IV, D-III

D) A-I, B-II, C-III, D-IV

244

EasyJEE Mains2023

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by :-

Options:

A) {{{t_P}} \over {100}} = {{{t_Q} - 180} \over {150}}

B) {{{t_P}} \over {180}} - {{{t_Q} - 40} \over {100}}

C) {{{t_Q}} \over {150}} = {{{t_P} - 180} \over {100}}

D) {{{t_Q}} \over {100}} = {{{t_P} - 30} \over {150}}

245

EasyJEE Mains2023

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

Options:

A) \frac{9}{2}R

B) \frac{5}{2}R

C) \frac{3}{2}R

D) \frac{7}{2}R

246

EasyJEE Mains2023

The root mean square velocity of molecules of gas is

Options:

A) Proportional to temperature ($T$)

B) Inversely proportional to square root of temperature $\left( {\sqrt {{1 \over T}} } \right)

C) Proportional to square of temperature ($T^2$)

D) Proportional to square root of temperature ($\sqrt T$)

247

MediumJEE Mains2023

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

Options:

A) 300 K

B) 1000 K

C) 900 K

D) 360 K

248

EasyJEE Mains2023

Let $\gamma_1 be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \gamma_2 be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, \frac{\gamma_1}{\gamma_2}$ is :

Options:

A) \frac{35}{27}

B) \frac{25}{21}

C) \frac{21}{25}

D) \frac{27}{35}

249

EasyJEE Mains2023

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $\mathrm{T_3 > T_2 > T_1}$ as :

Options:

250

EasyJEE Mains2023

1 g of a liquid is converted to vapour at 3 $\times 10^5 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm^3$ during this phase change, then the increase in internal energy in the process will be :

Options:

A) 4800 J

B) 4320 J

C) 432000 J

D) 4.32 $\times 10^8$ J

251

MediumJEE Mains2023

Given below are two statements : Statement I : The temperature of a gas is $-73^\circC. When the gas is heated to 527^\circ$C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the option given below :

Options:

A) Statement I is true but Statement II is false

B) Both Statement I and Statement II are true

C) Statement I is false but Statement II is true

D) Both Statement I and Statement II are false

252

MediumJEE Mains2022

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

Options:

A) -$450 J

B) 450 J

C) 900 J

D) 1350 J

253

MediumJEE Mains2022

The root mean square speed of smoke particles of mass $5 \times 10^{-17} \mathrm{~kg} in their Brownian motion in air at NTP is approximately. [Given \mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$]

Options:

A) 60 \mathrm{~mm} \mathrm{~s}^{-1}

B) 12 \mathrm{~mm} \mathrm{~s}^{-1}

C) 15 \mathrm{~mm} \mathrm{~s}^{-1}

D) 36 \mathrm{~mm} \mathrm{~s}^{-1}

254

MediumJEE Mains2022

A vessel contains $14 \mathrm{~g} of nitrogen gas at a temperature of 27^{\circ} \mathrm{C}. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be : Take \mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$.

Options:

A) 2229 J

B) 5616 J

C) 9360 J

D) 13,104 J

255

MediumJEE Mains2022

A Carnot engine has efficiency of $50 \%. If the temperature of sink is reduced by 40^{\circ} \mathrm{C}, its efficiency increases by 30 \%$. The temperature of the source will be:

Options:

A) 166.7 K

B) 255.1 K

C) 266.7 K

D) 367.7 K

256

MediumJEE Mains2022

Given below are two statements : Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2 v$. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are true

B) Both Statement I and Statement II are false

C) Statement I is true but Statement II is false

D) Statement I is false but Statement II is true

257

MediumJEE Mains2022

In $1^{\text {st }} case, Carnot engine operates between temperatures 300 \mathrm{~K} and 100 \mathrm{~K}. In 2^{\text {nd }} case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2^{\text {nd }}$ case) will be :

Options:

A) same as the $1^{\text {st }}$ case.

B) always greater than the $1^{\text {st }}$ case.

C) always less than the $1^{\text {st }}$ case.

D) may increase or decrease with respect to the $1^{\text {st }}$ case.

258

MediumJEE Mains2022

Which statements are correct about degrees of freedom ? (A) A molecule with n degrees of freedom has n$^{2} different ways of storing energy. (B) Each degree of freedom is associated with \frac{1}{2} RT average energy per mole. (C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom. (D) \mathrm{CH}_{4}$ has a total of 6 degrees of freedom. Choose the correct answer from the options given below :

Options:

A) (B) and (C) only

B) (B) and (D) only

C) (A) and (B) only

D) (C) and (D) only

259

MediumJEE Mains2022

If $K_{1} and K_{2} are the thermal conductivities, L_{1} and L_{2} are the lengths and A_{1} and A_{2} are the cross sectional areas of steel and copper rods respectively such that \frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2. Then, for the arrangement as shown in the figure, the value of temperature \mathrm{T}$ of the steel - copper junction in the steady state will be:

Options:

A) 18^{\circ} \mathrm{C}

B) 14^{\circ} \mathrm{C}

C) 45^{\circ} \mathrm{C}

D) 150^{\circ} \mathrm{C}

260

MediumJEE Mains2022

Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice. B. Two bodies $P and Q having equal surface areas are maintained at temperature 10^{\circ} \mathrm{C} and 20^{\circ} \mathrm{C}. The thermal radiation emitted in a given time by \mathrm{P} and \mathrm{Q} are in the ratio 1: 1.15. C. A Carnot Engine working between 100 \mathrm{~K} and 400 \mathrm{~K} has an efficiency of 75 \%$. D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

Options:

A) A, B, C only

B) A, B only

C) A, C only

D) B, C, D only

261

EasyJEE Mains2022

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1: 4, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be 1: 4. C. The ratio of pressure will be 1: 1. D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1: 4$. Choose the correct answer from the options given below :

Options:

A) A and C only

B) B and D only

C) A and B only

D) C and D only

262

MediumJEE Mains2022

An ice cube of dimensions $60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm} is placed in an insulation box of wall thickness 1 \mathrm{~cm}. The box keeping the ice cube at 0^{\circ} \mathrm{C} of temperature is brought to a room of temperature 40^{\circ} \mathrm{C}. The rate of melting of ice is approximately : (Latent heat of fusion of ice is 3.4 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1} and thermal conducting of insulation wall is 0.05 \,\mathrm{Wm}^{-1 \circ} \mathrm{C}^{-1}$ )

Options:

A) 61 \times 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1}

B) 61 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}

C) 208 \mathrm{~kg} \mathrm{~s}^{-1}

D) 30 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}

263

EasyJEE Mains2022

A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

Options:

A) \frac{n}{n+2}

B) \frac{n+2}{n}

C) \frac{n}{2n+2}

D) \frac{n}{n-2}

264

EasyJEE Mains2022

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $40 \mathrm{~K} at constant pressure. The increase in the internal energy of the gas in this process is : (Given \mathrm{R}=8.3 \,\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )

Options:

A) 5810 J

B) 3486 J

C) 11620 J

D) 6972 J

265

EasyJEE Mains2022

A monoatomic gas at pressure $\mathrm{P} and volume \mathrm{V}$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

Options:

A) P

B) 8P

C) 32P

D) 64P

266

MediumJEE Mains2022

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :

Options:

A) 1

B) 2

C) 3

D) 4

267

EasyJEE Mains2022

Let $\eta_{1} is the efficiency of an engine at T_{1}=447^{\circ} \mathrm{C} and \mathrm{T}_{2}=147^{\circ} \mathrm{C} while \eta_{2} is the efficiency at \mathrm{T}_{1}=947^{\circ} \mathrm{C} and \mathrm{T}_{2}=47^{\circ} \mathrm{C} The ratio \frac{\eta_{1}}{\eta_{2}}$ will be :

Options:

A) 0.41

B) 0.56

C) 0.73

D) 0.70

268

MediumJEE Mains2022

A certain amount of gas of volume $\mathrm{V} at 27^{\circ} \mathrm{C} temperature and pressure 2 \times 10^{7} \mathrm{Nm}^{-2} expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use \gamma=1.5)$ :

Options:

A) 3.536 \times 10^{5} \mathrm{~Pa}

B) 3.536 \times 10^{6} \mathrm{~Pa}

C) 1.25 \times 10^{6} \mathrm{~Pa}

D) 1.25 \times 10^{5} \mathrm{~Pa}

269

EasyJEE Mains2022

Following statements are given : (A) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (C) The average kinetic energy of a gas molecule decreases with increase in volume. (D) Pressure of a gas increases with increase in temperature at constant pressure. (E) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below :

Options:

A) (A) and (D) only

B) (A), (B) and (D) only

C) (B) and (D) only

D) (A), (B) and (E) only

270

EasyJEE Mains2022

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is : (Given 0$^\circ$C = 273 K)

Options:

A) 300 K

B) 400 K

C) 600 K

D) 491 K

271

MediumJEE Mains2022

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm 3 to 150 cm 3 adiabatically. In this process, the value of workdone on the gas will be :

Options:

A) 79 J

B) 405 J

C) 4050 J

D) 9590 J

272

EasyJEE Mains2022

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature (27$^\circC). (Given : coefficient of linear thermal expansion of gold \alpha L = 1.4 \times 10 -5 K -$1 )

Options:

A) 125.7$^\circ$C

B) 91.7$^\circ$C

C) 425.7$^\circ$C

D) 152.7$^\circ$C

273

MediumJEE Mains2022

Starting with the same initial conditions, an ideal gas expands from volume V 1 to V 2 in three different ways. The work done by the gas is W 1 if the process is purely isothermal, W 2 , if the process is purely adiabatic and W 3 if the process is purely isobaric. Then, choose the correct option

Options:

A) W 1 < W 2 < W 3

B) W 2 < W 3 < W 1

C) W 3 < W 1 < W 2

D) W 2 < W 1 < W 3

274

EasyJEE Mains2022

A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm 3 is :

Options:

A) 72 $\times$ 10 5

B) 32 $\times$ 10 5

C) 27 $\times$ 10 4

D) 54 $\times$ 10 4

275

EasyJEE Mains2022

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0$^\circC will be : (Given gas constant R = 8.3 JK -1 -mol -$1 )

Options:

A) 249 J

B) 415 J

C) 498 J

D) 830 J

276

EasyJEE Mains2022

In van der Waal equation $\left[ {P + {a \over {{V^2}}}} \right] [V - b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants {a \over b}$ is dimensionally equal to :

Options:

A) {P \over V}

B) {V \over P}

C) PV

D) PV 3

277

MediumJEE Mains2022

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The workdone by the gas during the part CA is :

Options:

A) 20 J

B) 30 J

C) -$30 J

D) -$60 J

278

EasyJEE Mains2022

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

Options:

A) The velocity of atomic oxygen remains same

B) The velocity of atomic oxygen doubles

C) The velocity of atomic oxygen becomes half

D) The velocity of atomic oxygen becomes four times

279

MediumJEE Mains2022

Given below are two statements : Statement I : When $\mu amount of an ideal gas undergoes adiabatic change from state (P 1 , V 1 , T 1 ) to state (P 2 , V 2 , T 2 ), then work done is W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}, where \gamma = {{{C_p}} \over {{C_v}}}$ and R = universal gas constant. Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise. Choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are true.

B) Both Statement I and Statement II are false.

C) Statement I is true but Statement II is false.

D) Statement I is false but Statement II is true.

280

MediumJEE Mains2022

For a perfect gas, two pressures P 1 and P 2 are shown in figure. The graph shows :

Options:

A) P 1 > P 2

B) P 1 < P 2

C) P 1 = P 2

D) Insufficient data to draw any conclusion

281

EasyJEE Mains2022

According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0$^\circC. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is {3 \over 2}{k_B}T$ (for monoatomic gases). Choose the most appropriate answer from the options given below :

Options:

A) A and C only

B) B and C only

C) A and B only

D) C and D only

282

MediumJEE Mains2022

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is : (Given : initial temperature of the bullet = 127$^\circC, Melting point of the bullet = 327^\circC, Latent heat of fusion of lead = 2.5 \times 10 4 J kg -$1 , Specific heat capacity of lead = 125 J/kg K)

Options:

A) 125 ms $-$1

B) 500 ms $-$1

C) 250 ms $-$1

D) 600 ms $-$1

283

MediumJEE Mains2022

A mixture of hydrogen and oxygen has volume 2000 cm 3 , temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be: [Take gas constant R = 8.3 JK $-1 mol -$1 ]

Options:

A) {1 \over 3}

B) {3 \over 1}

C) {1 \over 16}

D) {16 \over 1}

284

EasyJEE Mains2022

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$^\circ$C. The ratio of their average kinetic energy per molecule respectively will be :

Options:

A) 3 : 2

B) 9 : 4

C) 2 : 3

D) 1 : 1

285

EasyJEE Mains2022

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

Options:

A) 26.81%

B) 37.81%

C) 47.81%

D) 57.81%

286

MediumJEE Mains2022

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : (R = universal gas constant)

Options:

A) {{M{v^2}} \over {7R}}

B) {{M{v^2}} \over {5R}}

C) 2${{M{v^2}} \over {7R}}

D) 7${{M{v^2}} \over {5R}}

287

EasyJEE Mains2022

A solid metallic cube having total surface area 24 m 2 is uniformly heated. If its temperature is increased by 10$^\circC, calculate the increase in volume of the cube. (Given \alpha = 5.0 \times 10 -4 ^\circC -$1 ).

Options:

A) 2.4 $\times$ 10 6 cm 3

B) 1.2 $\times$ 10 5 cm 3

C) 6.0 $\times$ 10 4 cm 3

D) 4.8 $\times$ 10 5 cm 3

288

EasyJEE Mains2022

A copper block of mass 5.0 kg is heated to a temperature of 500$^\circC and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : 0.39 J g -1 ^\circC -1 and latent heat of fusion of water : 335 J g -$1 ]

Options:

A) 1.5 kg

B) 5.8 kg

C) 2.9 kg

D) 3.8 kg

289

EasyJEE Mains2022

The ratio of specific heats $\left( {{{{C_P}} \over {{C_V}}}} \right)$ in terms of degree of freedom (f) is given by :

Options:

A) \left( {1 + {f \over 3}} \right)

B) \left( {1 + {2 \over f}} \right)

C) \left( {1 + {f \over 2}} \right)

D) \left( {1 + {1 \over f}} \right)

290

EasyJEE Mains2022

The relation between root mean square speed (v rms ) and most probable sped (v p ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

Options:

A) {v_{rms}} = \sqrt {{2 \over 3}} {v_p}

B) {v_{rms}} = \sqrt {{3 \over 2}} {v_p}

C) {v_{rms}} = {v_p}

D) {v_{rms}} = \sqrt {{1 \over 3}} {v_p}

291

MediumJEE Mains2022

A Carnot engine takes 5000 kcal of heat from a reservoir at 727$^\circC and gives heat to a sink at 127^\circ$C. The work done by the engine is

Options:

A) 3 $\times$ 10 6 J

B) Zero

C) 12.6 $\times$ 10 6 J

D) 8.4 $\times$ 10 6 J

292

MediumJEE Mains2022

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms $-1 . What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron = 0.42 Jg -1 ^\circC -$1 ]

Options:

A) 675$^\circ$C

B) 1600$^\circ$C

C) 16.07$^\circ$C

D) 6.75$^\circ$C

293

EasyJEE Mains2022

A Carnot engine whose heat sinks at 27$^\circ$C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency?

Options:

A) Increases by 18$^\circ$C

B) Increases by 200$^\circ$C

C) Increases by 120$^\circ$C

D) Increases by 73$^\circ$C

294

MediumJEE Mains2022

Two metallic blocks M 1 and M 2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M 2 is K then the thermal conductivity of M 1 will be : [Assume steady state heat conduction]

Options:

A) 10 K

B) 8 K

C) 12.5 K

D) 2 K

295

MediumJEE Mains2021

Two thin metallic spherical shells of radii r 1 and r 2 (r 1 < r 2 ) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $\theta 1 and the outer shell at temperature \theta 2 (\theta 1 < \theta$ 2 ). The rate at which heat flows radially through the material is :-

Options:

A) {{4\pi K{r_1}{r_2}({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}

B) {{\pi {r_1}{r_2}({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}

C) {{K({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}

D) {{K({\theta _2} - {\theta _1})({r_2} - {r_1})} \over {4\pi {r_1}{r_2}}}

296

MediumJEE Mains2021

A mixture of hydrogen and oxygen has volume 500 cm 3 , temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

Options:

A) 3 : 8

B) 3 : 16

C) 16 : 3

D) 8 : 3

297

MediumJEE Mains2021

A reversible engine has an efficiency of ${1 \over 4}. If the temperature of the sink is reduced by 58^\circ$C, its efficiency becomes double. Calculate the temperature of the sink :

Options:

A) 174$^\circ$C

B) 280$^\circ$C

C) 180.4$^\circ$C

D) 382$^\circ$C

298

MediumJEE Mains2021

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation ${{dp} \over {dv}} = - ap$. If p = p 0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)

Options:

A) {{{p_0}} \over {aeR}}

B) {{a{p_0}} \over {eR}}

C) infinity

D) 0$^\circ$C

299

EasyJEE Mains2021

if the rms speed of oxygen molecules at 0$^\circC is 160 m/s, find the rms speed of hydrogen molecules at 0^\circ$C.

Options:

A) 640 m/s

B) 40 m/s

C) 80 m/s

D) 332 m/s

300

EasyJEE Mains2021

The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall? [Given 1 cal = 4.2 J and specific heat of water = 1 cal g $-1 ^\circ0C -$1 ]

Options:

A) 0.147$^\circ$ C

B) 14.76$^\circ$ C

C) 1.476$^\circ$ C

D) 0.014$^\circ$ C

301

MediumJEE Mains2021

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$^\circC. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is -7^\circ$C. Assuming the volume constant?

Options:

A) 181.46 kg

B) 214.15 kg

C) 219.07 kg

D) 123.54 kg

302

MediumJEE Mains2021

An ideal gas is expanding such that PT 3 = constant. The coefficient of volume expansion of the gas is :

Options:

A) {1 \over T}

B) {2 \over T}

C) {4 \over T}

D) {3 \over T}

303

MediumJEE Mains2021

The temperature of equal masses of three different liquids x, y and z are 10$^\circC, 20^\circC and 30^\circC respectively. The temperature of mixture when x is mixed with y is 16^\circC and that when y is mixed with z is 26^\circ$C. The temperature of mixture when x and z are mixed will be :

Options:

A) 28.32$^\circ$C

B) 25.62$^\circ$C

C) 23.84$^\circ$C

D) 20.28$^\circ$C

304

EasyJEE Mains2021

A cylindrical container of volume 4.0 $\times 10 -3 m 3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is : [Take gas constant as 8.3 J mol -1 K -$1 ]

Options:

A) 249 $\times$ 10 1 Pa

B) 24.9 $\times$ 10 3 Pa

C) 24.9 $\times$ 10 5 Pa

D) 24.9 Pa

305

MediumJEE Mains2021

A refrigerator consumes an average 35W power to operate between temperature $-10^\circC to 25^\circ$C. If there is no loss of energy then how much average heat per second does it transfer?

Options:

A) 263 J/s

B) 298 J/s

C) 350 J/s

D) 35 J/s

306

EasyJEE Mains2021

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $\times$ 10 3 J ?

Options:

A) 2.5 $\times$ 10 2 s

B) 4.1 $\times$ 10 1 s

C) 2.4 $\times$ 10 3 s

D) 2.5 $\times$ 10 1 s

307

EasyJEE Mains2021

The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are V H , V O and V C respectively then :

Options:

A) V H > V O > V C

B) V C > V O > V H

C) V H = V O > V C

D) V H = V O = V C

308

MediumJEE Mains2021

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$^\circ C to 37^\circ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol -1 k -$1 ]

Options:

A) work done by the gas is close to 332 J

B) work done on the gas is close to 582 J

C) work done by the gas is close to 582 J

D) work done on the gas is close to 332 J

309

MediumJEE Mains2021

Two Carnot engines A and B operate in series such that engine A absorbs heat at T 1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T 3 . When workdone in both the cases is equal, to value of T is :

Options:

A) {2 \over 3}{T_1} + {3 \over 2}{T_3}

B) {1 \over 3}{T_1} + {2 \over 3}{T_3}

C) {3 \over 2}{T_1} + {1 \over 3}{T_3}

D) {2 \over 3}{T_1} + {1 \over 3}{T_3}

310

EasyJEE Mains2021

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $\times 10 -$9 J per molecules is :

Options:

A) 0.75 $\times$ 10 11

B) 3 $\times$ 10 11

C) 1.5 $\times$ 10 11

D) 6 $\times$ 10 11

311

MediumJEE Mains2021

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $\to B and C \to$ D are T 1 and T 2 (T 1 > T 2 ) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.

Options:

A) W AB = W DC

B) W AD = W BC

C) W BC + W DA > 0

D) W AB < W CD

312

MediumJEE Mains2021

A heat engine has an efficiency of ${1 \over 6}. When the temperature of sink is reduced by 62^\circ$C, its efficiency get doubled. The temperature of the source is :

Options:

A) 124$^\circ$C

B) 37$^\circ$C

C) 62$^\circ$C

D) 99$^\circ$C

313

MediumJEE Mains2021

For a gas C P $- C V = R in a state P and C P -$ C V = 1.10 R in a state Q, T P and T Q are the temperatures in two different states P and Q respectively. Then

Options:

A) T P = T Q

B) T P < T Q

C) T P = 0.9 T Q

D) T P > T Q

314

EasyJEE Mains2021

A monoatomic ideal gas, initially at temperature T 1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T 2 by releasing the piston suddenly. If l 1 and l 2 are the lengths of the gas column, before and after the expansion respectively, then the value of ${{{T_1}} \over {{T_2}}}$ will be :

Options:

A) {\left( {{{{l_1}} \over {{l_2}}}} \right)^{{2 \over 3}}}

B) {\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}

C) {{{l_2}} \over {{l_1}}}

D) {{{l_1}} \over {{l_2}}}

315

EasyJEE Mains2021

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

Options:

A) {8 \over 3}

B) {3 \over 8}

C) {3 \over 4}

D) {4 \over 3}

316

EasyJEE Mains2021

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

Options:

A) {3 \over 2}{k_B}T

B) {k_B}T

C) {2 \over 3}{k_B}T

D) {1 \over 2}{k_B}T

317

MediumJEE Mains2021

Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

Options:

318

EasyJEE Mains2021

The correct relation between the degrees of freedom f and the ratio of specific heat $\gamma$ is :

Options:

A) f = {2 \over {\gamma - 1}}

B) f = {2 \over {\gamma + 1}}

C) f = {{\gamma + 1} \over 2}

D) f = {1 \over {\gamma + 1}}

319

EasyJEE Mains2021

Consider a mixture of gas molecule of types A, B and C having masses m A < m B < m C . The ratio of their root mean square speeds at normal temperature and pressure is :

Options:

A) {v_A} = {v_B} \ne {v_C}

B) {1 \over {{v_A}}} > {1 \over {{v_B}}} > {1 \over {{v_C}}}

C) {1 \over {{v_A}}} < {1 \over {{v_B}}} < {1 \over {{v_C}}}

D) {v_A} = {v_B} = {v_C} = 0

320

EasyJEE Mains2021

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$^\circ C to 50^\circ$ C when no work is done is ___________. (R is the universal gas constant).

Options:

A) 500 R

B) 250 R

C) 750 R

D) 175 R

321

MediumJEE Mains2021

The entropy of any system is given by $S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right] where \alpha and \beta are the constants. \mu, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take S = {{dQ} \over T}$] Choose the incorrect option from the following :

Options:

A) \alpha$ and J have the same dimensions.

B) S and $\alpha$ have different dimensions

C) S, $\beta, k and \mu$R have the same dimensions

D) \alpha$ and k have the same dimensions

322

EasyJEE Mains2021

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is 32g/mol; R = 8.3 J K $-1 mol -$1 )

Options:

A) \sqrt {{{3\pi } \over 8}}

B) \sqrt {{3 \over 3}}

C) \sqrt {{8 \over 3}}

D) \sqrt {{{8\pi } \over 3}}

323

EasyJEE Mains2021

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats) :

Options:

A) - {1 \over \gamma }{{dV} \over V}

B) - \gamma {V \over {dV}}

C) - \gamma {{dV} \over V}

D) {{dV} \over V}

324

EasyJEE Mains2021

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S 1 and that of the other part is S 2 . Given that S 1 > S 2 . If the piston is removed then the total entropy of the system will be :

Options:

A) S 1 $-$ S 2

B) {{{S_1}} \over {{S_2}}}

C) S 1 $\times$ S 2

D) S 1 + S 2

325

MediumJEE Mains2021

The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use $\gamma$ = 1.4) :

Options:

A) -$500 J

B) -$400 J

C) 400 J

D) 200 J

326

EasyJEE Mains2021

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? (k B is Boltzmann constant)

Options:

A) {1 \over 2}{k_B}T

B) {2 \over 3}{k_B}T

C) {3 \over 2}{k_B}T

D) {k_B}T

327

MediumJEE Mains2021

If one mole of the polyatomic gas is having two vibrational modes and $\beta is the ratio of molar specific heats for polyatomic gas \left( {\beta = {{{C_P}} \over {{C_V}}}} \right) then the value of \beta$ is :

Options:

A) 1.02

B) 1.35

C) 1.2

D) 1.25

328

MediumJEE Mains2021

Which one is the correct option for the two different thermodynamic processes?

Options:

A) (a) only

B) (c) and (d)

C) (b) and (c)

D) (c) and (a)

329

MediumJEE Mains2021

A polyatomic ideal gas has 24 vibrational modes. What is the value of $\gamma$?

Options:

A) 1.37

B) 1.30

C) 1.03

D) 10.3

330

MediumJEE Mains2021

Two ideal polyatomic gases at temperatures T 1 and T 2 are mixed so that there is no loss of energy. If F 1 and F 2 , m 1 and m 2 , n 1 and n 2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :

Options:

A) {{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{F_1} + {F_2}}}

B) {{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{n_1}{F_1} + {n_2}{F_2}}}

C) {{{n_1}{T_1} + {n_2}{T_2}} \over {{n_1} + {n_2}}}

D) {{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{n_1} + {n_2}}}

331

EasyJEE Mains2021

Two identical metal wires of thermal conductivities K 1 and K 2 respectively are connected in series. The effective thermal conductivity of the combination is :

Options:

A) {{2{K_1}{K_2}} \over {{K_1} + {K_2}}}

B) {{{K_1} + {K_2}} \over {{K_1}{K_2}}}

C) {{{K_1} + {K_2}} \over {2{K_1}{K_2}}}

D) {{{K_1}{K_2}} \over {{K_1} + {K_2}}}

332

EasyJEE Mains2021

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

Options:

A) 2400 J

B) 1600 J

C) 1800 J

D) 3200 J

333

MediumJEE Mains2021

Calculate the value of mean free path ($\lambda) for oxygen molecules at temperature 27^\circC and pressure 1.01 \times 10 5 Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 \times 10 -23 JK -$1 )

Options:

A) 32 nm

B) 58 nm

C) 86 nm

D) 102 nm

334

EasyJEE Mains2021

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will :

Options:

A) Neither bend nor shrink

B) Bend towards the left

C) Not bend but shrink

D) Bend towards the right

335

MediumJEE Mains2021

In thermodynamics, heat and work are :

Options:

A) Path functions

B) Point functions

C) Extensive thermodynamics state variables

D) Intensive thermodynamic state variables

336

EasyJEE Mains2021

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :

Options:

A) {{3RT} \over V}

B) {{4RT} \over V}

C) {{88RT} \over V}

D) {5 \over 2}{{RT} \over V}

337

MediumJEE Mains2021

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U $=$ 3PV + 4. The gas is :

Options:

A) either monoatomic or diatomic.

B) monoatomic only.

C) polyatomic only.

D) diatomic only.

338

EasyJEE Mains2021

The temperature $\theta at the junction of two insulating sheets, having thermal resistances R 1 and R 2 as well as top and bottom temperatures \theta 1 and \theta$ 2 (as shown in figure) is given by :

Options:

A) {{{\theta _1}{R_2} + {\theta _2}{R_1}} \over {{R_1} + {R_2}}}

B) {{{\theta _1}{R_1} + {\theta _2}{R_2}} \over {{R_1} + {R_2}}}

C) {{{\theta _1}{R_2} - {\theta _2}{R_1}} \over {{R_2} - {R_1}}}

D) {{{\theta _2}{R_2} - {\theta _1}{R_1}} \over {{R_2} - {R_1}}}

339

MediumJEE Mains2021

Given below are two statements : Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are true

B) Both Statement I and Statement II are false

C) Statement I is true but Statement II is false.

D) Statement I is false but Statement II is true.

340

EasyJEE Mains2021

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V 2 = 2V 1 then the ratio of temperature T 2 /T 1 is :

Options:

A) \sqrt 2

B) {1 \over {\sqrt 2 }}

C) {1 \over 2}

D) 2

341

EasyJEE Mains2021

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason R : On heating, the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) A is true but R is false

B) A is false but R is true

C) Both A and B are true but R is NOT the correct explanation of A

D) Both A and R are true and R is the correct explanation of A

342

EasyJEE Mains2021

A diatomic gas, having ${C_p} = {7 \over 2}R and {C_v} = {5 \over 2}R$, is heated at constant pressure. The ratio dU : dQ : dW :

Options:

A) 5 : 7 : 3

B) 3 : 7 : 2

C) 5 : 7 : 2

D) 3 : 5 : 2

343

MediumJEE Mains2021

If one mole of an ideal gas at (P 1 , V 1 ) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B $ \to $ C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to :

Options:

A) - {{RT} \over {2(\gamma - 1)}}

B) RT\left( {\ln 2 - {1 \over {2(\gamma - 1)}}} \right)

C) RT\ln 2

D) 0

344

EasyJEE Mains2021

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :

Options:

A) continuously lose their energy till it reaches wall.

B) are attracted by the walls of container.

C) suffer change in momentum when impinge on the walls of container.

D) continuously stick to the walls of container.

345

EasyJEE Mains2021

Match List I with List II. List I List II (a) Isothermal (i) Pressure constant (b) Isochoric (ii) Temperature constant (c) Adiabatic (iii) Volume constant (d) Isobaric (iv) Heat content is constant Choose the correct answer from the options given below :

Options:

A) (a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)

B) (a) - (ii), (b) - (iv), (c) - (iii), (d) - (i)

C) (a) - (iii), (b) - (ii), (c) - (i), (d) - (iv)

D) (a) - (i), (b) - (iii), (c) - (ii), (d) - (iv)

346

MediumJEE Mains2021

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A $ \to B : Isothermal expansion at temperature T so that the volume is doubled from V 1 to V 2 = 2V 1 and pressure charges from P 1 to P 2 B \to C : Isobaric compression at pressure P 2 to initial volume V 1 . C \to $ A : Isochoric change leading to change of pressure from P 2 to P 1 . Total workdone in the complete cycle ABCA is :

Options:

A) nRTln 2

B) 0

C) nRT\left( {\ln 2 - {1 \over 2}} \right)

D) nRT\left( {\ln 2 + {1 \over 2}} \right)

347

EasyJEE Mains2021

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '$\alpha'. The metal sheet is heated uniformly, by a small temperature \DeltaT, so that its new temperature is T + \Delta$T. Calculate the increase in the volume of the metal box.

Options:

A) 3a 3 $\alpha\Delta$T

B) 4$\pia 3 \alpha\Delta$T

C) {{4 \over 3}}\pia 3 \alpha\Delta$T

D) 4a 3 $\alpha\Delta$T

348

MediumJEE Mains2020

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as :

Options:

A) \sqrt T

B) T

C) {1 \over T}

D) {1 \over {\sqrt T }}

349

MediumJEE Mains2020

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K 1 , K 2 and K 3 , respecrtively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100 o C and the other at 0 o C (see figure). If the joints of the rod are at 70 o C and 20 o C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K 1 , K 2 and K 3 is :

Options:

A) K 1 : K 3 = 2 : 3, K 2 : K 3 = 2 : 5

B) K 1 < K 2 < K 3

C) K 1 : K 2 = 5 : 2, K 1 : K 3 = 3 : 5

D) K 1 > K 2 > K 3

350

MediumJEE Mains2020

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of $\gamma \left( { = {{{C_p}} \over {{C_v}}}} \right)$ are given, respectively by:

Options:

A) U = ${5 \over 2}RT and \gamma = {7 \over 5}

B) U = 5RT and $\gamma = {6 \over 5}

C) U = 5RT and $\gamma = {7 \over 5}

D) U = ${5 \over 2}RT and \gamma = {6 \over 5}

351

MediumJEE Mains2020

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :

Options:

A) 128

B) 32

C) 326

D) {1 \over {32}}

352

MediumJEE Mains2020

Two different wires having lengths L 1 and L 2 , and respective temperature coefficient of linear expansion $\alpha 1 and \alpha $ 2 , are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

Options:

A) 2\sqrt {{\alpha _1}{\alpha _2}}

B) 4{{{\alpha _1}{\alpha _2}} \over {{\alpha _1} + {\alpha _2}}}{{{L_2}{L_1}} \over {{{\left( {{L_2} + {L_1}} \right)}^2}}}

C) {{{\alpha _1} + {\alpha _2}} \over 2}

D) {{{\alpha _1}{L_1} + {\alpha _2}{L_2}} \over {{L_1} + {L_2}}}

353

MediumJEE Mains2020

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $ \to B, A \to C and A \to $ D. The change in internal energies during these process are taken as E AB , E AC and E AD and the work done as W AB , W AC and W AD . The correct relation between these parameters are :

Options:

A) E AB < E AC < E AD , W AB > 0, W AC > W AD

B) E AB = E AC = E AD , W AB > 0, W AC = 0, W AD < 0

C) E AB > E AC > E AD , W AB < W AC < W AD

D) E AB = E AC < E AD , W AB > 0, W AC = 0, W AD < 0

354

MediumJEE Mains2020

Number of molecules in a volume of 4 cm 3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 $ \times $ 10 –14 erg, g = 980 cm/s 2 , density of mercury = 13.6 g/cm 3 )

Options:

A) 5.8 $ \times $ 10 18

B) 4.0 $ \times $ 10 16

C) 5.8 $ \times $ 10 16

D) 4.0 $ \times $ 10 18

355

MediumJEE Mains2020

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g – o C) (1 cal = 4.2 × 10 7 ergs) close to :

Options:

A) 87.5 o C

B) 83.3 o C

C) 38.4 o C

D) 119.2 o C

356

MediumJEE Mains2020

Match the thermodynamic processes taking place in a system with the correct conditions. In the table : $\Delta Q is the heat supplied, \Delta W is the work done and \Delta U is change in internal energy of the system. Process Condition (I) Adiabatic (1) \Delta W = 0 (II) Isothermal (2) \Delta Q = 0 (III) Isochoric (3) \Delta U \ne 0, \Delta W \ne 0, \Delta Q \ne 0 (IV) Isobaric (4) \Delta $U = 0

Options:

A) (I) - (1), (II) - (1), (III) - (2), (IV) - (3)

B) (I) - (2), (II) - (4), (III) - (1), (IV) - (3)

C) (I) - (1), (II) - (2), (III) - (4), (IV) - (4)

D) (I) - (2), (II) - (1), (III) - (4), (IV) - (3)

357

MediumJEE Mains2020

Match the ${{{C_P}} \over {{C_V}}}$ ratio for ideal gases with different type of molecules : Molecule Type C P /C V (A) Monatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3

Options:

A) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

B) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)

C) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)

D) (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

358

MediumJEE Mains2020

The specific heat of water = 4200 J kg -1 K -1 and the latent heat of ice = 3.4 $ \times $ 10 5 J kg –1 . 100 grams of ice at 0 o C is placed in 200 g of water at 25 o C. The amount of ice that will melt as the temperature of water reaches 0 o C is close to (in grams) :

Options:

A) 63.8

B) 61.7

C) 69.3

D) 64.6

359

MediumJEE Mains2020

To raise the temperature of a certain mass of gas by 50 o C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100 o C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Options:

A) 6

B) 7

C) 5

D) 3

360

MediumJEE Mains2020

A calorimeter of water equivalent 20 g contains 180 g of water at 25 o C. ‘m’ grams of steam at 100 o C is mixed in it till the temperature of the mixure is 31 o C. The value of ‘m’ is close to : (Latent heat of water = 540 cal g –1 , specific heat of water = 1 cal g –1 o C –1 )

Options:

A) 2.6

B) 2

C) 4

D) 3.2

361

MediumJEE Mains2020

A balloon filled with helium (32 o C and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as

Options:

A) Irreversible adiabatic

B) Reversible adiabatic

C) Irreversible isothermal

D) Reversible isothermal

362

MediumJEE Mains2020

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is :

Options:

A) {3 \over 2}RT

B) {9 \over 2}RT

C) {5 \over 2}RT

D) 3RT

363

MediumJEE Mains2020

A heat engine is involved with exchange of heat of 1915 J, – 40J, + 125 J and –Q J, during one cycle achieving an efficiency of 50.0%. The value of Q is

Options:

A) 980 J

B) 40 J

C) 400 J

D) 640 J

364

MediumJEE Mains2020

When the temperature of a metal wire is increased from 0 o C to 10 o C, its length increases by 0.02%. The percentage change in its mass density will be closest to :

Options:

A) 0.008

B) 0.06

C) 0.8

D) 2.3

365

MediumJEE Mains2020

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases. (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time remains unchanged.

Options:

A) (C) and (D)

B) (A) and (D)

C) (B) and (C)

D) (A) and (B)

366

MediumJEE Mains2020

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :

Options:

A) 11

B) 20

C) 15

D) 13

367

MediumJEE Mains2020

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to :

Options:

A) 2.3

B) 1.83

C) 4.67

D) 3.67

368

MediumJEE Mains2020

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure ? where, 1 $ \to $ 2 is adiabatic. (Graphs are schematic and are not to scale)

Options:

369

MediumJEE Mains2020

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass ${m \over 4} . The ratio of the specific heats (C_V^A and C_V^B$ ) of gas A and B, respectively is :

Options:

A) 7 : 9

B) 5 : 7

C) 3 : 5

D) 5 : 9

370

MediumJEE Mains2020

Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C P /C V value will be :

Options:

A) 23/15

B) 67/45

C) 40/27

D) 19/13

371

MediumJEE Mains2020

A carnot engine having an efficiency of ${1 \over {10}}$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is :

Options:

A) 90 J

B) 99 J

C) 1 J

D) 100 J

372

MediumJEE Mains2020

A thermodynamic cycle xyzx is shown on a V-T diagram. The P-V diagram that best describes this cycle is : (Diagrams are schematic and not to scale)

Options:

373

MediumJEE Mains2020

The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

Options:

374

MediumJEE Mains2020

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, T 1 and T 2 . The temperature of the hot reservoir of the first engine is T 1 and the temperature of the cold reservoir of the second engine is T 2 . T is temperature of the sink of first engine which is also the source for the second which is also the source for the second engine. How is T related to T 1 and T 2 . If both engines perform equal amount of work?

Options:

A) T = {{2{T_1}{T_2}} \over {{T_1} + {T_2}}}

B) T = \sqrt {{T_1}{T_2}}

C) T = {{{T_1} + {T_2}} \over 2}

D) T = 0

375

MediumJEE Mains2020

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau _1} to {\tau _2} . If {{{C_p}} \over {{C_v}}} = \gamma for this gas then a good estimate for {{{\tau _2}} \over {{\tau _1}}}$ is given by :

Options:

A) {\left( 2 \right)^{{{1 + \gamma } \over 2}}}

B) 2

C) {\left( {{1 \over 2}} \right)^{{{1 + \gamma } \over 2}}}

D) {\left( {{1 \over 2}} \right)^\gamma }

376

MediumJEE Mains2020

Two moles of an ideal gas with ${{{C_P}} \over {{C_V}}} = {5 \over 3} are mixed with 3 moles of another ideal gas with {{{C_P}} \over {{C_V}}} = {4 \over 3}. The value of {{{C_P}} \over {{C_V}}}$ for the mixture is :

Options:

A) 1.50

B) 1.45

C) 1.47

D) 1.42

377

MediumJEE Mains2020

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma $ = 1.40, the work done by air is : (3 1.4 = 4.6555) [Take air to be an ideal gas]

Options:

A) 60.7 J

B) 100.8 J

C) 90.5 J

D) 48 J

378

MediumJEE Mains2019

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ?

Options:

A) 35 J

B) 30 J

C) 25 J

D) 40 J

379

MediumJEE Mains2019

One kg of water, at 20 o C, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 $\Omega $. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = 4200 J/(kg o C), Latent heat of water = 2260 kJ/kg]

Options:

A) 10 minutes

B) 22 minutes

C) 3 minutes

D) 16 minutes

380

MediumJEE Mains2019

A Carnot engine has an efficiency of ${1 \over 6}$. When the temperature of the sink is reduced by 62ºC, its efficiency is doubled. The temperatures of the source and the sink are, respectively

Options:

A) 99 o C, 37 o C

B) 124 o C, 62 o C

C) 37 o C, 99 o C

D) 62 o C, 124 o C

381

MediumJEE Mains2019

At 40 o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40 o C to 20 o C it regains its original length of 0.2 m. The value of M is close to : (Coefficient of linear expansion and Young’s modulus of brass are 10 –5 / o C and 10 11 N/m 2 , respectively; g= 10 ms –2 )

Options:

A) 1.5 kg

B) 0.5 kg

C) 9 kg

D) 0.9 kg

382

MediumJEE Mains2019

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

Options:

A) 21.6 J/mol K

B) 17.4 J/mol K

C) 15.7 J/mol K

D) 19.7 J/mol K

383

MediumJEE Mains2019

When M 1 gram of ice at –10 o C (specific heat = 0.5 cal g –1 o C –1 ) is added to M 2 gram of water at 50C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g –1 is :

Options:

A) {{50{M_2}} \over {{M_1}}} - 5

B) {{50{M_2}} \over {{M_1}}}

C) {{5{M_2}} \over {{M_1}}} - 5

D) {{5{M_1}} \over {{M_2}}} - 50

384

MediumJEE Mains2019

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:

Options:

A) 120 J

B) 130 J

C) 100 J

D) 140 J

385

MediumJEE Mains2019

One mole of ideal gas passes through a process where pressure and volume obey the relation $P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$. Here P 0 and V 0 are constants. Calculate the change in the temperature of the gas if its volume changes form V 0 to 2V 0

Options:

A) {3 \over 4}{{{P_0}{V_0}} \over R}

B) {1 \over 2}{{{P_0}{V_0}} \over R}

C) {5 \over 4}{{{P_0}{V_0}} \over R}

D) {1 \over 4}{{{P_0}{V_0}} \over R}

386

MediumJEE Mains2019

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta $T. the heat required to produce the same change in temperature, at a constant pressure is :

Options:

A) {7 \over 5}Q

B) {3 \over 2}Q

C) {2 \over 3}Q

D) {5 \over 3}Q

387

MediumJEE Mains2019

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R = 8.31 J mol –1 K –1 ]

Options:

A) 374 J

B) 700 J

C) 748 J

D) 350 J

388

MediumJEE Mains2019

n moles of an ideal gas with constant volume heat capcity C V undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :

Options:

A) {{nR} \over {{C_V} - nR}}

B) {{4nR} \over {{C_V} - nR}}

C) {{4nR} \over {{C_V} + nR}}

D) {{nR} \over {{C_V} + nR}}

389

MediumJEE Mains2019

A 25 × 10 –3 m 3 volume cylinder is filled with 1 mol of O 2 gas at room temperature (300K). The molecular diameter of O 2 , and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O 2 molecule ?

Options:

A) ~10 13

B) ~10 12

C) ~10 11

D) ~10 10

390

MediumJEE Mains2019

The specific heats, C P and C V of a gas of diatomic molecules, A, are given (in units of J mol –1 K –1 ) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

Options:

A) A is rigid but B has a vibrational mode

B) A has a vibrational mode but B has none

C) A has one vibrational mode and B has two

D) Both A and B have a vibrational mode each

391

MediumJEE Mains2019

A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)

Options:

A) 10 –3 K

B) 10 –1 K

C) 10 –5 K

D) 10 –4 K

392

MediumJEE Mains2019

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$\theta 2 ' and '\theta 1 ' respectively, (\theta 2 > \theta $ 1 ). The temperature at the interface is :-

Options:

A) {{{\theta _1}} \over {10}} + {{9{\theta _2}} \over {10}}

B) {{{\theta _2} + {\theta _1}} \over 2}

C) {{{\theta _1}} \over {6}} + {{5{\theta _2}} \over {6}}

D) {{{\theta _1}} \over {3}} + {{2{\theta _2}} \over {3}}

393

MediumJEE Mains2019

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\overline v $ , m is its mass and k B is Boltzmann constant, then its temperature will be :

Options:

A) {{m{{\overline v }^2}} \over {5{k_B}}}

B) {{m{{\overline v }^2}} \over {6{k_B}}}

C) {{m{{\overline v }^2}} \over {7{k_B}}}

D) {{m{{\overline v }^2}} \over {3{k_B}}}

394

MediumJEE Mains2019

Following figure shows two processes A and B for a gas. If $\Delta Q A and \Delta Q B are the amount of heat absorbed by the system in two cases, and \Delta U A and \Delta $U B are changes in internal energies, respectively, then :

Options:

A) \Delta Q A > \Delta Q B ; \Delta U A > \Delta $U B

B) \Delta Q A < \Delta Q B ; \Delta U A < \Delta $U B

C) \Delta Q A > \Delta Q B ; \Delta U A = \Delta $U B

D) \Delta Q A = \Delta Q B ; \Delta U A = \Delta $U B

395

MediumJEE Mains2019

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :

Options:

A) 100 m/s

B) 100 $\sqrt 5 $ m/s

C) 80 $\sqrt 5 $ m/s

D) 80 m/s

396

MediumJEE Mains2019

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to : [Boltzmann Constant k B = 1.38 × 10 –23 J/K Avogadro Number N A = 6.02 × 10 26 /kg Radius of Earth : 6.4 × 10 6 m Gravitational acceleration on Earth = 10ms –2 ]

Options:

A) 3 × 10 5 K

B) 10 4 K

C) 650 K

D) 800 K

397

MediumJEE Mains2019

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by :-

Options:

A) d a b c

B) a d b c

C) d a c b

D) a d c b

398

MediumJEE Mains2019

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 10 2 kg/m 3 and specific heat of 2000 J kg –1 K –1 while liquid in B has density of 10 3 kg m –3 and specific heat of 4000 J kg –1 K –1 . Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

Options:

399

MediumJEE Mains2019

A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to : (Latent heat of vaporization of water = 2.10 × 10 6 J kg –1 and Latent heat of Fusion of water = 3.36 × 10 5 J kg –1 )

Options:

A) 35 g

B) 130 g

C) 20 g

D) 150 g

400

MediumJEE Mains2019

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $ \times $ 10 –8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

Options:

A) 0.5 $ \times 10 -$8 s

B) 4 $ \times 10 -$8 s

C) 3 $ \times 10 -$6 s

D) 2 $ \times 10 -$7 s

401

MediumJEE Mains2019

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $\ell 1 , and that below the piston is \ell 2 , such that \ell 1 > \ell $ 2 . Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)

Options:

A) {{nRT} \over g}\left[ {{{{\ell _1} - {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]

B) {{RT} \over g}\left[ {{{2{\ell _1} + {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]

C) {{nRT} \over g}\left[ {{1 \over {{\ell _2}}} + {1 \over {{\ell _1}}}} \right]

D) {{RT} \over {ng}}\left[ {{{{\ell _1} - 3{\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]

402

MediumJEE Mains2019

For the given cyclic process CAB as shown for a gas, the work done is :

Options:

A) 1 J

B) 10 J

C) 5 J

D) 30 J

403

MediumJEE Mains2019

An ideal gas occupies a volume of 2m 3 at a pressure of 3 $ \times $ 10 6 Pa. The energy of the gas is :

Options:

A) 6 $ \times $ 10 4 J

B) 9$ \times $ 10 6 J

C) 3 $ \times $ 10 2 J

D) 10 8 J

404

MediumJEE Mains2019

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K 1 and the of the outer cylinder is K 2 . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

Options:

A) K 1 + K 2

B) {{{K_1} + 3{K_2}} \over 4}

C) {{{K_1} + {K_2}} \over 2}

D) {{2{K_1} + 3{K_2}} \over 5}

405

MediumJEE Mains2019

When 100 g of a liquid A at 100 o C is added to 50 g of a liquid B at temperature 75 o C, the temperature of the mixture becomes 90 o C. The temperature of the mixture, if 100 g of liquid A at 100 o C is added to 50 g of liquid B at 50 o C, will be :

Options:

A) 60 o C

B) 70 o C

C) 85 o C

D) 80 o C

406

MediumJEE Mains2019

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by $\Delta $T. The amount of heat absorbed by gas is (R is gas constant) :

Options:

A) {1 \over 2} KR\Delta $T

B) {1 \over 2} R\Delta $T

C) {3 \over 2} R\Delta $T

D) {2K \over 3} \Delta $T

407

MediumJEE Mains2019

Two rods A and B of identical dimensions are at temperature 30 ° C. If A is heated upto 180 o C and B upto T o C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is

Options:

A) 200 o C

B) 270 o C

C) 230 o C

D) 250 o C

408

MediumJEE Mains2019

A metal ball of mass 0.1 kg is heated upto 500 o C and dropped into a vessel of heat capacity 800 JK –1 and containing 0.5 kg water. The initial temperature of water and vessel is 30 o C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg –1 and 400 Jkg –1 K –1

Options:

A) 20%

B) 25%

C) 15%

D) 30%

409

MediumJEE Mains2019

A thermometer graduated according to a linear scale reads a value x 0 when in contact with boiling water, and x 0 /3 when in contact with ice. What is the temperature of an object in o C, if this thermometer in the contact with the object reads x 0 /2 ?

Options:

A) 60

B) 35

C) 25

D) 40

410

MediumJEE Mains2019

Ice at –20 o C is added to 50 g of water at 40 o C. When the temperature of the mixture reaches 0 o C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/ o C Specific heat of Ice = 2.1J/g/ o C Heat of fusion of water at 0 o C= 334J/g)

Options:

A) 100 g

B) 60 g

C) 50 g

D) 40 g

411

MediumJEE Mains2019

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TV x = constant, then x is :

Options:

A) {5 \over 3}

B) {2 \over 5}

C) {3 \over 5}

D) {2 \over 3}

412

MediumJEE Mains2019

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :

Options:

A) 12 RT

B) 20 RT

C) 4 RT

D) 15 RT

413

MediumJEE Mains2019

An unknown metal of mass 192 g heated to a temperature of 100 o C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4 o C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5 o C. (Specific heat of brass is 394 J kg –1 K –1 )

Options:

A) 458 J kg –1 K –1

B) 1232 J kg –1 K –1

C) 654 J kg –1 K –1

D) 916 J kg –1 K –1

414

MediumJEE Mains2019

Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20 o C to 90 o C. Work done by gas is close to – (Gas constant R = 8.31 J/mol.K)

Options:

A) 581 J

B) 73 J

C) 146 J

D) 291 J

415

MediumJEE Mains2019

Two kg of a monoatomic gas is at a pressure of 4 $ \times $ 10 4 N/m 2 . The density of the gas is 8 kg/m 3 . What is the order of energy of the gas due to its thermal motion ?

Options:

A) 10 4 J

B) 10 3 J

C) 10 5 J

D) 10 6 J

416

MediumJEE Mains2019

A heat source at T = 10 3 K is connected to another heat reservoir at T = 10 2 K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK –1 m –1 , the energy flux through it in the steady state is -

Options:

A) 200 Wm $-$2

B) 65 Wm $-$2

C) 120 Wm $-$2

D) 90 Wm $-$2

417

MediumJEE Mains2019

Three Carnot engines operate in series between a heat source at a temperature T 1 and a heat sink at temperature T 4 (see figure). There are two other reservoirs at temperature T 2 and T 3 , as shown, with T 1 > T 2 > T 3 > T 4 . The three engines are equally efficient if -

Options:

A) T 2 = (T 1 3 T 4 ) 1/4 ; T 3 = (T 1 T 4 3 ) 1/4

B) T 2 = (T 1 T 4 ) 1/2 ; T 3 = (T 1 2 T 4 ) 1/3

C) T 2 = (T 1 T 4 2 ) 1/3 ; T 3 = (T 1 2 T 4 ) 1/3

D) T 2 = (T 1 2 T 4 ) 1/3 ; T 3 = (T 1 T 4 2 ) 1/3

418

MediumJEE Mains2019

Two Carnot engines A and B are operated in series. The first one, A, receives heat at T 1 (= 600 K) and rejects to a reservoir at temperature T 2 . The second engine B receives heat rejected by the first engine and, in tum, rejects to a heat reservoir at T 3 (=400 K). Calculate the temperature T 2 if the work outputs of the two engines are equal :

Options:

A) 600 K

B) 400 K

C) 300 K

D) 500 K

419

MediumJEE Mains2019

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27 o C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]

Options:

A) 0.9 kJ

B) 6 kJ

C) 10 kJ

D) 14 kJ

420

MediumJEE Mains2019

Temperature difference of 120 o C is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length ${{3L} \over 2},$ is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to :

Options:

A) 45 o C

B) 75 o C

C) 60 o C

D) 35 o C

421

MediumJEE Mains2019

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$ is close to :

Options:

A) 3.16

B) 0.32

C) 0.45

D) 2.24

422

MediumJEE Mains2019

A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is :

Options:

A) 40 J

B) 80 J

C) 100 J

D) 20 J

423

MediumJEE Mains2019

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $\alpha / o C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \Delta $TK. Young's modulus, Y, for this metal is :

Options:

A) {F \over {A\alpha \Delta T}}

B) {F \over {A\alpha (\Delta T - 273)}}

C) {F \over {2A\alpha \Delta T}}

D) {{2F} \over {A\alpha \Delta T}}

424

MediumJEE Mains2018

One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

Options:

A) {{25} \over {16}}\,{{{P_o}{V_o}} \over R}

B) {{25} \over {8}}\,{{{P_o}{V_o}} \over R}

C) {{25} \over {4}}\,{{{P_o}{V_o}} \over R}

D) {{5} \over {8}}\,{{{P_o}{V_o}} \over R}

425

MediumJEE Mains2018

Two moles of helium are mixed with n moles of hydrogen. If ${{Cp} \over {Cv}} = {3 \over 2}$ for the mixture, then the value of n is :

Options:

A) 1

B) 3

C) 2

D) 3 / 2

426

MediumJEE Mains2018

Two moles of an ideal monatomic gas occupies a volume V at 27 o C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

Options:

A) (a) 195 K (b) 2.7 kJ

B) (a) 189 K (b) 2.7 kJ

C) (a) 195 K (b) –2.7 kJ

D) (a) 189 K (b) – 2.7 kJ

427

MediumJEE Mains2018

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms -1 is : [k B =1.4 $ \times 10 -23 J/K; m He = 7 \times $ 10 -27 kg ]

Options:

A) 1.3 $ \times $ 10 4

B) 1.3 $ \times $ 10 3

C) 1.3 $ \times $ 10 5

D) 1.3 $ \times $ 10 2

428

MediumJEE Mains2018

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two energies A and B are represented by ${\eta _A} and {\eta _B}, respectively, then what is the value of {{{\eta _B}} \over {{\eta _A}}}$ ?

Options:

A) {{12} \over 7}

B) {{7} \over 12}

C) {{12} \over 5}

D) {{5} \over 12}

429

MediumJEE Mains2018

A Carnot's engine works as a refrigerator between $250 K and 300 K. It receives 500$ cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

Options:

A) 420 J

B) 772 J

C) 2100 J

D) 2520 J

430

MediumJEE Mains2018

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, ${27^ \circ }C.$ The work done on the gas will be :

Options:

A) 300 R

B) 300 R ln 6

C) 300 R ln 2

D) 300 R ln 7

431

MediumJEE Mains2017

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

Options:

A) {1 \over 2}$ nRT

B) 0

C) {3 \over 2}$ nRT

D) {5 \over 2}$ nRT

432

MediumJEE Mains2017

A steel rail of length 5 m and area of cross section 40cm 2 is prevented from expanding along its length while the temperature rises by 10 o C. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10 −5 K −1 and 2×10 11 Nm −2 respectively, the force developed in the rail is approximately :

Options:

A) 2 $ \times $ 10 7 N

B) 1 $ \times $ 10 5 N

C) 2 $ \times $ 10 9 N

D) 3 $ \times 10 -$5 N

433

MediumJEE Mains2017

For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram ?

Options:

434

MediumJEE Mains2017

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150 o C. Immediately, it is put into water of volume 150 cc at 27 o C kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40 o C. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)

Options:

A) 378 J/kg $-$ o C

B) 315 J/kg $-$ o C

C) 476 J/kg $-$ o C

D) 434 J/kg $-$ o C

435

MediumJEE Mains2017

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is : (Take C v = 1.5 R, where R is gas constant)

Options:

A) 0.24

B) 0.15

C) 0.32

D) 0.08

436

MediumJEE Mains2017

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T. The net change in its length is zero. Let \ell be the length of the rod, A its area of cross-section,Y its Young’s modulus, and \alpha $ its coefficient of linear expansion. Then, F is equal to :

Options:

A) \ell 2 Y\alpha \Delta $T

B) \ell A Y\alpha \Delta $T

C) A Y$\alpha \Delta $T

D) {{AY} \over {\alpha \,\Delta T}}

437

MediumJEE Mains2017

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (C p ) and at constant volume (C v ) is :

Options:

A) 6

B) {7 \over 2}

C) {5 \over 2}

D) {7 \over 5}

438

MediumJEE Mains2017

An external pressure P is applied on a cube at 0 o C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

Options:

A) {P \over {3\alpha K}}

B) {P \over {\alpha K}}

C) {3 \alpha \over {P K}}

D) 3PK$\alpha

439

MediumJEE Mains2017

The temperature of an open room of volume 30 m 3 increases from 17 o C to 27 o C due to the sunshine. The atmospheric pressure in the room remains 1 $ \times $ 10 5 Pa. If N i and N f are the number of molecules in the room before and after heating, then N f – N i will be :

Options:

A) - 1.61 $ \times $ 10 23

B) 1.38 $ \times $ 10 23

C) 2.5 $ \times $ 10 25

D) - 2.5 $ \times $ 10 25

440

MediumJEE Mains2017

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75 o C. T is given by: (Given : room temperature = 30 o C, specific heat of copper = 0.1 cal/gm o C)

Options:

A) 825 o C

B) 800 o C

C) 885 o C

D) 1250 o C

441

MediumJEE Mains2017

C P and C v are specific heats at constant pressure and constant volume respectively. It is observed that C P – C v = a for hydrogen gas C P – C v = b for nitrogen gas The correct relation between a and b is

Options:

A) a = 28 b

B) a = 1/14 b

C) a = b

D) a = 14 b

442

MediumJEE Mains2016

A Carnot freezer takes heat from water at 0 o C inside it and rejects it to the room at a temperature of 27 o C. The latent heat of ice is 336×10 3 J kg −1 . If 5 kg of water at 0 o C is converted into ice at 0 o C by the freezer, then the energy consumed by the freezer is close to :

Options:

A) 1.67 $ \times $ 10 5 J

B) 1.68 $ \times $ 10 6 J

C) 1.51 $ \times $ 10 5 J

D) 1.71 $ \times $ 10 7 J

443

MediumJEE Mains2016

Which of the following shows the correct relationship between the pressure ‘P’ and density $\rho $ of an ideal gas at constant temperature ?

Options:

444

MediumJEE Mains2016

200 g water is heated from 40 o C to 60 o C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :

Options:

A) 8.4 kJ

B) 4.2 kJ

C) 16.7 kJ

D) 167.4 kJ

445

MediumJEE Mains2016

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

Options:

A) {3 \over 5}

B) {2 \over 3}

C) {3 \over 2}

D) {2 \over 5}

446

MediumJEE Mains2016

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0 o C. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $\alpha $ then the value of S is :

Options:

A) \alpha

B) {\alpha \over 2}

C) 2$\alpha

D) {1 \over \alpha }

447

MediumJEE Mains2016

'n' moles of an ideal gas undergoes a process A \to B$ as shown in the figure. The maximum temperature of the gas during the process will be :

Options:

A) {{9{P_0}{V_0}} \over {2nR}}

B) {{9{P_0}{V_0}} \over {nR}}

C) {{9{P_0}{V_0}} \over {4nR}}

D) {{3{P_0}{V_0}} \over {2nR}}

448

MediumJEE Mains2016

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C remains constant. If during this process the relation of pressure P and volume V is given by P{V^n} = constant, then n is given by (Here {C_p} and {C_v}$ are molar specific heat at constant pressure and constant volume, respectively:

Options:

A) n = {{{C_p} - C} \over {C - {C_v}}}

B) n = {{C - {C_v}} \over {C - {C_p}}}

C) n = {{{C_p}} \over {{C_v}}}

D) n = {{C - {C_p}} \over {C - {C_v}}}

449

MediumJEE Mains2016

A pendulum clock loses $12 s a day if the temperature is {40^ \circ }C and gains 4 s a day if the temperature is {20^ \circ }C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion \left( \alpha \right)$ of the metal of the pendulum shaft are respectively :

Options:

A) {30^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 3}}/{}^ \circ C

B) {55^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 2}}/{}^ \circ C

C) {25^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 5}}/{}^ \circ C

D) {60^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 4}}/{}^ \circ C

450

MediumJEE Mains2015

A solid body of constant heat capacity $1 J/{}^ \circ C is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir \,\,\,\,\,\,\,\,supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir \,\,\,\,\,\,\,\,\,\,supplies same amount of heat. In both the cases body is brought from initial temperature {100^ \circ }C to final temperature {200^ \circ }C$. Entropy change of the body in the two cases respectively is :

Options:

A) ln2, 2ln2

B) 2ln2, 8ln2

C) ln2, 4ln2

D) ln2, ln2

451

MediumJEE Mains2015

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as ${V^q}, where V is the volume of the gas. The value of q is: \left( {\gamma = {{{C_p}} \over {{C_v}}}} \right)

Options:

A) {{\gamma + 1} \over 2}

B) {{\gamma - 1} \over 2}

C) {{3\gamma + 5} \over 6}

D) {{3\gamma - 5} \over 6}

452

MediumJEE Mains2015

Consider a spherical shell of radius $R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = {U \over V}\, \propto \,{T^4} and pressure p = {1 \over 3}\left( {{U \over V}} \right) . If the shell now undergoes an adiabatic expansion the relation between T and R$ is:

Options:

A) T\, \propto {1 \over R}

B) T\, \propto {1 \over {{R^3}}}

C) T\, \propto \,{e^{ - R}}

D) T\, \propto \,{e^{ - 3R}}

453

MediumJEE Mains2014

Three rods of Copper, Brass and Steel are welded together to form a $Y shaped structure. Area of cross - section of each rod = 4c{m^2}. End of copper rod is maintained at {100^ \circ }C where as ends of brass and steel are kept at {0^ \circ }C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS$ units respectively. Rate of heat flow through copper rod is:

Options:

A) 1.2 cal/s

B) 2.4 cal/s

C) 4.8 cal/s

D) 6.0 cal/s

454

MediumJEE Mains2014

One mole of a diatomic ideal gas undergoes a cyclic process $ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K$ respectively. Choose the correct statement :

Options:

A) The change in internal energy in whole cyclic process is $250 R.

B) The change in internal energy in the process $CA is 700 R$.

C) The change in internal energy in the process $AB is - 350 R.

D) The change in internal energy in the process $BC is - 500 R.

455

MediumJEE Mains2013

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $T, density of liquid is \rho and L$ is its latent heat of vaporization.

Options:

A) \rho L/T

B) \sqrt {T/\rho L}

C) T/\rho L

D) 2T/\rho L

456

MediumJEE Mains2013

The above $p-v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Options:

A) {p_0}{v_0}

B) \left( {{{13} \over 2}} \right){p_0}{v_0}

C) \left( {{{11} \over 2}} \right){p_0}{v_0}

D) 4{p_0}{v_0}

457

MediumJEE Mains2012

A wooden wheel of radius $R is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2\pi R. To fit the ring on the wheel, it is heated so that its temperature rises by \Delta T and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is \alpha , and its Young's modulus is Y,$ the force that one part of the wheel applies on the other part is :

Options:

A) 2\pi SY\alpha \Delta T

B) SY\alpha \Delta T

C) \pi SY\alpha \Delta T

D) 2SY\alpha \Delta T

458

MediumJEE Mains2012

A Carnot engine, whose efficiency is $40\% , takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60\% .$ Then, the intake temperature for the same exhaust (sink) temperature must be :

Options:

A) efficiency of Carnot engine cannot be made larger than $50\%

B) 1200 K

C) 750 K

D) 600 K

459

MediumJEE Mains2012

Helium gas goes through a cycle $ABCD$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

Options:

A) 15.4\%

B) 9.1\%

C) 10.5\%

D) 12.5\%

460

MediumJEE Mains2011

A thermally insulated vessel contains an ideal gas of molecular mass $M and ratio of specific heats \gamma . It is moving with speed v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

Options:

A) {{\left( {\gamma - 1} \right)} \over {2\gamma R}}M{v^2}K

B) {{\gamma {M^2}v} \over {2R}}K

C) {{\left( {\gamma - 1} \right)} \over {2R}}M{v^2}K

D) {{\left( {\gamma - 1} \right)} \over {2\left( {\gamma + 1} \right)R}}M{v^2}K

461

MediumJEE Mains2011

100g of water is heated from {30^ \circ }C to {50^ \circ }C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K$):

Options:

A) 8.4 kJ

B) 84 kJ

C) 2.1 kJ

D) 4.2 kJ

462

MediumJEE Mains2011

Three perfect gases at absolute temperatures ${T_1},\,{T_2} and {T_3} are mixed. The masses of molecules are {m_1},{m_2} and {m_3} and the number of molecules are {n_1}, {n_2} and {n_3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

Options:

A) {{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}

B) {{{n_1}T_1^2 + {n_2}T_2^2 + {n_3}T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}

C) {{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}

D) {{\left( {{T_1} + {T_2} + {T_3}} \right)} \over 3}

463

MediumJEE Mains2011

A Carnot engine operating between temperatures ${{T_1}} and {{T_2}} has efficiency {1 \over 6}. When {T_2} is lowered by 62 K its efficiency increases to {1 \over 3}. Then {T_1} and {T_2}$ are, respectively:

Options:

A) 372 K and 330 K

B) 330 K and 268 K

C) 310 K and 248 K

D) 372 K and 310 K

464

MediumJEE Mains2010

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V to 32 V$, the efficiency of the engine is

Options:

A) 0.5

B) 0.75

C) 0.99

D) 0.25

465

MediumJEE Mains2009

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta along the length x$ of the bar from its hot end is best described by which of the following figures?

Options:

466

MediumJEE Mains2009

Two moles of helium gas are taken over the cycle $ABCD, as shown in the P-T diagram. Assuming the gas to be ideal the work done on the gas in taking it from A to B$ is :

Options:

A) 300 R

B) 400 R

C) 500 R

D) 200 R

467

MediumJEE Mains2009

One $kg of a diatomic gas is at a pressure of 8 \times {10^4}\,N/{m^2}. The density of the gas is 4kg/{m^3}$. What is the energy of the gas due to its thermal motion ?

Options:

A) 5 \times {10^4}\,J

B) 6 \times {10^4}\,J

C) 7 \times {10^4}\,J

D) 3 \times {10^4}\,J

468

MediumJEE Mains2009

Statement - 1: The temperature dependence of resistance is usually given as $R = {R_0}\left( {1 + \alpha \,\Delta t} \right). The resistance of wire changes from 100\Omega to 150\Omega when its temperature is increased from {27^ \circ }C to {227^ \circ }C. This implies that \alpha = 2.5 \times {10^{ - 3}}/C. Statement - 2: R = {R_0}\left( {1 + \alpha \,\Delta t} \right) is valid only when the change in the temperature \Delta T is small and \Delta T = \left( {R - {R_0}} \right) < < {R_0}.

Options:

A) Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1

B) Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1

C) Statement - 1 is false, Statement - 2 is true

D) Statement - 1 is true, Statement - 2 is false

469

MediumJEE Mains2009

Two moles of helium gas are taken over the cycle $ABCD, as shown in the P-T diagram. The work done on the gas in taking it from D to A$ is :

Options:

A) +414 R

B) -690 R

C) +690 R

D) -414 R

470

MediumJEE Mains2009

Two moles of helium gas are taken over the cycle $ABCD, as shown in the P-T diagram. The net work done on the gas in the cycle ABCDA$ is:

Options:

A) 276 R

B) 1076 R

C) 1904 R

D) zero

471

MediumJEE Mains2008

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${V_1} and contains ideal gas at pressure {P_1} and temperature {T_1}. The other chamber has volume {V_2} and contains ideal gas at pressure {P_2} and temperature {T_2}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Options:

A) {{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}

B) {{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \over {{P_1}{V_1} + {P_2}{V_2}}}

C) {{{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \over {{P_1}{V_1} + {P_2}{V_2}}}

D) {{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}}}

472

MediumJEE Mains2008

The speed of sound in oxygen $\left( {{O_2}} \right) at a certain temperature is 460\,\,m{s^{ - 1}}. The speed of sound in helium (He)$ at the same temperature will be (assume both gases to be ideal)

Options:

A) 1421\,\,m{s^{ - 1}}

B) 500\,\,m{s^{ - 1}}

C) 650\,\,m{s^{ - 1}}

D) 300\,\,m{s^{ - 1}}

473

MediumJEE Mains2007

When a system is taken from state $i to state f along the path iaf, it is found that Q=50 cal and W=20 cal. Along the path ibf Q=36 cal. W along the path ibf$ is

Options:

A) 14 cal

B) 6 cal

C) 16 cal

D) 66 cal

474

MediumJEE Mains2007

A Carnot engine, having an efficiency of $\eta = 1/10 as heat engine, is used as a refrigerator . If the work done on the system is 10 J$, the amount of energy absorbed from the reservoir at lower temperature is

Options:

A) 100 J

B) 99 J

C) 90 J

D) 1 J

475

MediumJEE Mains2007

If ${C_p} and {C_v}$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

Options:

A) {C_p} - {C_v} = 28R

B) {C_p} - {C_v} = R/28

C) {C_p} - {C_v} = R/14

D) {C_p} - {C_v} = R

476

MediumJEE Mains2007

One end of a thermally insulated rod is kept at a temperature ${T_1} and the other at {T_2}. The rod is composed of two sections of length {L_1} and {L_2} and thermal conductivities {K_1} and {K_2}$ respectively. The temperature at the interface of the two section is

Options:

A) {{\left( {{K_1}{L_1}{T_1} + {K_2}{L_2}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}

B) {{\left( {{K_2}{L_2}{T_1} + {K_1}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}

C) {{\left( {{K_2}{L_1}{T_1} + {K_1}{L_2}{T_2}} \right)} \over {\left( {{K_2}{L_1} + {K_1}{L_2}} \right)}}

D) {{\left( {{K_1}{L_2}{T_1} + {K_2}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_2} + {K_2}{L_1}} \right)}}

477

MediumJEE Mains2006

Assuming the Sun to be a spherical body of radius $R at a temperature of TK, evaluate the total radiant powered incident of Earth at a distance r from the Sun Where r 0 is the radius of the Earth and \sigma $ is Stefan's constant.

Options:

A) 4\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}

B) \pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}

C) r_0^2{R^2}\sigma {{{T^4}} \over {4\pi {r^2}}}

D) {R^2}\sigma {{{T^4}} \over {{r^2}}}

478

MediumJEE Mains2006

The work of $146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by {7^ \circ }C. The gas is \left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)

Options:

A) diatomic

B) triatomic

C) a mixture of monoatomic and diatomic

D) monoatomic

479

MediumJEE Mains2006

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature ${T_0}, while Box contains one mole of helium at temperature \left( {{7 \over 3}} \right){T_0}. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, {T_f} in terms of {T_0}$ is

Options:

A) {T_f} = {3 \over 7}{T_0}

B) {T_f} = {7 \over 3}{T_0}

C) {T_f} = {3 \over 2}{T_0}

D) {T_f} = {5 \over 2}{T_0}

480

MediumJEE Mains2005

A system goes from $A to B via two processes I and II as shown in figure. If \Delta {U_1} and \Delta {U_2} are the changes in internal energies in the processes I and II$ respectively, then

Options:

A) relation between $\Delta {U_1} and \Delta {U_2}$ can not be determined

B) \Delta {U_1} = \Delta {U_2}

C) \Delta {U_2} < \Delta {U_1}

D) \Delta {U_2} > \Delta {U_1}

481

MediumJEE Mains2005

The figure shows a system of two concentric spheres of radii ${r_1} and {r_2} are kept at temperatures {T_1} and {T_2}$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Options:

A) In\left( {{{{r_2}} \over {{r_1}}}} \right)

B) {{\left( {{r_2} - {r_1}} \right)} \over {\left( {{r_1}{r_2}} \right)}}

C) {\left( {{r_2} - {r_1}} \right)}

D) {{{r_1}{r_2}} \over {\left( {{r_2} - {r_1}} \right)}}

482

MediumJEE Mains2005

A gaseous mixture consists of $16 g of helium and 16 g of oxygen. The ratio {{Cp} \over {{C_v}}}$ of the mixture is

Options:

A) 1.62

B) 1.59

C) 1.54

D) 1.4

483

MediumJEE Mains2005

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

Options:

A) {1 \over 4}

B) {1 \over 2}

C) {2 \over 3}

D) {1 \over 3}

484

MediumJEE Mains2004

If the temperature of the sun were to increase from $T to 2T and its radius from R to 2R$, then the ratio of the radiant energy received on earth to what it was previously will be

Options:

A) 32

B) 16

C) 4

D) 64

485

MediumJEE Mains2004

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K and 2K and thickness x and 4x, respectively, are {T_2} and {T_1}\left( {{T_2} > {T_1}} \right). The rate of heat transfer through the slab, in a steady state is \left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f, with f$ equal to

Options:

A) {2 \over 3}

B) {1 \over 2}

C) 1

D) {1 \over 3}

486

MediumJEE Mains2004

One mole of ideal monatomic gas $\left( {\gamma = 5/3} \right) is mixed with one mole of diatomic gas \left( {\gamma = 7/5} \right). What is \gamma for the mixture? \gamma $ Denotes the ratio of specific heat at constant pressure, to that at constant volume

Options:

A) 35/23

B) 23/15

C) 3/2

D) 4/3

487

MediumJEE Mains2004

Two thermally insulated vessels $1 and 2 are filled with air at temperatures \left( {{T_1},{T_2}} \right), volume \left( {{V_1},{V_2}} \right) and pressure \left( {{P_1},{P_2}} \right)$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Options:

A) {T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \right)

B) \left( {{T_1} + {T_2}} \right)/2

C) {{T_1} + {T_2}}

D) {T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \right)

488

MediumJEE Mains2004

Time taken by a $836 W heater to heat one litre of water from 10{}^ \circ C to 40{}^ \circ C$ is

Options:

A) 150 s

B) 100 s

C) 50 s

D) 200 s

489

MediumJEE Mains2004

Which of the following statements is correct for any thermodynamic system ?

Options:

A) The change in entropy can never be zero

B) Internal energy and entropy and state functions

C) The internal energy changes in all processes

D) The work done in an adiabatic process is always zero,

490

MediumJEE Mains2003

A carnot engine takes $3 \times {10^6} cal. of heat from a reservoir at {627^ \circ }C, and gives it to a sink at {27^ \circ }C$. The work done by the engine is

Options:

A) 4.2 \times {10^6}J

B) 8.4 \times {10^6}J

C) 16.8 \times {10^6}J

D) zero

491

MediumJEE Mains2003

''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of :

Options:

A) second law of thermodynamics

B) conservation of momentum

C) conservation of mass

D) first law of thermodynamics

492

MediumJEE Mains2003

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_V}$ for the gas is

Options:

A) {4 \over 3}

B) 2

C) {5 \over 3}

D) {3 \over 2}

493

MediumJEE Mains2003

Which of the following parameters does not characterize the thermodynamic state of mattter?

Options:

A) Temperature

B) Pressure

C) Work

D) Volume

494

MediumJEE Mains2003

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

Options:

A) Rayleigh Jeans law

B) Planck's law of radiation

C) Stefan's law of radiation

D) Wien's law

495

MediumJEE Mains2002

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

Options:

A) increase

B) decrease

C) remain same

D) decrease for some, while increase for others

496

MediumJEE Mains2002

Which statement is incorrect?

Options:

A) all reversible cycles have same efficiency

B) reversible cycle has more efficiency than an irreversible one

C) Cannot cycle is a reversible one

D) Cannot cycle has the maximum efficiency in all cycles.

497

MediumJEE Mains2002

1 mole of a gas with $\gamma = 7/5 is mixed with 1 mole of a gas with \gamma = 5/3, then the value of \gamma $ for the resulting mixture is

Options:

A) 7/5

B) 2/5

C) 3/2

D) 12/7

498

MediumJEE Mains2002

Infrared radiation is detected by

Options:

A) spectrometer

B) pyrometer

C) nanometer

D) photometer

499

MediumJEE Mains2002

Which of the following is more close to a black body?

Options:

A) black board paint

B) green leaves

C) black holes

D) red roses

500

MediumJEE Mains2002

Heat given to a body which raises its temperature by ${1^ \circ }C$ is

Options:

A) water equivalent

B) thermal capacity

C) specific heat

D) temperature gradient

501

MediumJEE Mains2002

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Options:

A) increase

B) remain unchanged

C) decrease

D) first increase then decrease

502

MediumJEE Mains2002

Even Carnot engine cannot give $100\% $ efficiency because we cannot

Options:

A) prevent radiation

B) find ideal sources

C) reach absolute zero temperature

D) eliminate friction.

503

MediumJEE Mains2002

At what temperature is the $r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at {47^ \circ }C?

Options:

A) 80K

B) -73 K

C) 3 K

Options:

A) It is a restatement of the principle of conservation of energy

B) It is not applicable to any cyclic process

C) It introduces the concept of the entropy

D) It introduces the concept of the internal energy

577

MediumMHT CET2025

A black body has maximum wavelength ' \lambda_{\mathrm{m}} ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

Options:

A) \frac{3}{2} \lambda_{\mathrm{m}}

B) \frac{16}{81} \lambda_m

C) \frac{81}{16} \lambda_m

D) \frac{2}{3} \lambda_m

578

MediumMHT CET2025

The relation between efficiency (\eta) of Carnot engine and coefficient of performance \left(\eta_1\right) of refrigerator is

Options:

A) \eta=\frac{1}{1+\eta_1}

B) \eta=\frac{1}{1-\eta_1}

C) \quad \eta=\frac{\eta_1}{1-\eta_1}

D) \eta=\frac{1+\eta_1}{\eta_1}

579

MediumMHT CET2025

500 gram of a diatomic gas is enclosed at a pressure of 10^5 \mathrm{Nm}^{-2}. The density of the gas is 5 \mathrm{kgm}^{-3}. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]

Options:

A) 1.5 \times 10^4 \mathrm{~J}

B) 2.5 \times 10^4 \mathrm{~J}

C) 1.5 \times 10^7 \mathrm{~J}

D) 2.5 \times 10^7 \mathrm{~J}

580

MediumMHT CET2025

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' R ' from the centre of a star of radius ' r ' is (R>r)(\sigma= Stefan's constant )

Options:

A) \frac{\sigma \mathrm{r}^2 \mathrm{~T}^4}{\mathrm{R}^2}

B) \frac{\sigma r^2 T^4}{4 \pi R^2}

C) \frac{\sigma \mathrm{r}^2 \mathrm{~T}^4}{\mathrm{R}^4}

D) \frac{4 \pi \sigma r^2 T^4}{R^2}

581

MediumMHT CET2025

A gas having \gamma=\frac{5}{2} and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

Options:

A) \frac{\mathrm{P}}{4}

B) 8 P

C) 16 P

D) 32 P

582

MediumMHT CET2025

The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively 1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C} and 1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C} )

Options:

A) nearly 15 cm and 10 cm

B) nearly 14 cm and 9 cm

C) nearly 12 cm and 7 cm

D) nearly 13 cm and 8 cm

583

MediumMHT CET2025

Two spherical black bodies have radii ' R_1 ' and ' \mathrm{R}_2 '. Their surface temperatures are ' \mathrm{T}_1 ' and ' T_2 '. If they radiate same power, then \frac{R_2}{R_1} is

Options:

A) \frac{T_2}{T_1}

B) \frac{T_1}{T_2}

C) \left(\frac{T_2}{T_1}\right)^2

D) \left(\frac{T_1}{T_2}\right)^2

584

MediumMHT CET2025

An ideal gas taken through a process ABCA as shown in figure. If the net heat supplied to gas in the cycle is 5 J , then the work done by the gas in process from C to A is

Options:

A) -5 J

B) -10 J

C) -15 J

D) -20 J

585

MediumMHT CET2025

A calorimeter contains 10 g of water at 20^{\circ} \mathrm{C}. The temperature fall to 15^{\circ} \mathrm{C} in 10 min . When calorimeter contains 20 g of water at 20^{\circ} \mathrm{C}, it takes 15 min . for the temperature to become 15^{\circ} \mathrm{C}. The water equivalent at the calorimeter is

Options:

A) 50 g

B) 25 g

C) 10 g

D) 5 g

586

MediumMHT CET2025

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is \mathrm{dT}_{\mathrm{A}}, then the rise in temperature of the gas in B is \left(\gamma=\frac{C_p}{C_v}\right)

Options:

A) \frac{\mathrm{dT}_{\mathrm{A}}}{2}

B) \frac{\mathrm{dT}_{\mathrm{A}}}{\gamma}

C) \quad \gamma d T_A

D) \quad 2 \mathrm{dT}_{\mathrm{A}}

587

MediumMHT CET2025

A black sphere has radius R whose rate of radiation is E at temperature T . If radius is made R / 2 and temperature 3T, the rate of radiation will be

Options:

A) \frac{3 \mathrm{E}}{2}

B) \frac{27 \mathrm{E}}{8}

C) \frac{81 \mathrm{E}}{4}

D) \frac{9 \mathrm{E}}{4}

588

MediumMHT CET2025

In the thermodynamic processes, which of the following statements is NOT true?

Options:

A) In an isothermal process, the temperature remains constant.

B) In an adiabatic process, the system is insulated from surroundings.

C) In an isochoric process, pressure remains constant.

D) In an adiabatic process, \mathrm{PV}^\gamma= constant.

589

MediumMHT CET2025

In case of free expansion, which one of the following statements is WRONG?

Options:

A) It is an instantaneous change.

B) The system is not in thermodynamic equilibrium.

C) Free expansion can be plotted on a P-V diagram.

D) It is an uncontrolled change.

590

MediumMHT CET2025

An ideal gas expands adiabatically, (\gamma=1.5). To reduce the r.m.s. velocity of the molecules 4 times, the gas has to be expanded

Options:

A) 256 times

B) 128 times

C) 64 times

D) 8 times

591

MediumMHT CET2025

The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at 57^{\circ} \mathrm{C} is (molecular masses of oxygen and helium are 32 and 4 respectively.)

Options:

A) 1320 K

B) 2240 K

C) 2640 K

D) 3230 K

592

MediumMHT CET2025

Two black spheres \mathrm{P} \& \mathrm{Q} have radii in the ratio 4: 3. The wavelength of maximum intensity of radiation are in the ratio 4: 5 respectively. The ratio of radiated power by P to Q is

Options:

A) \frac{625}{144}

B) \frac{125}{81}

C) \frac{25}{9}

D) \frac{5}{3}

593

MediumMHT CET2025

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by 48^{\circ} \mathrm{C} at constant pressure is (Molecular weight of nitrogen =28, R= gas constant, \mathrm{C}_{\mathrm{p}}=\frac{7}{2} \mathrm{R} for diatomic gas)

Options:

A) 76 R

B) 84 R

C) 90 R

D) 96 R

594

MediumMHT CET2025

The difference in length between two rods A and B is 60 cm at all temperatures. If \alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C} and \alpha_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}, then the length of \operatorname{rod} \mathrm{A} and \operatorname{rod} \mathrm{B} at 0^{\circ} \mathrm{C} is respectively

Options:

A) l_{\mathrm{A}}=120 \mathrm{~cm}, l_{\mathrm{B}}=60 \mathrm{~cm}.

B) l_{\mathrm{A}}=180 \mathrm{~cm}, l_{\mathrm{B}}=120 \mathrm{~cm}.

C) l_{\mathrm{A}}=240 \mathrm{~cm}, l_{\mathrm{B}}=180 \mathrm{~cm}.

D) l_{\mathrm{A}}=270 \mathrm{~cm}, l_{\mathrm{B}}=210 \mathrm{~cm}.

595

MediumMHT CET2025

The initial average kinetic energy of the molecules was E , when a gas sample is at 27^{\circ} \mathrm{C}. When the gas is heated to 327^{\circ} \mathrm{C}, then the final average kinetic energy will be

Options:

A) \quad \sqrt{2} \mathrm{E}

B) 2 E

C) 300 E

D) 327 E

596

MediumMHT CET2025

A sample of an ideal gas \left(\gamma=\frac{5}{3}\right) is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is

Options:

A) 150 J

B) 60 J

C) 40 J

D) 250 J

597

MediumMHT CET2025

A balloon is filled at 27^{\circ} \mathrm{C} and 1 atmospheric pressure by volume 500 \mathrm{~m}^3 helium gas. At -3^{\circ} \mathrm{C} and 0.5 atmospheric pressure, the volume of helium gas will be

Options:

A) 500 \mathrm{~m}^3

B) 700 \mathrm{~m}^3

C) 900 \mathrm{~m}^3

D) 1000 \mathrm{~m}^3

598

MediumMHT CET2025

The volume of a metal sphere increases by 0.33 \% when its temperature is raised by 50^{\circ} \mathrm{C}. The coefficient of linear expansion of the metal is

Options:

A) 2.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}

B) 6.6 \times 10^{-5} /{ }^{\circ} \mathrm{C}

C) 13.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}

D) 19.8 \times 10^{-5} /{ }^{\circ} \mathrm{C}

599

MediumMHT CET2025

Heat supplied d Q= increased in internal energy dU is true for

Options:

A) isothermal process.

B) adiabatic process.

C) isobaric process.

D) isochoric process.

600

MediumMHT CET2025

A black body emits radiation of maximum intensity at wavelength ' \lambda ' at temperature T K. Its corresponding wavelength at temperature 1.5 T K will be

Options:

A) \frac{2 \lambda}{3}

B) \frac{4 \lambda}{3}

C) \frac{16 \lambda}{81}

D) \frac{81 \lambda}{16}

601

MediumMHT CET2025

A rectangular black body of temperature 127^{\circ} \mathrm{C} has surface area 4 \mathrm{~cm} \times 2 \mathrm{~cm} and rate of radiation is E . If its temperature is increased by 400^{\circ} \mathrm{C} and surface area is reduced to half of the initial value then the rate of radiation is

Options:

A) 4 E

B) E

C) 2 E

D) 16 E

602

MediumMHT CET2025

The temperature of an ideal gas is increased from 100 K to 400 K . If ' x ' is the root mean square velocity of its molecules at 100 K , r.m.s. velocity becomes

Options:

A) \frac{x}{4}

B) 2 x

C) 3 x

D) 4 x

603

MediumMHT CET2025

According to the kinetic theory of gases, when two molecules of a gas collide with each other then

Options:

A) both kinetic energy and momentum are conserved.

B) neither kinetic energy nor momentum is conserved.

C) momentum is conserved but kinetic energy is not conserved.

D) kinetic energy is conserved but momentum is not conserved.

604

MediumMHT CET2025

During the isothermal expansion, a confined ideal gas does (-150) \mathrm{J} of work against its surroundings. This means that

Options:

A) 150 J of heat has been added to the gas

B) 150 J of heat has been removed from the gas

C) 300 J of heat has been added to the gas

D) no heat is transferred because the process is isothermal

605

MediumMHT CET2025

A body cools from 80^{\circ} \mathrm{C} to 50^{\circ} \mathrm{C} in 5 min . In the next time of ' t ' in, the body continues to cool from 50^{\circ} \mathrm{C} to 30^{\circ} \mathrm{C}. The total time taken by the body to cool from 80^{\circ} \mathrm{C} to 30^{\circ} \mathrm{C} is [The temperature of the surroundings is 20^{\circ} \mathrm{C}.]

Options:

A) 10 min

B) 7.5 min

C) 15.0 min

D) 12.5 min

606

MediumMHT CET2025

The volume of given mass of a gas is increased by 7 \% at constant temperature. The pressure should be increased by

Options:

A) 7 \%

B) 14 \%

C) 7.52 \%

D) 14.52 \%

607

MediumMHT CET2025

A monoatomic ideal gas is compressed adiabatically to \left(\frac{1}{27}\right) of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K , the value of ' x ' is

Options:

A) 7

B) 9

C) 11

D) 13

608

MediumMHT CET2025

Select the correct statement.

Options:

A) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

B) The temperature of gas is -73^{\circ} \mathrm{C}. When the gas is heated to 527^{\circ} \mathrm{C}, the r.m.s. speed of the molecules is doubled.

C) The temperature of gas is -100^{\circ} \mathrm{C}. When the gas is heated to +627^{\circ} \mathrm{C}, the r.m.s. speed of the molecules is four times.

D) The product of pressure and volume of an ideal gas will be equal to half the translational kinetic energy.

609

MediumMHT CET2025

A polyatomic gas at pressure P , having volume ' V ' expands isothermally to a volume ' 3 V ' and then adiabatically to a volume ' 24 V '. The final pressure of gas is (for moderate temperature changes)

Options:

A) 16 P

B) 24 P

C) P / 36

D) P / 48

610

MediumMHT CET2025

A stationary object at 4^{\circ} \mathrm{C} and weighing 3.5 kg falls from a height of 2000 m on snow mountain at 0^{\circ} \mathrm{C}. If the temperature of the object just before hitting the snow is 0^{\circ} \mathrm{C} and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity =10 \mathrm{~m} / \mathrm{s}^2, Latent heat of ice =3.5 \times 10^5 \mathrm{~J} / \mathrm{kg} )

Options:

A) 2 gram

B) 20 gram

C) 200 gram

D) 2 kg

611

MediumMHT CET2025

Six molecules of a gas in container have speeds 2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, and 5 \mathrm{~m} / \mathrm{s}. The r.m.s. speed is

Options:

A) 4 \mathrm{~m} / \mathrm{s}

B) 1.7 \mathrm{~m} / \mathrm{s}

C) 4.24 \mathrm{~m} / \mathrm{s}

D) 5 \mathrm{~m} / \mathrm{s}

612

MediumMHT CET2025

During thermodynamic process, the increase in internal energy of a system is equal to the \mathrm{w}_{0 r k} done on the system. Which process does the system undergo?

Options:

A) Isothermal

B) Adiabatic

C) Isochoric

D) Isobaric

613

MediumMHT CET2025

How much should the pressure be increased in order to reduce the volume of a given mass of gas by 5 \% at the constant temperature?

Options:

A) 5 \%

B) 10 \%

C) 5.26 \%

D) 4 \%

614

MediumMHT CET2025

A polyatomic gas is compressed to \left(\frac{1}{8}\right)^{\text {th }} of its volume adiabatically. If its initial pressure is \mathrm{P}_0, its new pressure will be [Given, \frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3} ]

Options:

A) \quad 6 \mathrm{P}_0

B) \quad 2 \mathrm{P}_0

C) \quad 8 \mathrm{P}_0

D) 16 \mathrm{P}_0

615

MediumMHT CET2025

The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' A ' and the gas in other jar ' B ' is at pressure ' 2 P ', volume ' V ' and temperature ' \frac{T}{4} '. Then the ratio of the number of molecules in jar A and jar B will be

Options:

A) 1: 1

B) 1: 2

C) 2: 1

D) 4: 1

616

MediumMHT CET2025

Two moles of an ideal monoatomic gas undergo a cyclic process as shown in figure. The temperatures in different states are given as 6 \mathrm{~T}_1=3 \mathrm{~T}_2=2 \mathrm{~T}_4=\mathrm{T}_3=2400 \mathrm{~K}. The work done by the gas during the complete cycle is ( \mathrm{R}= Universal gas constant)

Options:

A) -1600 R

B) 1600 R

C) -1200 R

D) 800 R

617

MediumMHT CET2025

Two spherical black bodies have radii ' R_1 ' and ' R_2 '. Their surface temperatures are T_1 K and T_2 K respectively. If they radiate the same power, the ratio \frac{R_1}{R_2} is

Options:

A) \left(\frac{T_1}{T_2}\right)^4

B) \left(\frac{T_1}{T_2}\right)^2

C) \left(\frac{T_2}{T_1}\right)^4

D) \left(\frac{T_2}{T_1}\right)^2

618

MediumMHT CET2025

A thermometer bulb has volume 10^{-6} \mathrm{~m}^3 and cross-section of the stem is 0.002 \mathrm{~cm}^2. The bulb is filled with mercury at 0^{\circ} \mathrm{C}. If the thermometer reads temperature as 100^{\circ} \mathrm{C}, then the length of mercury column is (coefficient of cubical expansion of mercury =18 \times 10^{-5} /{ }^{\circ} \mathrm{C} )

Options:

A) 90 cm

B) 9 mm

C) 9 cm

D) 0.9 mm

619

MediumMHT CET2025

The two ends of a rod of length ' x ' and uniform cross-sectional area ' A ' are kept at temperatures ' \mathrm{T}_1 ' and ' \mathrm{T}_2 ' respectively ( \mathrm{T}_1>\mathrm{T}_2 ). If the rate of heat transfer is ' \mathrm{Q} / \mathrm{t} ', through the rod in steady state, then the coefficient of thermal conductivity ' K ' is

Options:

A) \frac{A Q}{\operatorname{tx}\left(T_1-T_2\right)}

B) \frac{x Q}{t A\left(T_1-T_2\right)}

C) \frac{x A Q}{t\left(T_1-T_2\right)}

D) \frac{Q}{\operatorname{txA}\left(T_1-T_2\right)}

620

MediumMHT CET2025

When the pressure of the gas contained in a closed vessel is increased by 2.3 \%, the temperature of the gas increases by 4 K . The initial temperature of the gas is

Options:

A) 80 K

B) 150 K

C) 160 K

D) 320 K

621

MediumMHT CET2025

Black bodies A and B radiate maximum energy with wavelength difference 4 \mu \mathrm{~m}. The absolute temperature of body A is 3 times that of B. The wavelength at which body B radiates maximum energy is

Options:

A) 4 \mu \mathrm{~m}

B) 6 \mu \mathrm{~m}

C) 2 \mu \mathrm{~m}

D) 8 \mu \mathrm{~m}

622

MediumMHT CET2025

A monoatomic ideal gas, initially at temperature \mathrm{T}_1 is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature \mathrm{T}_2. If \mathrm{L}_1 and \mathrm{L}_2 are the lengths of the gas columns before and after expansion respectively, then \left(T_2 / T_1\right) is given by

Options:

A) \frac{\mathrm{L}_1}{\mathrm{~L}_2}

B) \frac{\mathrm{L}_2}{\mathrm{~L}_1}

C) \left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{2 / 3}

D) \left(\frac{L_2}{L_1}\right)^{2 / 3}

623

MediumMHT CET2025

Two bodies A and B at temperatures ' \mathrm{T}_1 ' K and ' \mathrm{T}_2 ' K respectively have the same dimensions. Their emissivities are in the ratio 16: 1. At \mathrm{T}_1=\mathrm{xT}_2, they radiate the same amount of heat per unit area per unit time. The value of x is

Options:

A) 8

B) 4

C) 2

D) 0.5

624

MediumMHT CET2025

In an isobaric process of an ideal gas, the ratio of heat supplied and work done by the system \left(\frac{\mathrm{Q}}{\mathrm{W}}\right) is \left[\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma\right].

Options:

A) 1

B) \gamma

C) \frac{\gamma}{\gamma-1}

D) \frac{\gamma-1}{\gamma}

625

MediumMHT CET2025

The temperature of a body on Kelvin scale is ' x ' K. When it is measured by a Fahrenheit thermometer, it is found to be ' x ' { }^{\circ} \mathrm{F}. The value of ' x ' is (nearly)

Options:

A) 40

B) 313

C) 574

D) 301

626

MediumMHT CET2025

For a gas at a particular temperature on an average, the quantity which remains same for all molecules is

Options:

A) velocity

B) momentum

C) kinetic energy

D) angular momentum

627

MediumMHT CET2025

If 120 J of thermal energy is incident on area 3 \mathrm{~m}^2, the amount of heat transmitted is 12 J , coefficient of absorption is 0.6 , then the amount of heat reflected is

Options:

A) 24 J

B) 30 J

C) 36 J

D) 40 J

628

MediumMHT CET2025

When an ideal gas \left(\gamma=\frac{5}{3}\right) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?

Options:

A) 60 \%

B) 20 \%

C) 30 \%

D) 40 \%

629

MediumMHT CET2025

The mean kinetic energy of the molecules of an ideal gas at 399^{\circ} \mathrm{C} is ' E '. The temperature at which the mean kinetic energy of its molecules will be ' \mathrm{E} / 2 ', is

Options:

A) 336^{\circ} \mathrm{C}

B) 276^{\circ} \mathrm{C}

C) 123^{\circ} \mathrm{C}

D) 63^{\circ} \mathrm{C}

630

MediumMHT CET2025

A gas undergoes a change in which its pressure ' P ' and volume ' V ' are related as \mathrm{PV}^{\mathrm{n}}= constant, where n is a constant. If the specific heat of the gas in this change is zero, then the value of n is ( \gamma= adiabatic ratio)

Options:

A) 1-\gamma

B) \gamma+1

C) \quad \gamma-1

D) \gamma

631

MediumMHT CET2025

Hot water cools from 80^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C} in 1 minutes. In cooling from 60^{\circ} \mathrm{C} to 50^{\circ} \mathrm{C} it will take (room temperature =30^{\circ} \mathrm{C} )

Options:

A) 48 s

B) 42 s

C) 50 s

D) 45 s

632

MediumMHT CET2025

A Carnot engine has efficiency \frac{1}{6}. It becomes \frac{1}{3}, when the temperature of \operatorname{sink} is lowered by 57 K . The temperature of the source is

Options:

A) 171 K

B) 399 K

C) 342 K

D) 285 K

633

MediumMHT CET2025

The r.m.s. speed of gas molecules at 800 K will be

Options:

A) same as at 200 K

B) twice the value at 200 K

C) four times the value at 200 K

D) half the value at 200 K

634

MediumMHT CET2025

If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' \mathrm{R}_0 ', the same body at 900 K , surrounded by same atmosphere, will have rate of cooling nearly

Options:

A) 4 \mathrm{R}_0

B) 16 \mathrm{R}_0

C) 36 \mathrm{R}_0

D) \frac{81 R_0}{16}

635

MediumMHT CET2025

The temperature of an ideal gas is increased from 100 K to 400 K . If ' x ' is the R.M.S. velocity of its molecules at 100 K , it becomes

Options:

A) \frac{x}{4}

B) 2 x

C) 3 x

D) 4 x

636

MediumMHT CET2025

Heat is given to an ideal gas in an isothermal process. Then A. internal energy of the gas will decrease. B. internal energy of the gas will increase. C. internal energy of the gas will not change. D. the gas will do negative work.

Options:

A) B

B) C

C) D

D) A

637

MediumMHT CET2025

A rectangular block of surface area A emits energy E per second at 27^{\circ} \mathrm{C}. If length and breadth is reduced to half of initial value and temperature is raised to 327^{\circ} \mathrm{C} then energy emitted per second becomes

Options:

A) 2 E

B) 4 E

C) E

D) 8 E

638

MediumMHT CET2025

When a diatomic gas (rigid) undergoes adiabatic change, its pressure (\mathrm{P}) and temperature (\mathrm{T}) are related as P \propto T^c. The value of c is

Options:

A) 2.5

B) 3.5

C) 1.5

D) 5.2

639

MediumMHT CET2025

For an ideal gas, the density of the gas is \rho_0 when temperature and pressure of the gas are \mathrm{T}_0 and P_0 respectively. when the temperature of the gas is 2 \mathrm{~T}_0, its pressure becomes 3 \mathrm{P}_0. The new density will be

Options:

A) \frac{2}{3} \rho_0

B) \frac{3}{4} \rho_0

C) \frac{4}{3} \rho_0

D) \frac{3}{2} \rho_0

640

MediumMHT CET2025

A centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit temperature observed is 140^{\circ} \mathrm{F}. At that time the temperature registered by the centigrade thermometer is

Options:

A) 80^{\circ} \mathrm{C}

B) 60^{\circ} \mathrm{C}

C) 40^{\circ} \mathrm{C}

D) 20^{\circ} \mathrm{C}

641

MediumMHT CET2025

An engine operating between temperatures T_1 and T_2 has efficiency \frac{1}{5}. When T_2 is lowered by 45 K , its efficiency becomes \frac{1}{2}. Temperatures T_1 and T_2 are respectively

Options:

A) 100 \mathrm{~K}, 70 \mathrm{~K}

B) 160 \mathrm{~K}, 120 \mathrm{~K}

C) 140 \mathrm{~K}, 110 \mathrm{~K}

D) 150 \mathrm{~K}, 120 \mathrm{~K}

642

MediumMHT CET2025

Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K . The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 49 K , then the rise in temperature of the gas in A is

Options:

A) 30 K

B) 35 K

C) 70 K

D) 75 K

643

MediumMHT CET2025

If a gas is compressed isothermally then the r.m.s. velocity of its molecules

Options:

A) increases.

B) decreases.

C) remains the same.

D) first increases and then decreases.

644

MediumMHT CET2025

The following graph represents the radiant power versus wavelength of the black body. The area under the curve represents

Options:

A) the maximum wavelength emitted by the object.

B) the minimum wavelength emitted by the object.

C) the total energy emitted per unit time by the black body at some particular wavelength

D) the total energy emitted per unit time per unit area by the black body at all wavelengths.

645

MediumMHT CET2025

In a cyclic process, work done by the system is

Options:

A) more than the heat given to the system.

B) equal to the heat given to the system.

C) zero.

D) independent of the heat given to the system.

646

MediumMHT CET2025

A metal sphere cools at a rate of 1.5^{\circ} \mathrm{C} / \mathrm{min} when its temperature is 80^{\circ} \mathrm{C}. When the temperature of the sphere is 40^{\circ} \mathrm{C}, its rate of cooling is 0.3^{\circ} \mathrm{C} / \mathrm{min}. The temperature of the surrounding \left(\theta_0\right) is

Options:

A) 30^{\circ} \mathrm{C}

B) 35^{\circ} \mathrm{C}

C) 25^{\circ} \mathrm{C}

D) 27^{\circ} \mathrm{C}

647

MediumMHT CET2025

The change in the internal energy of the mass of gas, when the volume changes from V to 2 V at constant pressure P is \left(\gamma=\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)

Options:

A) \frac{\mathrm{V}}{\mathrm{P}(\gamma-1)}

B) \frac{\mathrm{P}}{\mathrm{V}(\gamma-1)}

C) \frac{\mathrm{PV}}{\gamma+1}

D) \frac{\mathrm{PV}}{\gamma-1}

648

MediumMHT CET2025

For a perfectly black body, coefficient of emission is

Options:

A) zero.

B) unity.

C) less than one (non-zero).

D) infinity.

649

MediumMHT CET2025

A body cools from 60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C} in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10^{\circ} \mathrm{C} )

Options:

A) 24^{\circ} \mathrm{C}

B) 28^{\circ} \mathrm{C}

C) 18^{\circ} \mathrm{C}

D) 32^{\circ} \mathrm{C}

650

MediumMHT CET2025

A tyre of a vehicle is filled with air having pressure 270 kPa at 27^{\circ} \mathrm{C}. The air pressure in the tyre when the temperature increases to 37^{\circ} \mathrm{C} is

Options:

A) 282 kPa

B) 270 kPa

C) 265 kPa

D) 279 kPa

651

MediumMHT CET2025

The average force applied on the walls of a closed container depends as \mathrm{T}^{\mathrm{x}} where T is the temperature of an ideal gas. The value of x is

Options:

A) 1

B) 2

C) 3

D) 4

652

MediumMHT CET2025

A diatomic gas \left(\gamma=\frac{7}{5}\right) is compressed adiabatically to volume \frac{\mathrm{V}_0}{32}, where \mathrm{V}_0 is its initial volume. The initial temperature of the gas is \mathrm{T}_{\mathrm{i}} in kelvin and the final temperature is \mathrm{xT}_{\mathrm{i}} in kelvin. The value of x is

Options:

A) 5

B) 4

C) 3

D) 2

653

MediumMHT CET2025

The work done by a gas as it is taken in a cyclic process (shown in graph) is

Options:

A) 2 pv

B) -2 pv

C) 3 pv

D) -3 pv

654

MediumMHT CET2025

Two gases A and B are at absolute temperatures 350 K and 420 K respectively. The ratio of average kinetic energy of the molecules of gas B to that of gas A is

Options:

A) 6: 5

B) \sqrt{6}: \sqrt{5}

C) 36: 25

D) 5: 6

655

MediumMHT CET2025

A composite slab consists of two materials having coefficients of thermal conductivity K and 2 K, thickness x and 4 x respectively. The temperatures of two outer surfaces of a composite slab are \mathrm{T}_2 and \mathrm{T}_1 respectively \left(\mathrm{T}_2>\mathrm{T}_1\right). The rate of heat transfer through the slab in a steady state is \left[\frac{A\left(T_2-T_1\right) K}{x}\right] f, where f is equal to

Options:

A) 1

B) \frac{2}{3}

C) \frac{1}{2}

D) \frac{1}{3}

656

MediumMHT CET2025

The co-efficient of absorption and the coefficient of reflection of a thin uniform plate are 0.77 and 0.17 respectively. If 250 kcal of heat is incident on the surface of the plate, the quantity of heat transmitted is

Options:

A) 7 kcal

B) 12 kcal

C) 15 kcal

D) 22 kcal

657

MediumMHT CET2025

An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' V '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' P '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is

Options:

A) \frac{2 \mathrm{~V}}{\mathrm{RT}}\left(\mathrm{P}-\mathrm{P}^{\prime}\right)

B) \frac{\mathrm{V}}{\mathrm{RT}}\left(\mathrm{P}-\mathrm{P}^{\prime}\right)

C) \frac{\mathrm{V}}{\mathrm{RT}}\left(\mathrm{P}+\mathrm{P}^{\prime}\right)

D) \frac{\mathrm{V}}{2 \mathrm{RT}}\left(\mathrm{P}+\mathrm{P}^{\prime}\right)

658

MediumMHT CET2025

If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at 47^{\circ} \mathrm{C}, the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)

Options:

A) 23^{\circ} \mathrm{C}

B) 47^{\circ} \mathrm{C}

C) 80^{\circ} \mathrm{C}

D) 114^{\circ} \mathrm{C}

659

MediumMHT CET2025

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is A and B respectively. Then the ratio, \mathrm{A}: \mathrm{B} is

Options:

A) 5: 3

B) 2: 3

C) 3: 2

D) 2: 5

660

MediumMHT CET2025

Black sphere of radius R radiates power P at certain temperature T. If the temperature is doubled, the radius gets doubled. Now the power radiated would be

Options:

A) 4 P

B) 8 P

C) 16 P

D) 64 P

661

MediumMHT CET2025

Three samples X, Y, and Z of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X , adiabatic for Y and isobaric for Z . If the final pressures are equal for the three samples, the ratio of the initial pressures is ( \gamma=3 / 2)

Options:

A) 1: \sqrt{2}: 2 \sqrt{3}

B) 2: 2 \sqrt{2}: 1

C) 3: 3 \sqrt{3}: 1

D) 5: 5 \sqrt{5}: 1

662

MediumMHT CET2025

Two rods of different materials have lengths ' l ' and ' l_2 ' whose coefficient of linear expansions are ' \alpha_1 ' and ' \alpha_2 ' respectively. If the difference between the two lengths is independent of temperature then

Options:

A) \alpha_1^2 l_1=\alpha_2^2 l_2

B) \frac{l_1}{l_2}=\frac{\alpha_2}{\alpha_1}

C) \frac{l_1}{l_2}=\frac{\alpha_1}{\alpha_2}

D) l_1^2 \alpha_2=l_2^2 \alpha_1

663

MediumMHT CET2025

The molar specific heat of an ideal gas at constant pressure and constant volume is ' \mathrm{C}_{\mathrm{p}} ' and ' \mathrm{C}_{\mathrm{v}} ' respectively. If ' R ' is a universal gas constant and the ratio of ' \mathrm{C}_{\mathrm{p}} ' to ' \mathrm{C}_{\mathrm{v}} ' is \gamma, then ' \mathrm{C}_{\mathrm{p}} ' is equal to

Options:

A) \left(\frac{\gamma-1}{\gamma+1}\right) \mathrm{R}

B) \frac{(\gamma-1) R}{\gamma}

C) \frac{\mathrm{R} \gamma}{(\gamma-1)}

D) \frac{\mathrm{R} \gamma}{(\gamma+1)}

664

MediumMHT CET2025

For ideal non-rigid diatomic gas, the value of \frac{\mathrm{R}}{\mathrm{C}_{\mathrm{V}}} is nearly \left(\gamma=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{9}{7}\right)

Options:

A) 0.4

B) 0.66

C) 0.28

D) 1.28

665

MediumMHT CET2025

When the heat is given to a gas in an Isothermal process, then there will be

Options:

A) external work done.

B) rise in temperature.

C) increase in internal energy.

D) external work done and also rise in temperature.

666

MediumMHT CET2024

During an experiment, an ideal gas is found to obey an additional law \mathrm{VP}^2= constant. The gas is initially at temperature ' T ' and volume ' V '. What will be the temperature of the gas when it expands to a volume 2 V ?

Options:

A) \sqrt{3} \mathrm{~T}

B) \sqrt{\frac{1}{2 T}}

C) \sqrt{2} \mathrm{~T}

D) \sqrt{3 \mathrm{~T}}

667

MediumMHT CET2024

The first operation involved in a Carnot cycle is

Options:

A) isothermal expansion.

B) adiabatic expansion.

C) isothermal compression.

D) adiabatic compression.

668

MediumMHT CET2024

Temperature remaining constant, the pressure of gas is decreased by 20 \%. The percentage change in volume

Options:

A) increases by 29 \%

B) decreases by 20 \%

C) increases by 25 \%

D) decreases by 25 \%

669

MediumMHT CET2024

At certain temperature, \operatorname{rod} \mathrm{A} and \operatorname{rod} \mathrm{B} of different materials have lengths \mathrm{L}_{\mathrm{A}} and \mathrm{L}_B respectively. Their co-efficients of linear expansion are \alpha_A and \alpha_B respectively. It is observed that the difference between their lengths remain constant at all temperatures. The ratio L_A / L_B is given by

Options:

A) \frac{\alpha_A}{\alpha_B}

B) \frac{\alpha_B}{\alpha_A}

C) \frac{\alpha_A+\alpha_B}{\alpha_A}

D) \frac{\alpha_A+\alpha_B}{\alpha_B}

670

MediumMHT CET2024

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy is

Options:

A) 30 \%

B) 40 \%

C) 50 \%

D) 60 \%

671

MediumMHT CET2024

The ratio of the specific heats \frac{C_p}{C_v}=\gamma, in terms of degrees of freedom ( n ) is

Options:

A) \left(1+\frac{1}{n}\right)

B) \left(1+\frac{2}{n}\right)

C) \left(1+\frac{\mathrm{n}}{3}\right)

D) \left(1+\frac{\mathrm{n}}{2}\right)

672

MediumMHT CET2024

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

Options:

A) \left(\frac{3}{4}\right)^{\text {th }} of kinetic energy per unit volume of a gas.

B) \left(\frac{2}{3}\right)^{\text {rd }} of kinetic energy per unit volume of a gas.

C) \left(\frac{1}{3}\right)^{\mathrm{rd}} of kinetic energy per unit volume of a gas.

D) \left(\frac{3}{2}\right)^{\text {rd }} of kinetic energy per unit volume of a gas.

673

MediumMHT CET2024

If heat energy \Delta \mathrm{Q} is supplied to an ideal diatomic gas, the increase in internal energy is \Delta U and the amount of work done by the gas is \Delta \mathrm{W}. The ratio \Delta \mathrm{W}: \Delta \mathrm{U}: \Delta \mathrm{Q} is

Options:

A) 2: 3: 5

B) 2: 5: 7

C) 7: 5: 9

D) 1: 2: 5

674

MediumMHT CET2024

The power radiated by a black body is P and it radiates maximum energy around the wavelength \lambda_0. Now the temperature of the black body is changed so that it radiates maximum energy around wavelength \left(\frac{\lambda_0}{2}\right). The power radiated by it will now increase by a factor of

Options:

A) 2

B) 8

C) 16

D) 32

675

MediumMHT CET2024

A bucket full of hot water is kept in a room. If it cools from 75^{\circ} \mathrm{C} to 70^{\circ} \mathrm{C} in t_1 minutes, from 70^{\circ} \mathrm{C} to 65^{\circ} \mathrm{C} in \mathrm{t}_2 minutes and 65^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C} in t_3 minutes, then

Options:

A) \mathrm{t}_1<\mathrm{t}_2<\mathrm{t}_3

B) \mathrm{t_1>t_2>t_3}

C) \mathrm{t}_1=\mathrm{t}_2=\mathrm{t}_3

D) \mathrm{t}_1<\mathrm{t}_2=\mathrm{t}_3

676

MediumMHT CET2024

An ideal diatomic gas is heated at constant pressure. What is the fraction of total energy applied, which increases the internal energy for the gas?

Options:

A) \frac{2}{5}

B) \frac{5}{7}

C) \frac{3}{7}

D) \frac{3}{5}

677

MediumMHT CET2024

In ideal gas of 27^{\circ} \mathrm{C} is compressed adiabatically to (8 / 27) of its original volume. If \gamma=\frac{5}{3}, the rise in temperature of a gas is

Options:

A) 300 K

B) 375 K

C) 400 K

D) 450 K

678

MediumMHT CET2024

A cylindrical rod is having temperatures \theta_1 and \theta_2 at its ends. The rate of heat flow is \mathrm{Q} J / \mathrm{S}. All the linear dimensions of the rod are doubled by keeping the temperature constant. The new rate of flow of heat is

Options:

A) \mathrm{4Q}

B) \mathrm{2 Q}

C) \frac{\mathrm{Q}}{2}

D) \mathrm{\frac{Q}{4}}

679

MediumMHT CET2024

A monoatomic ideal gas, initially at temperature T_1 is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature T_2 by releasing the piston suddenly. L_1 and L_2 are the lengths of the gas columns before and after the expansion respectively. The ratio T_2 / T_1 is

Options:

A) \left[\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right]^{2 / 3}

B) \left[\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right]^{2 / 3}

C) \left[\frac{L_2}{L_1}\right]^{1 / 2}

D) \left[\frac{L_1}{L_2}\right]^{1 / 2}

680

MediumMHT CET2024

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as \mathrm{T}^{\mathrm{x}}. The value of x is

Options:

A) 0.25

B) 2

C) 0.5

D) 1

681

MediumMHT CET2024

Heat engine operating between temperature T_1 and T_2 has efficiency \frac{1}{6}. When T_2 is lowered by 62 K , its efficiency increases to \frac{1}{3}. Then T_1 and T_2 respectively are

Options:

A) 372 \mathrm{~K}, 310 \mathrm{~K}

B) 372 \mathrm{~K}, 330 \mathrm{~K}

C) 330 \mathrm{~K}, 268 \mathrm{~K}

D) 310 \mathrm{~K}, 248 \mathrm{~K}

682

MediumMHT CET2024

The absolute temperature of a gas is determined by

Options:

A) the average momentum of the molecule.

B) the velocity of sound in the gas.

C) the number of molecules in the gas.

D) the mean square velocity of the molecules.

683

MediumMHT CET2024

When a system is taken from state ' a ' to state ' c ' along a path abc, it is found that \mathrm{Q}=80 \mathrm{cal} and \mathrm{W}=35 \mathrm{cal}. Along path adc \mathrm{Q}=65 \mathrm{cal} the work done W along path adc is

Options:

A) 20 cal.

B) 35 cal.

C) 45 cal.

D) 65 cal.

684

MediumMHT CET2024

The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is

Options:

A) \frac{3}{7}

B) \frac{2}{7}

C) \frac{4}{7}

D) \frac{5}{7}

685

MediumMHT CET2024

The internal energy of an ideal diatomic gas corresponding to volume ' V ' and pressure ' P ' is 2.5 PV. The gas expands from 1 litre to 2 litre at a constant pressure of 10^5 \mathrm{~N} / \mathrm{m}^2. The heat supplied to a gas is

Options:

A) 350 J

B) 300 J

C) 250 J

D) 200 J

686

MediumMHT CET2024

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. \left[C_{\mathrm{v}}\right. for hydrogen =\frac{5}{2} R, C_v for helium =\frac{3}{2} R, \quad C_{\mathrm{v}} for water vapour \left.=3 \mathrm{R}\right] What is the molar specific heat at constant pressure of the mixture?

Options:

A) \frac{11}{3} \mathrm{R}

B) \frac{23}{7} R

C) \frac{16}{7} R

D) \frac{23}{3} R

687

MediumMHT CET2024

A sheet of steel is 40 cm long and 5 cm broad at 0^{\circ} \mathrm{C}. The surface area of the sheet increases by 1.4 \mathrm{~cm}^2 at 100^{\circ} \mathrm{C}. Coefficient of linear expansion of steel is

Options:

A) 1.9 \times 10^{-5} /{ }^{\circ} \mathrm{C}

B) 2.4 \times 10^{-5} /^{\circ} \mathrm{C}

C) 3.5 \times 10^{-5} /^{\circ} \mathrm{C}

D) 7 \times 10^{-5} / \mathrm{C}

688

MediumMHT CET2024

A quantity of heat ' Q ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is \left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]

Options:

A) 3: 5

B) 5: 3

C) 2: 5

D) 3: 2

689

MediumMHT CET2024

What is the pressure of hydrogen in a cylinder of volume 10 litre if its total energy of translation is 7.5 \times 10^3 \mathrm{~J} ?

Options:

A) 5 \times 10^5 \mathrm{Nm}^{-2}

B) 10^6 \mathrm{Nm}^{-2}

C) 0.5 \times 10^5 \mathrm{Nm}^{-2}

D) 5 \times 10^6 \mathrm{Nm}^{-2}

690

MediumMHT CET2024

' N ' molecules of gas A, each having mass ' m ' and ' 2 N ' molecules of gas B , each of mass ' 2 m ' are contained in the same vessel which is at constant temperature ' T '. The mean square velocity of B is V^2 and mean square of x -component of A is \omega^2. The value of \frac{\omega^2}{\mathrm{~V}^2} is

Options:

A) 3: 2

B) 2: 3

C) 1: 2

D) 2: 1

691

MediumMHT CET2024

The \mathrm{p}-\mathrm{V} diagram for a fixed mass of an ideal gas undergoing cyclic process is as shown in figure. AB represents isothermal process and CA represents adiabatic process. Which one of the following graphs represents the p-T diagram of this cyclic process?

Options:

A) (G)

B) (F)

C) (H)

D) (E)

692

MediumMHT CET2024

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' T ' K . The piston of cylinder A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise temperature of the gas in A is ' \mathrm{dT}_{\mathrm{A}} ', then the rise in temperature of the gas in cylinder B is \left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)

Options:

A) 2 \mathrm{dt}_{\mathrm{A}}

B) \frac{\mathrm{dT}_{\mathrm{A}}}{2}

C) \mathrm{\gamma d T_A}

D) \frac{\mathrm{dT}_A}{\gamma}

693

MediumMHT CET2024

A metal rod having coefficient of linear expansion 2 \times 10^{-5} /^{\circ} \mathrm{C} is 0.75 m long at 45^{\circ} \mathrm{C}. When the temperature rises to 65^{\circ} \mathrm{C}, the increase in length of the rod will be

Options:

A) 3.0 mm

B) 0.75 mm

C) 0.30 mm

D) 0.15 mm

694

MediumMHT CET2024

The ratio of the velocity of sound in hydrogen gas \left(\gamma=\frac{7}{5}\right) to that in helium gas \left(\gamma=\frac{5}{3}\right) at the same temperature is

Options:

A) 1: 1

B) 7: 3

C) 21: 25

D) \sqrt{42}: 5

695

MediumMHT CET2024

Two spheres S_1 and S_2 have same radii but temperatures T_1 and T_2 respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio T_1: T_2 is

Options:

A) 2: 1

B) \sqrt{2}: 1

C) 1: \sqrt{2}

D) 1: 2

696

MediumMHT CET2024

Two gases A and B having same initial state ( \mathrm{P}, \mathrm{V}, \mathrm{n}, \mathrm{T} ). Now gas A is compressed to \frac{\mathrm{V}}{8} by isothermal process and other gas B is compressed to \frac{\mathrm{V}}{8} by adiabatic process. The ratio of final pressure of gas A and B is (Both gases are monoatomic, \gamma=5 / 3)

Options:

A) \frac{1}{8}

B) \frac{1}{4}

C) \frac{1}{64}

D) \frac{1}{12}

697

MediumMHT CET2024

Two vessels separately contain two ideal gases A and B at the same temperature, pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weights of A and B is

Options:

A) 1: 2

B) 2: 3

C) 3: 4

D) 2: 1

698

MediumMHT CET2024

An insulated container contains a diatomic gas of molar mass ' m '. The container is moving with velocity ' V ', if it is stopped suddenly, the change in temperature is ( R= gas constant)

Options:

A) \frac{\mathrm{mV}^2}{3 \mathrm{R}}

B) \frac{\mathrm{mV}^2}{5 \mathrm{R}}

C) \frac{\mathrm{mV}}{7 \mathrm{R}}

D) \frac{5 m V}{3 R}

699

MediumMHT CET2024

Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature 17^{\circ} \mathrm{C}. The maximum temperature that can be reached is 45^{\circ} \mathrm{C}. The gap to be kept between the two segments of railway track is $\left(\alpha_{\text {steel }}=1.3 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)

Options:

A) 1.68 mm

B) 2.06 mm

C) 3.64 mm

D) 4.32 mm

700

MediumMHT CET2024

In an adiabatic process for an ideal gas, the relation between the universal gas constant ' R ' and specific heat at constant volume ' \mathrm{C}_{\mathrm{v}} ' is R=0.4 C_v. The pressure ' P ' of the gas is proportional to the temperature ' T ', of the gas as T^k. The value of constant ' K ' is

Options:

A) \frac{7}{2}

B) \frac{7}{3}

C) 5

D) 5

701

MediumMHT CET2024

The black discs \mathrm{x}, \mathrm{y} and z have radii 1 \mathrm{~m}, 2 \mathrm{~m} and 3 m respectively. The wavelengths corresponding to maximum intensity are 200 \mathrm{~nm}, 300 \mathrm{~nm} and 400 nm respectively. The relation between emissive power E_x, E_y and E_z is

Options:

A) \mathrm{E}_{\mathrm{x}}>\mathrm{E}_{\mathrm{y}}>\mathrm{E}_{\mathrm{z}}

B) \mathrm{E}_{\mathrm{x}}<\mathrm{E}_{\mathrm{y}}<\mathrm{E}_{\mathrm{z}}

C) \mathrm{E}_{\mathrm{x}}=\mathrm{E}_{\mathrm{y}}=\mathrm{E}_{\mathrm{z}}

D) \mathrm{E}_{\mathrm{y}}>\mathrm{E}_{\mathrm{x}}<\mathrm{E}_{\mathrm{z}}

702

MediumMHT CET2024

For a gas, \frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0.4 where R is the universal gas constant and ' \mathrm{C}_{\mathrm{V}} ' is molar specific heat at constant volume. The gas is made up of molecules which are

Options:

A) rigid diatomic.

B) monoatomic.

C) non-rigid diatomic.

D) polyatomic.

703

MediumMHT CET2024

In a thermodynamic system ' \Delta \mathrm{U} ' represents the increase in internal energy and ' W ' the work done by the system. Which of the following statement is true?

Options:

A) \Delta \mathrm{U}=-\mathrm{W} in an adiabatic process.

B) \Delta \mathrm{U}=\mathrm{W} in an isothermal process.

C) \Delta \mathrm{U}=-\mathrm{W} in an isothermal process.

D) \Delta \mathrm{U}=\mathrm{W} in an adiabatic process.

704

MediumMHT CET2024

Rate of radiation by a black body is ' R ' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3T. Its rate of radiation is

Options:

A) (162) R

B) (81) \mathrm{R}

C) (16.2) R

D) (8.1) \mathrm{R}

705

MediumMHT CET2024

A Carnot's cycle operating between T_H=600 \mathrm{~K} and T_c=300 \mathrm{~K} produces 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoir is

Options:

A) 2.5 kJ

B) 3.0 kJ

C) 3.5 kJ

D) 4.0 kJ

706

MediumMHT CET2024

An ordinary body cools from ' 4 \theta^{\prime} ' to ' 3 \theta^{\prime} ' in ' t ' minutes. The temperature of that body after next 't' minutes is (Assume Newton's law of cooling and room temperature is \theta)

Options:

A) \frac{9 \theta}{4}

B) \frac{2 \theta}{5}

C) \frac{5 \theta}{3}

D) \frac{7 \theta}{3}

707

MediumMHT CET2024

A black sphere has radius R whose rate of radiation is E at temperature T . If radius is made half and temperature 4 T , the rate of radiation will be

Options:

A) 64 E

B) 32 E

C) 16 E

D) 8 E

708

MediumMHT CET2024

Ordinary bodies P and Q radiate maximum energy with wavelength difference 3 \mu \mathrm{~m}. The absolute temperature of body P is four times that of Q. The wavelength at which body Q radiates maximum energy is

Options:

A) 2 \mum

B) 4 \mum

C) 6 \mum

D) 8 \mum

709

MediumMHT CET2024

The average force applied on the wall of a closed container depends as \mathrm{T}^{\mathrm{x}} where T is the temperature of an ideal gas. The value of x is

Options:

A) 0.5

B) 1

C) 2

D) 1.5

710

MediumMHT CET2024

Which of the following graphs between pressure and volume correctly show isochoric process?

Options:

A) D

B) A

C) C

D) B

711

MediumMHT CET2024

Initial pressure and volume of a gas are ' P ' and ' V ' respectively. First its volume is expanded to ' 4 V ' by isothermal process and then again its volume is reduced to ' V ' by adiabatic process then its final pressure if \left(\gamma=\frac{3}{2}\right)

Options:

A) P

B) 2P

C) 3P

D) 4P

712

MediumMHT CET2024

The P-V diagrams for particular gas of different thermodynamic processes are given by

Options:

A) Figure (a) and (b) show isobaric curve and isothermal curve respectively.

B) Figure (a) and (c) show isothermal curve and isochoric curve respectively.

C) Figure (b) and (c) show isobaric curve and isochoric curve respectively.

D) Figure (a) and (c) show isothermal curve and isobaric curve respectively.

713

MediumMHT CET2024

An ideal gas (\gamma=1.5) is expanded adiabatically. To reduce root mean square velocity of molecules two times, the gas should be expanded

Options:

A) 20 times

B) 16 times

C) 12 times

D) 8 times

714

MediumMHT CET2024

A black body radiates power ' P ' and maximum energy is radiated by it at a wavelength \lambda_0. The temperature of the black body is now so changed that it radiates maximum energy at the wavelength \frac{\lambda_0}{4}. The power radiated by it at new temperature is

Options:

A) 64 P

B) 256 P

C) 4 P

D) 16 P

715

MediumMHT CET2024

The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid falls from 342 K to 338 K is [Let the room temperature be 296 K ]

Options:

A) 6 min

B) 4 min

C) 3 min

D) 2 min

716

MediumMHT CET2024

In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged (\mathrm{Q}) is \left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)

Options:

A) \gamma

B) \gamma-1

C) \frac{\gamma}{\gamma-1}

D) \frac{\gamma-1}{\gamma}

717

MediumMHT CET2024

Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling

Options:

A) black, red, white

B) white, red, black,

C) red, black, white

D) red, white, black

718

MediumMHT CET2024

At certain temperature, \operatorname{rod} \mathrm{A} and \operatorname{rod} \mathrm{B} of different materials have lengths \mathrm{L}_{\mathrm{A}} and \mathrm{L}_{\mathrm{B}} respectively. Their coefficients of linear expansion are \alpha_A and \alpha_B respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio \mathrm{L}_{\mathrm{A}}: \mathrm{L}_{\mathrm{B}} is given by

Options:

A) \frac{\alpha_A}{\alpha_B}

B) \frac{\alpha_B}{\alpha_A}

C) \frac{\alpha_A+\alpha_B}{\alpha_A}

D) \frac{\alpha_A+\alpha_B}{\alpha_B}

719

MediumMHT CET2024

The internal energy of a gas will increase when it

Options:

A) expands adiabatically.

B) is compressed adiabatically.

C) expands isothermally.

D) is compressed isothermally.

720

MediumMHT CET2024

A gas is contained in closed vessel. The initial temperature of the gas is 100^{\circ} \mathrm{C}. If the pressure of the gas is increased by 4 \%, the increase in the temperature of the gas is

Options:

A) 2^{\circ} \mathrm{C}

B) 3^{\circ} \mathrm{C}

C) 4^{\circ} \mathrm{C}

D) 5^{\circ} \mathrm{C}

721

MediumMHT CET2024

For an ideal gas, in an isobaric process, the ratio of heat supplied ' Q ' to the work done ' w ' by the system is ( \gamma= ratio of specific heat at constant pressure to that at constant volume)

Options:

A) \frac{1}{\gamma}

B) \frac{1}{\gamma-1}

C) \frac{\gamma}{\gamma-1}

D) \frac{\gamma-1}{\gamma}

722

MediumMHT CET2024

The temperature of a gas is -80^{\circ} \mathrm{C}. To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?

Options:

A) 499^{\circ} \mathrm{C}

B) 772^{\circ} \mathrm{C}

C) 1464^{\circ} \mathrm{C}

D) 1737^{\circ} \mathrm{C}

723

MediumMHT CET2024

Two bodies ' X ' and ' Y ' at temperatures ' \mathrm{T}_1 ' K and ' T_2 ' K respectively have the same dimensions. If their emissive powers are same, the relation between their temperatures is

Options:

A) \frac{T_1}{T_2}=\frac{1}{3}

B) \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{81}{1}

C) \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{3^{\frac{1}{4}}}{1}

D) \frac{T_1}{T_2}=\frac{9^{\frac{1}{4}}}{1}

724

MediumMHT CET2024

A lead bullet moving with velocity ' v ' strikes a wall and stops. If 50 \% of its energy is converted into heat, then the increase in temperature is ( s= specific heat of lead)

Options:

A) \frac{\mathrm{v}^2 \mathrm{~s}}{2 \mathrm{~J}}

B) \frac{v^2}{4 \mathrm{Js}}

C) \frac{\mathrm{v}^2 \mathrm{~s}}{\mathrm{~J}}

D) \frac{2 v^2}{\mathrm{Js}}

725

MediumMHT CET2024

If C_p and C_v are molar specific heats of an ideal gas at constant pressure and volume respectively and ' \gamma ' is \mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}} then \mathrm{C}_{\mathrm{p}}= ( \mathrm{R}= universal gas constant)

Options:

A) \frac{\gamma \mathrm{R}}{\gamma-1}

B) \gamma \mathrm{R}

C) \frac{1+\gamma}{1-\gamma}

D) \frac{\mathrm{R}}{\gamma-1}

726

MediumMHT CET2024

The change in the internal energy of the mass of gas, when the volume changes from ' V ' to ' 2 V ' at constant pressure ' P ' is ( \gamma is the ratio of specific heat of gas at constant pressure to specific heat at constant volume)

Options:

A) \frac{\mathrm{PV}}{\gamma-1}

B) \frac{\mathrm{PV}}{\gamma+1}

C) \frac{\gamma-1}{\mathrm{PV}}

D) \frac{\gamma+1}{\mathrm{PV}}

727

MediumMHT CET2024

A pergect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will

Options:

A) increase by 10 times

B) decrease by 10 times

C) increase by 5 times

D) remain unchanged

728

MediumMHT CET2024

A real gas behaves as an ideal gas at

Options:

A) low pressure and low temperature.

B) low pressure and high temperature.

C) high pressure and low temperature.

D) high pressure and high temperature.

729

MediumMHT CET2024

According to the law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is

Options:

A) \frac{9}{2} \mathrm{R}

B) \frac{5}{2} R

C) \frac{3}{2} R

D) \frac{7}{2} R

730

MediumMHT CET2024

A carnot engine, whose efficiency is 40 \% takes heat from a source maintained at temperature 600 K . It is desired to have an efficiency 60 \%, then the intake temperature for the same exhaust (sink) temperature should be

Options:

A) 1800 K

B) 1200 K

C) 900 K

D) 600 K

731

MediumMHT CET2024

Two rods of same length \& material transfer a given amount of heat in 12 s when they are joined end to end. But when they are joined length wise parallel to each other they will transfer same amount of heat in same condition in time

Options:

A) 24 s

B) 3 s

C) 1.5 s

D) 48 s

732

MediumMHT CET2024

An insulated container contains a monoatomic gas of molar mass ' m '. The container is moving with velocity ' V '. If it is stopped suddenly, the change in temperature is ( R= gas constant)

Options:

A) \frac{\mathrm{mV}^2}{5 \mathrm{R}}

B) \frac{\mathrm{mV}^2}{3 \mathrm{R}}

C) \frac{\mathrm{mV}^2}{7 \mathrm{R}}

D) \frac{m V^2}{9 R}

733

MediumMHT CET2024

In an isobaric process of an ideal gas, the ratio of work done by the system to the heat supplied \left(\frac{W}{Q}\right) is

Options:

A) \frac{1}{\gamma-1}

B) \gamma

C) \frac{\gamma}{\gamma-1}

D) \frac{\gamma-1}{\gamma}

734

MediumMHT CET2024

A sphere is at temperature 600 K . In an external environment of 200 K , its cooling rate is ' R ' When the temperature of the sphere falls to 400 K , then cooling rate ' R ' will become

Options:

A) \frac{3}{16} \mathrm{R}

B) \frac{9}{16} R

C) \frac{16}{9} R

D) \frac{16}{3} R

735

MediumMHT CET2024

A gas expands in such a way that its pressure and volume satisfy the condition \mathrm{PV}^2= constant. Then the temperature of the gas

Options:

A) will decrease.

B) will increase.

C) will not change.

D) may increase or decrease depending upon the values of pressure and volume.

736

MediumMHT CET2024

The r.m.s. velocity of gas molecules kept at temperature 27^{\circ} \mathrm{C} in a vessel is 61 \mathrm{~m} / \mathrm{s}. Molecular weight of gas is nearly $\left[\mathrm{R}=8.31 \frac{\mathrm{~J}}{\mathrm{~mol} \mathrm{~K}}\right]

Options:

A) 2

B) 4

C) 28

D) 32

737

MediumMHT CET2024

A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as \mathrm{P} \propto \mathrm{T}^{\mathrm{x}} where the value of x is

Options:

A) 3.5

B) 2.5

C) 4.5

D) 3

738

MediumMHT CET2024

A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is

Options:

A) 30%

B) 40%

C) 50%

D) 60%

739

MediumMHT CET2024

Two rods, one of copper ( Cu) and the other of iron ( Fe ) having initial lengths \mathrm{L}_1 and \mathrm{L}_2 respectively are connected together to form a single rod of length L_1+L_2. The coefficient of linear expansion of Cu and Fe are \alpha_c and \alpha_i respectively. If the length of each rod increases by the same amount when their temperatures are raised by t^{\circ} \mathrm{C}, then ratio of \frac{L_1-L_2}{L_1+L_2} will be

Options:

A) \frac{\alpha_i}{\alpha_c+\alpha_i}

B) \frac{\alpha_c}{\alpha_c+\alpha_i}

C) \frac{\alpha_i-\alpha_c}{\alpha_c+\alpha_i}

D) \frac{\alpha_c-\alpha_i}{\alpha_c+\alpha_i}

740

MediumMHT CET2024

The specific heat of argon at constant pressure and constant volume are C_p and C_v respectively. It's density ' \rho ' at N.T.P. will be [\mathrm{P} and T are pressure and temperature respectively at N.T.P.]

Options:

A) \frac{P}{T\left(C_p-C_v\right)}

B) \frac{\mathrm{PT}}{\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}

C) \frac{T\left(C_p-C_v\right)}{P}

D) \frac{\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}{\mathrm{PT}}

741

MediumMHT CET2024

The r.m.s. velocity of hydrogen at S.T.P. is ' u ' \mathrm{m} / \mathrm{s}. If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively

Options:

A) 819 \mathrm{~K},(\sqrt{3}) \mathrm{um} / \mathrm{s}

B) 1092 \mathrm{~K}, 3 \mathrm{um} / \mathrm{s}

C) 819 \mathrm{~K}, \frac{\mathrm{u}}{\sqrt{3}} \mathrm{~m} / \mathrm{s}

D) 1092 \mathrm{~K}, \frac{\mathrm{u}}{3} \mathrm{~m} / \mathrm{s}

742

MediumMHT CET2024

There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compressed from volume v to \frac{\mathrm{v}}{2}. Sample A is compressed isothermally while sample B is compressed adiabatically. The final pressure of A is

Options:

A) twice that of B.

B) equal to that of B.

C) more than that of B.

D) less than that of B .

743

MediumMHT CET2024

Two rods, one of aluminium and the other of steel, having initial lengths ' \mathrm{L}_1 ' and ' \mathrm{L}_2 ' are connected together to form a single rod of length \left(L_1+L_2\right). The coefficients of linear expansion of aluminium and steel are ' \alpha_1 ' and ' \alpha_2 ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by \mathrm{t}^{\mathrm{L}} \mathrm{C}, then the ratio \frac{L_1}{L_1+L_2} will be

Options:

A) \frac{\alpha_2}{\alpha_1}

B) \frac{\alpha_1}{\alpha_2}

C) \frac{\alpha_2}{\alpha_1+\alpha_2}

D) \frac{\alpha_1}{\alpha_1-\alpha_2}

744

MediumMHT CET2024

Given that ' x ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' y ' joule. The absorption coefficient of body is

Options:

A) \frac{x}{y}

B) \frac{y}{x}

C) \frac{x-y}{x}

D) \frac{y-x}{x}

745

MediumMHT CET2024

A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V , the efficiency of the engine is

Options:

A) 0.25

B) 0.50

C) 0.75

D) 0.90

746

MediumMHT CET2024

Two spherical black bodies of radii ' R_1 ' and ' \mathrm{R}_2 ' and with surface temperature ' \mathrm{T}_1 ' and ' \mathrm{T}_2 ' respectively radiate the same power. The ratio of ' R_1 ' to ' R_2 ' will be

Options:

A) \left(\frac{T_2}{T_1}\right)^4

B) \left(\frac{T_2}{T_1}\right)^2

C) \left(\frac{T_1}{T_2}\right)^4

D) \left(\frac{T_1}{T_2}\right)^2

747

MediumMHT CET2024

Rate of flow of heat through a cylindrical rod is ' \mathrm{H}_1 '. The temperature at the ends of the rod are ' T_1 ' and ' T_2 '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' \mathrm{H}_2 '. Then

Options:

A) \mathrm{H}_2=4 \mathrm{H}_1

B) \mathrm{H}_2=2 \mathrm{H}_1

C) \mathrm{H}_2=\frac{\mathrm{H}_1}{2}

D) \mathrm{H}_2=\frac{\mathrm{H}_1}{4}

748

MediumMHT CET2024

A fixed mass of gas at constant pressure occupies a volume ' V '. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

Options:

A) \frac{V}{2}

B) \frac{\mathrm{V}}{\sqrt{2}}

C) 2 \mathrm{~V}

D) 4 V

749

MediumMHT CET2024

In an isobaric process

Options:

A) pressure is constant.

B) volume is constant.

C) temperature is constant.

D) internal energy is constant.

750

MediumMHT CET2024

The average translational kinetic energy of nitrogen (molar mass 28) molecules at a particular temperature is 0.042 eV . The translational kinetic energy of oxygen molecules (molar mass 32) in eV at double the temperature is

Options:

A) 0.021

B) 0.048

C) 0.056

D) 0.084

751

MediumMHT CET2024

The first operation involved in a carnot cycle is

Options:

A) isothermal expansion.

B) adiabatic expansion.

C) isothermal compression.

D) adiabatic compression.

752

MediumMHT CET2024

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at 47^{\circ} \mathrm{C} is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)

Options:

A) 47^{\circ} \mathrm{C}

B) 132^{\circ} \mathrm{C}

C) 320^{\circ} \mathrm{C}

D) 405^{\circ} \mathrm{C}

753

MediumMHT CET2024

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of \mathrm{O}_2 \& \mathrm{H}_2 is 32 and 2 respectively)

Options:

A) 1: 4

B) 1: 8

C) 16: 1

D) 12: 1

754

MediumMHT CET2024

The P-V graph of an ideal gas, cycle is shown. The adiabatic process is described by the region

Options:

A) AB and BC

B) AB and CD

C) AD and BC

D) BC and CD

755

MediumMHT CET2024

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature 17^{\circ} \mathrm{C}. The maximum temperature that can be reached is 45^{\circ} \mathrm{C}. Increase in length of the segment of railway track is ' x ' \times 10^{-5} \mathrm{~m}. The value of ' x ' is \left(\alpha_{\text {steel }}=\right. \left.1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)

Options:

A) 168

B) 204

C) 336

D) 530

756

MediumMHT CET2024

At S.T.P., the mean free path of gas molecule is 1500 d , where ' d ' is diameter of molecule. What will be the mean free path at 373 K at constant volume?

Options:

A) 1500 d

B) \frac{373}{273} \times 1500 \mathrm{~d}

C) \frac{273}{373} \times 1500 \mathrm{~d}

D) \sqrt{\frac{373}{273}} \times 1500 \mathrm{~d}

757

MediumMHT CET2024

One mole of an ideal gas at an initial temperature of ' T ' K does ' 6 R ' of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5 / 3, the final temperature of gas will be \left(\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mole}^{-1} \mathrm{~K}^{-1}\right)

Options:

A) (\mathrm{T}+4 \cdot 2) \mathrm{K}

B) (\mathrm{T}-4 \cdot 2) \mathrm{K}

C) \mathrm{(T+4) K}

D) (\mathrm{T}-4) \mathrm{K}

758

MediumMHT CET2024

The frequency ' v_{\mathrm{m}} ' corresponding to which the energy emitted by a black body is maximum may vary with the temperature ' T ' of the body as shown by the curves ' A ', ' B ', ' C ' and ' D ' in the figure. Which one of these represents the correct variation?

Options:

A) straight line D

B) curve C

C) straight line B

D) curve A

759

MediumMHT CET2023

A metal rod cools at the rate of $4{ }^{\circ} \mathrm{C} / \mathrm{min} whon its temperature is 90^{\circ} \mathrm{C} and the rate of 1{ }^{\circ} \mathrm{C} / \mathrm{m}{\text {in }} when its temperature is 30^{\circ} \mathrm{C}$. The temperature of the surrounding is

Options:

A) 20^{\circ} \mathrm{C}

B) 15{ }^{\circ} \mathrm{C}

C) 10^{\circ} \mathrm{C}

D) 5^{\circ} \mathrm{C}

760

MediumMHT CET2023

The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is

Options:

A) 2

B) 4

C) 16

D) 32

761

MediumMHT CET2023

At constant temperature, increasing the pressure of a gas by $5 \%$ its volume will decrease by

Options:

A) 5 \%

B) 5.26 \%

C) 4.20 \%

D) 4.70 \%

762

MediumMHT CET2023

The temperature of a gas is measure of

Options:

A) the average kinetic energy of gas molecules.

B) the average potential energy of gas molecules.

C) the average distance between the molecules of a gas

D) the size of the molecules of a gas

763

MediumMHT CET2023

An ideal refrigerator has freezer at a temperature of $-13^{\circ} \mathrm{C}$. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is

Options:

A) 320^{\circ} \mathrm{C}

B) 39^{\circ} \mathrm{C}

C) 325 \mathrm{~K}

D) 325^{\circ} \mathrm{C}

764

MediumMHT CET2023

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right) changes adiabatically from (\mathrm{P}, \rho) to \left(\mathrm{P}^{\prime}, \rho^{\prime}\right). If \frac{\rho^{\prime}}{\rho}=32 then \frac{\mathrm{P}^{\prime}}{\mathrm{P}}$ should be

Options:

A) \frac{1}{128}

B) 128

C) 32

D) 64

765

MediumMHT CET2023

A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and in same atmosphere. The ratio of their rate of loss of heat will be

Options:

A) 1: 1

B) \left(\frac{\pi}{6}\right)^{\frac{2}{3}}

C) \left(\frac{\pi}{6}\right)^{\frac{1}{3}}

D) \frac{4 \pi}{3}: 1

766

MediumMHT CET2023

A body is said to be opaque to the radiation if (a, r and t are coefficient of absorption, reflection and transmission respectively)

Options:

A) \mathrm{t}=0 and \mathrm{a}+\mathrm{r}=1

B) \mathrm{a}=\mathrm{r}=\mathrm{t}

C) t \neq 0

D) \mathrm{a}=0, \mathrm{r}=1, \mathrm{t}=1

767

MediumMHT CET2023

In a thermodynamic system, $\Delta U$ represents the increases in its internal energy and dW is the work done by the system then correct statement out of the following is

Options:

A) \Delta \mathrm{U}=\mathrm{dW}$ is an isothermal process

B) \Delta \mathrm{U}=-\mathrm{dW}$ is an adiabatic process

C) \Delta \mathrm{U}=-\mathrm{dW}$ is an isothermal process

D) \Delta \mathrm{U}=\mathrm{dW}$ is an adiabatic process

768

MediumMHT CET2023

The temperature of a gas is $-68^{\circ} \mathrm{C}$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

Options:

A) 357^{\circ} \mathrm{C}

B) 457^{\circ} \mathrm{C}

C) 547^{\circ} \mathrm{C}

D) 820^{\circ} \mathrm{C}

769

MediumMHT CET2023

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $200^{\circ} \mathrm{C}$. When these are left in a room.

Options:

A) the sphere reaches room temperature fast

B) the cube reaches room temperature fast

C) the circular plate reaches room temperature fast

D) all will reach the room temperature simultaneously

770

MediumMHT CET2023

The efficiency of a heat engine is '$\eta' and the coefficient of performance of a refrigerator is '\beta$'. Then

Options:

A) \eta=\frac{1}{\beta}

B) \eta=\frac{1}{\beta+1}

C) \eta \beta=\frac{1}{2}

D) \eta=\frac{1}{\beta-1}

771

MediumMHT CET2023

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is

Options:

A) 1: 4

B) 4: 1

C) 1: 16

D) 16: 1

772

MediumMHT CET2023

The internal energy of a monoatomic ideal gas molecule is

Options:

A) partly kinetic and partly potential

B) totally kinetic

C) totally potential

D) Neither kinetic nor potential

773

MediumMHT CET2023

A gas at pressure $p_0$ is contained in a vessel. If the masses of all the molecules are halved and their velocities are doubled, then the resulting pressure would be equal to

Options:

A) 4 p_0

B) 2 p_0

C) p_0

D) p_0 / 2

774

MediumMHT CET2023

For an adiabatic process, which one of the following is wrong statement?

Options:

A) Equation of state is $p V=$ constant

B) There is exchange of heat with surrounding

C) All the work is utilised to change the internal energy of the system

D) Temperature of the system changes i.e. $\Delta T \neq 0

775

MediumMHT CET2023

Which one of the following is based on convection?

Options:

A) Heating of a copper utensil

B) Heating a room by heater

C) Heating of iron rod

D) Heat transferred from sun to earth

776

MediumMHT CET2023

A carnot engine operates with source at $227^{\circ} \mathrm{C} and sink at 27^{\circ} \mathrm{C}. If the source supplies 50 \mathrm{~kJ}$ of heat energy, the work done by the engine is

Options:

A) 2 kJ

B) 5 kJ

C) 10 kJ

D) 20 kJ

777

MediumMHT CET2023

Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $(\mathrm{T})$ under constant pressure conditions?

Options:

A) P

B) Q

C) R

D) S

778

MediumMHT CET2023

\mathrm{dQ} is the heat energy supplied to an ideal gas under isochoric conditions. If \mathrm{dU} and \mathrm{dW}$ denote the change in internal energy and the work done respectively then

Options:

A) \mathrm{dQ}=\mathrm{dW}

B) \mathrm{dQ}>\mathrm{dU}

C) \mathrm{dQ}<\mathrm{dU}

D) \mathrm{dQ}=\mathrm{dU}

779

MediumMHT CET2023

A black body at temperature $127^{\circ} \mathrm{C} radiates heat at the rate of 5 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}. At a temperature 927^{\circ} \mathrm{C}, its rate of emission in units of \mathrm{cal} / \mathrm{cm}^2 \mathrm{~s}$ will be

Options:

A) 405

B) 35

C) 45

D) 350

780

MediumMHT CET2023

A Carnot engine has the same efficiency between (i) $100 \mathrm{~K} and 600 \mathrm{~K} and (ii) \mathrm{T} \mathrm{K} and 960 \mathrm{~K}. The temperature \mathrm{T}$ in kelvin of the sink is

Options:

A) 120

B) 160

C) 240

D) 320

781

MediumMHT CET2023

For an ideal gas the density of the gas is $\rho_0 when temperature and pressure of the gas are T_0 and P_0 respectively. When the temperature of the gas is 2 \mathrm{~T}_0, its pressure will be 3 \mathrm{P}_0$. The new density will be

Options:

A) \frac{3}{2} \rho_0

B) \frac{4}{3} \rho_0

C) \frac{3}{4} \rho_0

D) \frac{2}{3} \rho_0

782

MediumMHT CET2023

The temperature gradient in a rod of length $75 \mathrm{~cm} is 40^{\circ} \mathrm{C} / \mathrm{m}. If the temperature of cooler end of the rod is 10^{\circ} \mathrm{C}$, then the temperature of hotter end is

Options:

A) 50^{\circ} \mathrm{C}

B) 40^{\circ} \mathrm{C}

C) 35^{\circ} \mathrm{C}

D) 25^{\circ} \mathrm{C}

783

MediumMHT CET2023

A black body radiates maximum energy at wavelength '$\lambda' and its emissive power is 'E'. Now due to a change in temperature of that body, it radiates maximum energy at wavelength \frac{\lambda}{3}$. At that temperature emissive power is

Options:

A) 16: 1

B) 256: 1

C) 81: 1

D) 128: 1

784

MediumMHT CET2023

For polyatomic gases, the ratio of molar specific heat at constant pressure to constant volume is ( $\mathrm{f}=$ degrees of freedom)

Options:

A) \frac{2+\mathrm{f}}{3+\mathrm{f}}

B) \frac{3+\mathrm{f}}{2+\mathrm{f}}

C) \frac{3+\mathrm{f}}{4+\mathrm{f}}

D) \frac{4+\mathrm{f}}{3+\mathrm{f}}

785

MediumMHT CET2023

Select the WRONG statement from the following. For an isothermal process

Options:

A) Energy exchanged is used to do work

B) Perfect thermal equilibrium with environment

C) Equation of state PV is not constant.

D) No change internal energy.

786

MediumMHT CET2023

Compare the rate of loss of heat from a metal sphere at $627^{\circ} \mathrm{C} with the rate of loss of heat from the same sphere at 327^{\circ} \mathrm{C}, if the temperature of the surrounding is 27^{\circ} \mathrm{C}$. (nearly)

Options:

A) 6.2

B) 5.3

C) 4.8

D) 7.4

787

MediumMHT CET2023

The volume of a metal block increases by $0.225 \% when its temperature is increased by 30^{\circ} \mathrm{C}$. Hence coefficient of linear expansion of the material of metal block is

Options:

A) 7.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.

B) 6.75 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.

C) 2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.

D) 1.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.

788

MediumMHT CET2023

A monoatomic ideal gas initially at temperature '$\mathrm{T}_1' is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly the gas is allowed to expand to adiabatically to a temperature '\mathrm{T}_2'. If '\mathrm{L}_1' and '\mathrm{L}_2' are the lengths of the gas columns before and after expansion respectively, then \frac{\mathrm{T}_2}{\mathrm{~T}_1}$ is

Options:

A) \frac{\mathrm{L}_1}{\mathrm{~L}_2}

B) \frac{\mathrm{L}_2}{\mathrm{~L}_1}

C) \left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{2 / 3}

D) \left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{2 / 3}

789

MediumMHT CET2023

Let $\gamma_1 be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \gamma_2 be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio \frac{\gamma_2}{\gamma_1}$ is

Options:

A) \frac{37}{21}

B) \frac{27}{35}

C) \frac{21}{25}

D) \frac{35}{27}

790

MediumMHT CET2023

The molar specific heat of an ideal gas at constant pressure and constant volume is $\mathrm{C}_{\mathrm{p}} and \mathrm{C}_{\mathrm{v}} respectively. If \mathrm{R} is universal gas constant and \gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}} then \mathrm{C}_{\mathrm{v}}=

Options:

A) \frac{1-\gamma}{1+\gamma}

B) \frac{1+\gamma}{1-\gamma}

C) \frac{\gamma-1}{\mathrm{R}}

D) \frac{\mathrm{R}}{\gamma-1}

791

MediumMHT CET2023

A composite slab consists of two materials having coefficient of thermal conductivity $\mathrm{K} and 2 \mathrm{~K}, thickness \mathrm{x} and 4 \mathrm{x} respectively. The temperature of the two outer surfaces of a composite slab are \mathrm{T}_2 and \mathrm{T}_1\left(\mathrm{~T}_2 > \mathrm{T}_1\right). The rate of heat transfer through the slab in a steady state is \left[\frac{\mathrm{A}\left(\mathrm{T}_2-\mathrm{T}_1\right) \mathrm{K}}{\mathrm{x}}\right] \cdot \mathrm{f} where '\mathrm{f}$' is equal to

Options:

A) 1

B) \frac{2}{3}

C) \frac{1}{2}

D) \frac{1}{3}

792

MediumMHT CET2023

A black sphere has radius '$R' whose rate of radiation is 'E' at temperature 'T'. If radius is made R / 3 and temperature '3 T$', the rate of radiation will be

Options:

A) E

B) 3E

C) 6E

D) 9E

793

MediumMHT CET2023

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma=1.5$, then the increase in its temperature is

Options:

A) 273 K

B) 373 K

C) 473 K

D) 573 K

794

MediumMHT CET2023

About black body radiation, which of the following is the wrong statement?

Options:

A) For all wavelengths, intensity is same.

B) For shorter wavelengths, intensity is more.

C) For longer wavelengths, intensity is less.

D) All wavelengths are emitted by a black body.

795

MediumMHT CET2023

For a gas, $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0 \cdot 4, where \mathrm{R} is universal gas constant and \mathrm{C}_{\mathrm{v}}$ is molar specific heat at constant volume. The gas is made up of molecules which are

Options:

A) rigid diatomic

B) monoatomic

C) non-rigid diatomic

D) polyatomic

796

MediumMHT CET2023

Two bodies $\mathrm{A} and \mathrm{B} at temperatures '\mathrm{T}_1' \mathrm{K} and '\mathrm{T}_2' \mathrm{K} respectively have the same dimensions. Their emissivities are in the ratio 1: 3. If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures \left(\mathrm{T}_1: \mathrm{T}_2\right)$ is

Options:

A) 1: 3

B) 3^{1 / 4}: 1

C) 9^{1 / 4}: 1

D) 81: 1

797

MediumMHT CET2023

If temperature of gas molecules is raised from $127^{\circ} \mathrm{C} to 527^{\circ} \mathrm{C}$, the ratio of r.m.s. speed of the molecules is respectively

Options:

A) 1: 2

B) 2: 1

C) 1: \sqrt{2}

D) 2: \sqrt{2}

798

MediumMHT CET2023

According to Boyle's law, the product PV remains constant. The unit of $\mathrm{PV}$ is same as that of

Options:

A) energy

B) force

C) impulse

D) momentum

799

MediumMHT CET2023

The difference in length between two rods $\mathrm{A} and \mathrm{B} is 60 \mathrm{~cm} at all temperatures. If \alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C} and \beta_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, the lengths of the two rods are

Options:

A) l_{\mathrm{A}}=200 \mathrm{~cm}, l_{\mathrm{B}}=140 \mathrm{~cm}

B) l_{\mathrm{A}}=180 \mathrm{~cm}, l_{\mathrm{B}}=120 \mathrm{~cm}

C) l_{\mathrm{A}}=160 \mathrm{~cm}, l_{\mathrm{B}}=100 \mathrm{~cm}

D) l_{\mathrm{A}}=120 \mathrm{~cm}, l_{\mathrm{B}}=60 \mathrm{~cm}

800

MediumMHT CET2023

An ideal gas expands adiabatically. $(\gamma=1 \cdot 5)$ To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded

Options:

A) 81 times

B) 27 times

C) 9 times

D) 3 times

801

MediumMHT CET2023

Two spherical black bodies of radii '$r_1' and 'r_2' at temperature '\mathrm{T}_1' and '\mathrm{T}_2' respectively radiate power in the ratio 1: 2 Then r_1: r_2$ is

Options:

A) \frac{1}{2}\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4

B) \frac{1}{\sqrt{2}}\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^2

C) 2\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^4

D) 2\left(\frac{T_1}{T_2}\right)^2

802

MediumMHT CET2023

The rate of flow of heat through a metal rod with temperature difference $40^{\circ} \mathrm{C} is 1600 \mathrm{~cal} / \mathrm{s}. The thermal resistance of metal rod in { }^{\circ} \mathrm{C} \mathrm{s} / \mathrm{cal}$ is

Options:

A) 0.025

B) 0.25

C) 2.5

D) 40

803

MediumMHT CET2023

If the temperature of a hot body is increased by $50 \%$, then the increase in the quantity of emitted heat radiation will be approximately

Options:

A) 125 \%

B) 200 \%

C) 300 \%

D) 400 \%

804

MediumMHT CET2023

A monoatomic gas at pressure '$\mathrm{P}', having volume '\mathrm{V}' expands isothermally to a volume '2 \mathrm{~V}' and then adiabatically to a volume '16 \mathrm{~V}'. The final pressure of the gas is (Take \gamma=5 / 3$ )

Options:

A) \mathrm{P} / 64

B) \mathrm{P} / 32

C) 16 \mathrm{P}

D) 32 \mathrm{P}

805

MediumMHT CET2023

A diatomic gas $\left(\gamma=\frac{7}{5}\right) is compressed adiabatically to volume \frac{V_i}{32} where V_i is its initial volume. The initial temperature of the gas is T_i in Kelvin and the final temperature is 'x T_i'. The value of 'x$' is

Options:

A) 5

B) 4

C) 3

D) 2

806

MediumMHT CET2023

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

Options:

A) decreases.

B) increases.

C) remains the same.

D) first decreases and then increases.

807

MediumMHT CET2023

A black body radiates maximum energy at wavelength '$\lambda' and its emissive power is 'E' Now due to change in temperature of that body, it radiates maximum energy at wavelength \frac{2 \lambda}{3}$. At that temperature emissive power is

Options:

A) \frac{81}{16}

B) \frac{27}{32}

C) \frac{18}{10}

D) \frac{9}{4}

808

MediumMHT CET2023

Which of the following graphs between pressure (P) and volume (V) correctly shows isochoric changes?

Options:

A) D

B) B

C) C

D) A

809

MediumMHT CET2023

A metal rod $2 \mathrm{~m} long increases in length by 1.6 \mathrm{~mm}, when heated from 0^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C}$. The coefficient of linear expansion of metal rod is

Options:

A) 1.33 \times 10^{-5} /{ }^{\circ} \mathrm{C}

B) 1.66 \times 10^{-5} /{ }^{\circ} \mathrm{C}

C) 1.33 \times 10^{-3} /{ }^{\circ} \mathrm{C}

D) 1.66 \times 10^{-3} /{ }^{\circ} \mathrm{C}

810

MediumMHT CET2023

We have a jar filled with gas characterized by parameters $\mathrm{P}, \mathrm{V}, \mathrm{T} and another jar B filled with gas having parameters 2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

Options:

A) 1: 1

B) 1: 2

C) 2: 1

D) 4: 1

811

MediumMHT CET2023

An insulated container contains a monoatomic gas of molar mass '$\mathrm{m}'. The container is moving with velocity '\mathrm{V}$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]

Options:

A) \frac{\mathrm{MV}^2}{\mathrm{R}}

B) \frac{M V^2}{2 R}

C) \frac{\mathrm{MV}^2}{3 \mathrm{R}}

D) \frac{3 \mathrm{MV}^2}{2 \mathrm{R}}

812

MediumMHT CET2023

In a vessel, the ideal gas is at a pressure $\mathrm{P}$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

Options:

A) 4 \mathrm{P}

B) 2 \mathrm{P}

C) \mathrm{P}

D) \frac{\mathrm{P}}{2}

813

MediumMHT CET2023

The average force applied on the walls of a closed container depends on $T^x where T is the temperature of an ideal gas. The value of 'x$' is

Options:

A) 4

B) 3

C) 2

D) 1

814

MediumMHT CET2023

A black body radiates maximum energy at wavelength '$\lambda' and its emissive power is \mathrm{E}. Now due to change in temperature of that body, it radiates maximum energy at wavelength \frac{2 \lambda}{3}$. At that temperature emissive power is

Options:

A) \frac{51 \mathrm{E}}{8}

B) \frac{81 \mathrm{E}}{16}

C) \frac{61 E}{27}

D) \frac{71 \mathrm{E}}{19}

815

MediumMHT CET2023

A Carnot engine with efficiency $50 \% takes heat from a source at 600 \mathrm{~K}. To increase the efficiency to 70 \%$, keeping the temperature of the sink same, the new temperature of the source will be

Options:

A) 360 \mathrm{~K}

B) 1000 \mathrm{~K}

C) 900 \mathrm{~K}

D) 300 \mathrm{~K}

816

MediumMHT CET2023

A piece of metal at $850 \mathrm{~K} is dropped in to 1 \mathrm{~kg} water at 300 \mathrm{~K}. If the equilibrium temperature of water is 350 \mathrm{~K} then the heat capacity of the metal, expressed in \mathrm{JK}^{-1} is (1 \mathrm{~cal}=4.2 \mathrm{~J})

Options:

A) 420

B) 240

C) 100

D) No Solution

817

MediumMHT CET2023

Heat energy is incident on the surface at the rate of X J/min . If '$a' and 'r' represent coefficient of absorption and reflection respectively then the heat energy transmitted by the surface in 't$' minutes is

Options:

A) (a+r) x t

B) \frac{(\mathrm{a}+\mathrm{r})}{\mathrm{xt}}

C) -(a+r) x t

D) \frac{\mathrm{xt}}{(\mathrm{a}+\mathrm{r})}

818

MediumMHT CET2023

A sample of gas at temperature $T is adiabatically expanded to double its volume. The work done by the gas in the process is \left(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma=\frac{3}{2}\right) \quad(\mathrm{R}= gas constant )

Options:

A) \operatorname{TR}(\sqrt{2}-2)

B) \frac{\mathrm{T}}{\mathrm{R}}(\sqrt{2}-2)

C) \frac{\mathrm{R}}{\mathrm{T}}(2-\sqrt{2})

D) \mathrm{RT}(2-\sqrt{2})

819

MediumMHT CET2023

An ideal gas in a container of volume 500 c.c. is at a pressure of $2 \times 10^{+5} \mathrm{~N} / \mathrm{m}^2. The average kinetic energy of each molecule is 6 \times 10^{-21} \mathrm{~J}$. The number of gas molecules in the container is

Options:

A) 5 \times 10^{25}

B) 5 \times 10^{23}

C) 25 \times 10^{23}

D) 2.5 \times 10^{22}

820

MediumMHT CET2023

A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $\gamma=1.5$, then the final pressure is

Options:

A) 4 times

B) 1.5 times

C) 8 times

D) \frac{1}{4}$ times

821

MediumMHT CET2023

A gas is compressed at a constant pressure of $50 \mathrm{~N} / \mathrm{m}^2 from a volume of 10 \mathrm{~m}^3 to a volume of 4 \mathrm{~m}^3. Energy of 100 \mathrm{~J}$ is then added to the gas by heating. Its internal energy is

Options:

A) increased by $400 \mathrm{~J}

B) increased by $200 \mathrm{~J}

C) increased by $100 \mathrm{~J}

D) decreased by $200 \mathrm{~J}

822

MediumMHT CET2023

The pressure exerted by an ideal gas at a particular temperature is directly proportional to

Options:

A) the mean speed of the gas molecules.

B) mean of the square of the speed of the gas molecules.

C) the square of the mean speed of the gas molecules.

D) the root mean square speed of the gas molecules.

823

MediumMHT CET2023

The side of a copper cube is $1 \mathrm{~m} at 0^{\circ} \mathrm{C}. What will be the change in its volume, when it is heated to 100^{\circ} \mathrm{C} ? \left[\alpha_{\text {copper }}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]

Options:

A) 45 \times 10^{-4} \mathrm{~m}^3

B) 54 \times 10^{-4} \mathrm{~m}^3

C) 34 \times 10^{-4} \mathrm{~m}^3

D) 64 \times 10^{-4} \mathrm{~m}^3

824

MediumMHT CET2023

The temperature of an ideal gas is increased from $27^{\circ} \mathrm{C} to 927^{\circ} \mathrm{C}$. The r.m.s. speed of its molecules becomes

Options:

A) twice

B) four times.

C) half.

D) one-fourth.

825

MediumMHT CET2023

A jar '$\mathrm{P}' is filled with gas having pressure, volume and temperature \mathrm{P}, \mathrm{V}, \mathrm{T} respectively. Another gas jar Q filled with a gas having pressure 2 \mathrm{P}, volume \frac{\mathrm{V}}{4} and temperature 2 \mathrm{~T}. The ratio of the number of molecules in jar \mathrm{P} to those in jar Q$ is

Options:

A) 1: 1

B) 1: 2

C) 2: 1

D) 4: 1

826

MediumMHT CET2023

For a gas having '$\mathrm{X}' degrees of freedom, '\gamma' is (\gamma= ratio of specific heats =\mathrm{C_P / C_V}$)

Options:

A) \frac{1+X}{2}

B) 1+\frac{X}{2}

C) 1+\frac{2}{x}

D) 1+\frac{1}{x}

827

MediumMHT CET2023

Two uniform brass rods $A and B of length 'l' and '2 l' and their radii '2 r' and 'r' respectively are heated to same temperature. The ratio of the increase in the volume of \operatorname{rod} \mathrm{A} to that of \operatorname{rod} \mathrm{B}$ is

Options:

A) 1: 1

B) 1: 2

C) 2: 1

D) 1: 4

828

MediumMHT CET2023

A gas at N.T.P. is suddenly compressed to $\left(\frac{1}{4}\right)^{\text {th }} of its original volume. The final pressure in (Given \gamma= ratio of sp. heats =\frac{3}{2} ) atmosphere is ( \mathrm{P}=$ original pressure)

Options:

A) 4 \mathrm{P}

B) \frac{3}{2} \mathrm{P}

C) 8 \mathrm{P}

D) \frac{1}{4} \mathrm{P}

829

MediumMHT CET2023

In a thermodynamic process, there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

Options:

A) isothermal

B) isobaric

C) isochoric

D) adiabatic

830

MediumMHT CET2023

According to kinetic theory of gases, which one of the following statements is wrong?

Options:

A) All the molecules of a gas are identical.

B) Collisions between the molecules of a gas and that of the molecules with the walls of the container are perfectly elastic.

C) The molecules do not exert appreciable force on one another except during collision.

D) The pressure exerted by a gas is due to the collision between the molecules of the gas.

831

MediumMHT CET2022

Three discs $\mathrm{x}, \mathrm{y} and \mathrm{z} having radii 2 \mathrm{~m}, 3 \mathrm{~m} and 6 \mathrm{~m} respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are 300 \mathrm{~nm}, 400 \mathrm{~nm} and 500 \mathrm{~nm} respectively. If \mathrm{P}_{\mathrm{x}}, \mathrm{P}_{\mathrm{y}} and \mathrm{P}_{\mathrm{z}}$ are power radiated by them respectively then

Options:

A) \mathrm{P}_{\mathrm{X}}$ is maximum

B) \mathrm{P}_{\mathrm{Z}}$ is maximum

C) \mathrm{P}_{\mathrm{y}}$ is maximum

D) \mathrm{P_x=P_y=P_z}

832

MediumMHT CET2022

When the rms velocity of a gas is denoted by '$v', which one of the following relations is true? (\mathrm{T}=$ Absolute temperature of the gas.)

Options:

A) \frac{\mathrm{v}^2}{\mathrm{~T}}=$ constant

B) \mathrm{v}^2 \mathrm{T}=$ constant

C) \mathrm{vT}^2=$ constant

D) \frac{\mathrm{v}}{\mathrm{T}^2}=$ constant

833

MediumMHT CET2022

A monoatomic gas $\left(\gamma=\frac{5}{3}\right) initially at 27^{\circ} \mathrm{C} having volume '\mathrm{V}' is suddenly compressed to one-eighth of its original volume \left(\frac{\mathrm{V}}{8}\right)$. After the compression its temperature becomes

Options:

A) 580 K

B) 1200 K

C) 1160 K

D) 927 K

834

MediumMHT CET2022

Two monatomic ideal gases A and B of molecular masses '$m_1' and 'm_2$' respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas A to that in gas B is given by

Options:

A) \sqrt{\frac{\mathrm{m}_2}{\mathrm{~m}_1}}

B) \frac{\mathrm{m}_1}{\mathrm{~m}_2}

C) \sqrt{\frac{\mathrm{m}_1}{\mathrm{~m}_2}}

D) \frac{\mathrm{m}_2}{\mathrm{~m}_1}

835

MediumMHT CET2022

The thermodynamic process in which no work is done on or by the gas is

Options:

A) isochoric process

B) adiabatic process

C) isothermal process

D) isobaric process

836

MediumMHT CET2022

Heat given to a body, which raises its temperature by 1ºC is known as

Options:

A) specific heat

B) thermal capacity

C) water equivalent

D) temperature gradient

837

MediumMHT CET2021

Which one of the following is NOT a correct expression for an ideal gas? [$\mathrm{C_p}= Molar specific heat of a gas at constant pressure, \mathrm{C_v}= Molar specific heat of a gas at constant volume, \mathrm{Y}= Ratio of two specific heats of a gas, \mathrm{R}=$ Universal gas constant]

Options:

A) C_v=C_p+R

B) R=C_v(\gamma-1)

C) \frac{C_v}{\mathrm{C}_{\mathrm{p}}}=\frac{1}{\gamma}

D) R=\frac{C_{\mathrm{p}}(\gamma-1)}{\gamma}

838

MediumMHT CET2021

The molecular masses of helium and oxygen are 4 and 32 respectively. The ratio of r.m.s. speed of helium at 327$^\circ to r.m.s. speed of oxygen at 27^\circ$ will be

Options:

A) 1 : 6

B) 8 : 1

C) 1 : 8

D) 4 : 1

839

MediumMHT CET2021

Which one of the following p-V diagram is correct for an isochoric process:

Options:

A) IV

B) II

C) III

D) I

840

MediumMHT CET2021

Assume that for solar radiation, surface temperature of the sun is $6000 \mathrm{~K}. If Wien's constant 'b' is 2.897 \times 10^{-3} \mathrm{~mK}$, the value of maximum wavelength will be

Options:

A) 4828$\mathop A\limits^o

B) 3648$\mathop A\limits^o

C) 6400$\mathop A\limits^o

D) 5890$\mathop A\limits^o

841

MediumMHT CET2021

A metal sphere cools at the rate of $1.5^{\circ} \mathrm{C} / \mathrm{min} when its temperature is 80^{\circ} \mathrm{C}. At what rate will it cool when its temperature falls to 50^{\circ} \mathrm{C}. [Temperature of surrounding is 30^{\circ} \mathrm{C}$]

Options:

A) 0.9^{\circ} \mathrm{C} / \mathrm{min}

B) 0.6^{\circ} \mathrm{C} / \mathrm{min}

C) 1.5^{\circ} \mathrm{C} / \mathrm{min}

D) 1.2^{\circ} \mathrm{C} / \mathrm{min}

842

MediumMHT CET2021

A monoatomic gas is suddenly compressed to $(1 / 8)^{\text {th }} of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is (\gamma=5 / 3)

Options:

A) 32

B) 8

C) \frac{40}{3}

D) \frac{24}{5}

843

MediumMHT CET2021

A monoatomic ideal gas initially at temperature $\mathrm{T}_1 is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature \mathrm{T}_2 by releasing the piston suddenly. \mathrm{L}_1 and \mathrm{L}_2 are the lengths of the gas columns before and after the expansion respectively. Then \frac{\mathrm{T}_2}{\mathrm{~T}_1}$ is

Options:

A) \left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{2 / 3}

B) \left(\frac{L_1}{L_2}\right)^{2 / 3}

C) \left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{1 / 2}

D) \left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{1 / 2}

844

MediumMHT CET2021

For a monoatomic gas, the work done at constant pressure is '$\mathrm{W}' The heat supplied at constant volume for the same rise in temperature of the gas is [\gamma=\frac{C_p}{C_v}=\frac{5}{2}$ for monoatomic gas]

Options:

A) 2 \mathrm{~W}

B) \mathrm{W}

C) \frac{W}{2}

D) \frac{3 W}{2}

845

MediumMHT CET2021

An ideal gas with pressure $\mathrm{P}, volume \mathrm{V} and temperature \mathrm{T} is expanded isothermally to a volume 2 \mathrm{~V} and a final pressure \mathrm{P}_{\mathrm{i}}. The same gas is expanded adiabatically to a volume 2 \mathrm{~V}, the final pressure is \mathrm{P}_{\mathrm{a}}. In terms of the ratio of the two specific heats for the gas '\gamma', the ratio \frac{P_i}{P_a}$ is

Options:

A) 2^{\gamma+1}

B) 2^{\gamma-1}

C) 2^{1-\gamma}

D) 2^\gamma

846

MediumMHT CET2021

At what temperature does the average translational kinetic energy of a molecule in a gas becomes equal to kinetic energy of an electron accelerated from rest through potential difference of 'V' volt? ($\mathrm{N}= number of molecules, \mathrm{R}= gas constant, \mathrm{c}=$ electronic charge)

Options:

A) \frac{2 \mathrm{eVN}}{3 \mathrm{R}}

B) \mathrm{\frac{e V N}{R}}

C) \mathrm{\frac{e V N}{4 R}}

D) \mathrm{\frac{3 e V N}{2 R}}

847

MediumMHT CET2021

The temperature difference between two sides of an iron plate, $1.8 \mathrm{~cm} thick is 9^{\circ} \mathrm{C}. Heat is transmitted through the plate 10 \mathrm{k} \mathrm{cal} / \mathrm{sm}^2$ at steady state. The thermal conductivity of iron is

Options:

A) 0.02 \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}

B) 0.04 \frac{\mathrm{kcal}}{\mathrm{ms}{ }^{\circ} \mathrm{C}}

C) 0.05 \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}

D) 0.004 \frac{\mathrm{kcal}}{\mathrm{ms}{ }^{\circ}}

848

MediumMHT CET2021

Internal energy of $n_1 moles of hydrogen at temperature 'T' is equal to internal energy of 'n_2' moles of helium at temperature 2 T, then the ratio \mathrm{n}_1: \mathrm{n}_2 is [Degree of freedom of \mathrm{He}=3, Degree of freedom of \mathrm{H}_2=5$]

Options:

A) 5: 3

B) 6: 5

C) 2: 3

D) 3: 5

849

MediumMHT CET2021

For an ideal gas, $R=\frac{2}{3} C_v. This suggests that the gas consists of molecules, which are [\mathrm{R}=$ universal gas constant]

Options:

A) polyatomic

B) diatomic

C) monoatomic

D) a mixture of diatomic and polyatomic molecules

850

MediumMHT CET2021

The rms speed of a gas molecule is '$\mathrm{V}' at pressure '\mathrm{P}$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be

Options:

A) \mathrm{V}

B) \sqrt{2} \mathrm{~V}

C) \frac{V}{3}

D) \frac{V}{2}

851

MediumMHT CET2021

Equal volumes of two gases, having their densíties in the ratio of $1: 16 exert equal pressures on the walls of two containers. The ratio of their rms speads (\mathrm{C}_1: \mathrm{C}_2)$ is

Options:

A) 1: 4

B) 4: 1

C) 8: 1

D) 1: 8

852

MediumMHT CET2021

A cylindrical rod has temperatures '$T_1' and 'T_2' at its ends. The rate of flow of heat is 'Q_1' cal \mathrm{s}^{-1}. If length and radius of the rod are doubled keeping temperature constant, then the rate of flow of heat '\mathrm{Q}_2$' will be

Options:

A) \mathrm{Q}_2=\frac{\mathrm{Q}_1}{2}

B) \mathrm{Q}_2=\frac{\mathrm{Q}_1}{4}

C) \mathrm{Q_2=4 Q_1}

D) \mathrm{Q}_2=2 \mathrm{Q}_1

853

MediumMHT CET2021

The initial pressure and volume of a gas is '$\mathrm{P}' and '\mathrm{V}' respectively. First by isothermal process gas is expanded to volume '9 \mathrm{~V}' and then by adiabatic process its volume is compressed to '\mathrm{V}' then its final pressure is (Ratio of specific heat at constant pressure to constant volume =\frac{3}{2}$)

Options:

A) 6 P

B) 27 P

C) 3 P

D) 9 P

854

MediumMHT CET2021

If $\mathrm{m}' represents the mass of each molecules of a gas and \mathrm{T}$' its absolute temperature then the root mean square speed of the gas molecule is proportional to

Options:

A) \mathrm{m^{-\frac{1}{2}}T^{\frac{1}{2}}}

B) mT

C) \mathrm{m^{\frac{1}{2}}T^{-\frac{1}{2}}}

D) \mathrm{m^{\frac{1}{2}}T^{\frac{1}{2}}}

855

MediumMHT CET2021

An ideal gas at pressure '$p' is adiabatically compressed so that its density becomes twice that of the initial. If \gamma=\frac{c_p}{c_v}=\frac{7}{5}$, then final pressure of the gas is

Options:

A) p

B) 2p

C) \frac{7}{5}$p

D) 2.63p

856

MediumMHT CET2021

Which one of the following statements is wrong for an isobaric process?

Options:

A) The pressure of the system remains constant

B) There is change in volume, when work is done

C) Temperature of the system remains constant

D) Energy exchanged is used to do work to change internal energy

857

MediumMHT CET2021

For a perfectly black body, coefficient of emission is

Options:

A) zero

B) infinity

C) unity

D) less than one (non-zero)

858

MediumMHT CET2021

Two rods of different metals have coefficients of linear expansion '$\alpha_1' and '\alpha_2' respectvely. Their respective lengths are '\mathrm{L}_1' and '\mathrm{L}_2'. At all temperatures (\mathrm{L}_2-\mathrm{L}_1$) is same. The correct relation is

Options:

A) \mathrm{L}_1 \alpha_1^2=\mathrm{L}_2 \alpha_2^2

B) \mathrm{L}_1^2 \alpha_1^2=\mathrm{L}_2^2 \alpha_2^2

C) \mathrm{L}_1 \alpha_2=\mathrm{L}_2 \alpha_1

D) \mathrm{L}_1 \alpha_1=\mathrm{L}_2 \alpha_2

859

MediumMHT CET2021

The temperature of a black body is increased by $50 \%$, then the percentage increase in the rate of radiation by the body is approximated

Options:

A) 50%

B) 100%

C) 400%

D) 150%

860

MediumMHT CET2021

The emissive power of sphere of area $0.04 \mathrm{~m}^2 is 0.7 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}$. The amount of heat radiated in 20 second is

Options:

A) 2.8 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}

B) 0.28 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}

C) 5.6 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}

D) 0.56 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}

861

MediumMHT CET2021

The rate of flow of heat through a copper rod with temperature difference $28^{\circ} \mathrm{C} is 1400 \mathrm{~cal} \mathrm{~s}^{-1}$. The thermal resistance of copper rod will be

Options:

A) 0.05 \frac{{ }^{\circ} \mathrm{C} \mathrm{s}}{\mathrm{cal}}

B) 0.02 \frac{{ }^{\circ} \mathrm{C} \mathrm{s}}{\mathrm{cal}}

C) 5 \frac{{ }^{\circ} \mathrm{C} \mathrm{s}}{\mathrm{cal}}

D) 2 \frac{{ }^{\circ} \mathrm{Cs}}{\text { cal }}

862

MediumMHT CET2021

The change in internal energy of the mass of a gas, when the volume changes from '$\mathrm{V}' to '2 \mathrm{~V}' at constant pressure 'P' is (\gamma=$ Ratio of Cp to Cv)

Options:

A) \frac{\mathrm{PV}}{(\gamma-1)}

B) \frac{\mathrm{P}}{(\gamma-1)}

C) PV

D) \frac{\gamma \mathrm{PV}}{(\gamma-1)}

863

MediumMHT CET2021

If the pressure of an ideal gas is decreased by $10 \%$ isothermally, then its volume will

Options:

A) decrease by $8 \%

B) decrease by $9 \%

C) increase by $8 \%

D) increase by $11.1 \%

864

MediumMHT CET2021

An ideal gas having molar mass '$\mathrm{M}_0$', has r.m.s. velocity 'V' at temperature 'T'. Then

Options:

A) \mathrm{VT}^2=$ constant

B) \frac{\mathrm{v}^2}{\mathrm{~T}}=$ constant

C) \mathrm{V}^2 \mathrm{T}=$ constant

D) \mathrm{V} is independent of \mathrm{T}

865

MediumMHT CET2021

An ideal gas at $27^{\circ} \mathrm{C} is compressed adiabatically to (8 / 27) of its original volume. If ratio of specific heats, \gamma=5 / 3$ then the rise in temperature of the gas is

Options:

A) 500 K

B) 125 K

C) 250 K

D) 375 K

866

MediumMHT CET2021

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled

Options:

A) by increasing $\mathrm{T} to 4 \mathrm{~T}

B) by increasing $\mathrm{T} to 2 \mathrm{~T}

C) by decreasing $\mathrm{T} to \mathrm{T} / 2

D) by increasing $\mathrm{T} to \sqrt{2} \mathrm{~T}

867

MediumMHT CET2021

A polyatomic gas $(\gamma=4 / 3) is compressed to \left(\frac{1}{8}\right)^{\text {th }} of its volume adiabatically. If its initial pressure is \mathrm{P}_0$, its new pressure will be

Options:

A) 2 \mathrm{P}_0

B) 8 \mathrm{P}_0

C) 6 \mathrm{P}_0

D) 16 \mathrm{P}_0

868

MediumMHT CET2021

If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor

Options:

A) 8

B) 2

C) 4

D) 16

869

MediumMHT CET2021

Which of the following statements is true? ($\Delta \mathrm{U}= increase in internal energy, \mathrm{dW}=$ work done by the system)

Options:

A) In an adiabatic process $\Delta \mathrm{U}=\mathrm{dW}

B) In an adiabatic process $\Delta \mathrm{U}=-\mathrm{dW}

C) In an isothermal process $\Delta \mathrm{U}=-\mathrm{dW}$.

D) In an isothermal process $\Delta \mathrm{U}=\mathrm{dW}

870

MediumMHT CET2021

Let '$\mathrm{W}_1' be the work done in blowing a soap bubble of radius 'r' from soap solution at room temperature. The soap solution is now heated and second soap bubble of radius '2 r' is blown from the heated soap solution. If 'W_2$' is the work done in forming this bubble then

Options:

A) \mathrm{W}_2=2 \mathrm{~W}_1

B) \mathrm{W}_2=4 \mathrm{~W}_1

C) \mathrm{W}_2>4 \mathrm{~W}_1

D) \mathrm{W}_2<4 \mathrm{~W}_1

871

MediumMHT CET2021

A cylindrical rod is having temperatures $\theta_1 and \theta_2 at its ends. The rate of heat flow is 'Q' \mathrm{J}{\mathrm{s}}^{-1}$. All the linear dimensions of the rod are doubled by keeping the temperatures constant. What is the new rate of flow of heat?

Options:

A) \frac{Q}{2}

B) \frac{Q}{4}

C) 2 \mathrm{Q}

D) \frac{3 Q}{2}

872

MediumMHT CET2021

For a gas molecule with 6 degrees of freedom, which one of the following relation between gas constant '$\mathrm{R}' and molar specific heat '\mathrm{C}_{\mathrm{v}}$' is correct?

Options:

A) R=\frac{C_v}{3}

B) \mathrm{R}=\frac{5 \mathrm{C}_{\mathrm{v}}}{4}

C) \mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{2}

D) \mathrm{R}=\frac{3 \mathrm{C}_{\mathrm{v}}}{4}

873

MediumMHT CET2021

What is the ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right) to that in helium \left(\gamma=\frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

Options:

A) \frac{\sqrt{42}}{5}

B) \frac{5}{\sqrt{42}}

C) \frac{\sqrt{21}}{5}

D) \frac{5}{\sqrt{21}}

874

MediumMHT CET2021

Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal pressures on the wall of their respective containers. Then the ratio of their r.m.s. velocities is

Options:

A) 16 : 1

B) 1 : 8

C) 4 : 1

D) 1 : 12

875

MediumMHT CET2021

In thermodynamics, for an isochoric process, which one of the following statement is INCORRECT?

Options:

A) Energy exchanged is used to do work and also to change internal energy.

B) No work is done in the process.

C) It is a constant volume process.

D) Temperature of the system changes during the process.

876

MediumMHT CET2021

If '$\mathrm{E}' is the kinetic energy per mole of an ideal gas and '\mathrm{T}$' is the absolute temperature, then the universal gas constant is given as

Options:

A) \frac{2 \mathrm{~T}}{3 \mathrm{E}}

B) \frac{2 \mathrm{E}}{3 \mathrm{~T}}

C) \frac{3 \mathrm{~T}}{2 \mathrm{E}}

D) \frac{3 \mathrm{E}}{2 \mathrm{~T}}

877

MediumMHT CET2021

Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in parallel they transfer same amount of heat in same conditions in time

Options:

A) 3 s

B) 2 s

C) 1 s

D) 4 s

878

MediumMHT CET2021

The molar specific heats of an ideal gas at constant pressure and volume are denoted by '$\mathrm{C}_{\mathrm{p}}' and 'C_v' respectively. If \gamma=\frac{C_p}{C_v} and 'R' is universal gas constant, then C_v$ is equal to

Options:

A) \frac{\mathrm{R}}{\gamma-1}

B) \gamma \mathrm{R}

C) \frac{1+\gamma}{1-\gamma}

D) \frac{\gamma-1}{\mathrm{R}}

879

MediumMHT CET2021

The temperature difference bewtween two sides of metal plate, $3 \mathrm{~cm} thick is 15^{\circ} \mathrm{C}. Heat is transmitted through plate at the rate of 900 \mathrm{~kcal} per minute per \mathrm{m}^2$ at steady state. The thermal conductivity of metal is

Options:

A) 1.8 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}

B) 4.5 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}

C) 3 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}

D) 6 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}

880

MediumMHT CET2021

A black body has maximum wavelength '$\lambda_{\mathrm{m}}' at temperature 2000 \mathrm{~K}. Its corresponding wavelength at temperature 3000 \mathrm{~K}$ will be

Options:

A) \frac{4 \lambda_m}{9}

B) \frac{2 \lambda_m}{3}

C) \frac{3 \lambda_{\mathrm{m}}}{2}

D) \frac{9}{4} \lambda_{\mathrm{m}}

881

MediumMHT CET2021

A monoatomic gas at pressure '$\mathrm{P}' having volume '\mathrm{V}' expands isothermally to a volume 2 \mathrm{~V} and then adiabatically to a volume 16 \mathrm{~V}. The final pressure of the gas is \left(\gamma=\frac{5}{3}\right)

Options:

A) \frac{P}{64}

B) \frac{\mathrm{P}}{128}

C) \frac{P}{8}

D) \frac{\mathrm{P}}{32}

882

MediumMHT CET2021

A black reactangular surface of area '$a' emits energy '\mathrm{E}' per second at 27^{\circ} \mathrm{C}. If length and breadth is reduced to \left(\frac{1}{3}\right)^{\text {rd }} of initial value and temperature is raised to 327^{\circ} \mathrm{C}$ then energy emitted per second becomes

Options:

A) \frac{16 \mathrm{E}}{9}

B) \frac{8 \mathrm{E}}{9}

C) \frac{4 \mathrm{E}}{9}

D) \frac{12 \mathrm{E}}{9}

883

MediumMHT CET2021

Find the value of $-197^\circ$C temperature in Kelvin.

Options:

A) 47 K

B) 76 K

C) 470 K

D) 760 K

884

MediumMHT CET2021

Which one of the following equations specifies an isobaric process? $[Q= heat supplied \Delta P, \Delta V and \Delta T$ are change in pressure, volume and temperature respectively]

Options:

A) Q=0

B) \Delta \mathrm{T}=0

C) \Delta \mathrm{V}=0

D) \Delta \mathrm{P}=0

885

MediumMHT CET2021

A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

Options:

A) decrease 5 times

B) remain unchanged

C) increase 5 times

D) increase 10 times

886

MediumMHT CET2021

The relation obeyed by a perfect gas during an adiabatic process is $\mathrm{PV}^{3 / 2}. The initial temperature of the gas is '\mathrm{T}$'. When the gas is compressed to half of its Initial volume, the final temperature of the gas is

Options:

A) 2 \sqrt{2} \mathrm{~T}

B) 4 \mathrm{~T}

C) \sqrt{2} \mathrm{~T}

D) 2 \mathrm{~T}

887

MediumMHT CET2021

A black rectangular surface of area '$\mathrm{A}' emits energy '\mathrm{E}' per second at 27^{\circ} \mathrm{C}. If length and breadth is reduced to (1 / 3)^{\text {rd }} of its initial value and temperature is raised to 327^{\circ} \mathrm{C}$ then energy emitted per second becomes

Options:

A) \frac{20 \mathrm{E}}{9}

B) \frac{8 \mathrm{E}}{9}

C) \frac{16 \mathrm{E}}{9}

D) \frac{4 \mathrm{E}}{9}

888

MediumMHT CET2021

A monoatomic gas is suddenly compressed to (1/8) th of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is ($\gamma=5/3$)

Options:

A) 32

B) 8

C) \frac{40}{3}

D) \frac{24}{5}

889

MediumMHT CET2021

A conducting rod of length $1 \mathrm{~m} has area of cross-section 10^{-3} \mathrm{~m}^2. One end is immersed in baiting water \left(100^{\circ} \mathrm{C}\right) and the other end in Ice \left(0^{\circ} \mathrm{C}\right). If coefficient of thermal conductivity of \mathrm{rod} is 96 \mathrm{~cal} / \mathrm{sm}^{\circ} \mathrm{C} and latent heat for ice is 8 \times 10^{-4} \mathrm{cal} / \mathrm{kg}$ then the amount of ice which will melt in one minute is

Options:

A) 5.4 \times 10^{-3} \mathrm{~kg}

B) 7.2 \times 10^{-3} \mathrm{~kg}

C) 1.8 \times 10^{-3} \mathrm{~kg}

D) 3.6 \times 0^{-3} \mathrm{~kg}

890

MediumMHT CET2021

Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures $\left(\mathrm{T}_{\mathrm{P}}\right. and \left.\mathrm{T}_{\mathrm{Q}}\right)$ is

Options:

A) \mathrm{T_P=T_Q}

B) \mathrm{T}_{\mathrm{P}}=\frac{\mathrm{T}_{\mathrm{Q}}}{2}

C) \mathrm{T}_{\mathrm{P}}>\mathrm{T}_{\mathrm{Q}}

D) \mathrm{T}_{\mathrm{P}}<\mathrm{T}_{\mathrm{Q}}

891

MediumMHT CET2021

A perfectly black body emits a radiation at temperature 'T$_1' K. If it is to radiate at 16 times this power, its temperature 'T_2$' K should be

Options:

A) 8T$_1

B) 4T$_1

C) 2T$_1

D) 16T$_1

892

MediumMHT CET2021

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto {1 \over {\sqrt V }}. The value of \gamma for the gas is (\gamma = {{{C_p}} \over {{C_v}}},V = $ Volume of the gas)

Options:

A) 1.8

B) 1.5

C) 1.3

D) 1.4

893

MediumMHT CET2021

On an imaginary linear scale of temperature (called 'W' scale) the freezing and boiling points of water are 39$^\circ W and 239^\circ W respectively. The temperature on the new scale corresponding to 39^\circ$C temperature on Celsius scale will be

Options:

A) 139$^\circ$ W

B) 78$^\circ$ W

C) 117$^\circ$ W

D) 200$^\circ$ W

894

MediumMHT CET2021

Specific heats of an ideal gas at constant pressure and volume are denoted by $\mathrm{C}_{\mathrm{p}} and \mathrm{C}_{\mathrm{v}} respectively. If \gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}} and \mathrm{R} it's the universal gas constant then \mathrm{C}_{\mathrm{v}}$ is equal to

Options:

A) \frac{(\gamma-1)}{(\gamma+1)}

B) \frac{(\gamma-1)}{\mathrm{R}}

C) \mathrm{R} \gamma

D) \frac{R}{(\gamma-1)}

895

MediumMHT CET2021

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

Options:

A) W

B) \mathrm{\frac{5W}{2}}

C) \mathrm{\frac{W}{2}}

D) \mathrm{\frac{3W}{2}}

896

MediumMHT CET2020

The root mean square velocity of molecules of a gas is 200 \mathrm{~m} / \mathrm{s}. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

Options:

A) 50 \mathrm{~m} / \mathrm{s}

B) 200 \mathrm{~m} / \mathrm{s}

C) 100 \mathrm{~m} / \mathrm{s}

D) \frac{100}{\sqrt{2}} \mathrm{~m} / \mathrm{s}

897

MediumMHT CET2020

Two spherical black bodies of radius $r_1 and r_2 with surface temperature T_1 and T_2 respectively, radiate same power, then r_1: r_2$ is

Options:

A) \left(\frac{T_2}{T_1}\right)^4

B) \left(\frac{T_2}{T_1}\right)^2

C) \left(\frac{T_1}{T_2}\right)^2

D) \left(\frac{T_1}{T_2}\right)^4

898

MediumMHT CET2020

A diatomic gas undergoes adiabatic change. Its pressure $p and temperature T are related as p \propto T^x, where x$ is

Options:

A) 3.0

B) 1.5

C) 2.5

D) 3.5

899

MediumMHT CET2020

For a gas, $\frac{R}{C_V}=0.4, where R is universal gas constant and C_V$ is the molar specific heat at constant volume. The gas is made up of molecules, which are

Options:

A) polyatomic

B) rigid diatomic

C) monoatomic

D) non-rigid diatomic

900

MediumMHT CET2020

A monoatomic gas of pressure $p having volume V expands isothermally to a volume 2V and then adiabatically to a volume 16 \mathrm{~V}. The final pressure of the gas is (ratio of specific heats =\frac{5}{3}

Options:

A) \frac{p}{8}

B) \frac{p}{16}

C) \frac{p}{64}

D) \frac{p}{32}

901

MediumMHT CET2019

The SI unit and dimensions of Stefan's constant \sigma in case of Stefan's law of radiation is

Options:

A) \frac{\mathrm{J}}{\mathrm{m}^3 \mathrm{~s}^4}, \left[M^1 L^0 T^{-3} K^{-4}\right]

B) \frac{\mathrm{J}}{\mathrm{m}^2 \mathrm{~s}^4 \mathrm{~K}}, \left[M^1 L^0 T^{-3} K^3\right]

C) \frac{\mathrm{J}}{\mathrm{m}^3 \mathrm{~s} \mathrm{~K}^4},\left[\mathrm{M}^{1} \mathrm{L}^0 \mathrm{~T}^{-3} \mathrm{~K}^4\right]

D) \frac{\mathrm{J}}{\mathrm{m}^2 \mathrm{~s} \mathrm{~K}^4},\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right]

902

MediumMHT CET2019

The rms speed of oxygen molecule in a gas is u, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be

Options:

A) 4u

B) u

C) 2u

D) u\sqrt2

903

MediumMHT CET2019

The equation of state for 2 g of oxygen at a pressure ' P ' and temperature ' T, when occupying a volume ' V ' will be

Options:

A) p V=16 R T

B) p V=R T

C) p V=\frac{1}{16} R T

D) p V=2 R T

904

MediumMHT CET2019

The maximum wavelength of radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant =5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}, Wien's constant, b=2898 \mu \mathrm{mK} )

Options:

A) 5.67 \times 10^{-12} \mathrm{Wm}^{-2}

B) 10.67 \times 10^{14} \mathrm{Wm}^{-2}

C) 5.67 \times 10^8 \mathrm{Wm}^{-2}

D) 10.67 \times 10^7 \mathrm{Wm}^{-2}

905

MediumMHT CET2019

If ' C_P ' and ' C_V ' are molar specific heats of an ideal gas at constant pressure and volume respectively. If ' \lambda ' is the ratio of two specific heats and ' R ' is universal gas constant then ' C_p ' is equal to

Options:

A) \frac{R \gamma}{\gamma-1}

B) \gamma R

C) \frac{1+\gamma}{1-\gamma}

D) \frac{R}{\gamma-1}

906

MediumMHT CET2019

A clock pendulum having coefficient of linear expansion. \alpha=9 \times 10^{-7} /{ }^{\circ} \mathrm{C}^{-1} has a period of 0.5 s at 20^{\circ} \mathrm{C}. If the clock is used in a climate, where the temperature is 30^{\circ} \mathrm{C}, how much time does the clock lose in each oscillation? ( g= constant)

Options:

A) 25 \times 10^{-7} \mathrm{~s}

B) 5 \times 10^{-7} \mathrm{~s}

C) 1.125 \times 10^{-6} \mathrm{~s}

D) 2.25 \times 10^{-6} \mathrm{~s}

907

MediumMHT CET2019

If \alpha is the coefficient of performance of a refrigerator and ' Q ' is heat released to the hot reservoir, then the heat extracted from the cold reservoir ' Q_2 ' is

Options:

A) \frac{\alpha Q_1}{\alpha-1}

B) \frac{\alpha-1}{\alpha} Q_1

C) \frac{\alpha Q_1}{1+\alpha}

D) \frac{1+\alpha}{\alpha} Q_1

908

MediumNEET2025

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2 K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3 T and the right end at T. The rods are thermally insulated from outside. In steady state, temperature at the left junction is T_1 and that at the right junction is T_2. The ratio T_1 / T_2 is

Options:

A) \frac{5}{3}

B) \frac{5}{4}

C) \frac{3}{2}

D) \frac{4}{3}

909

MediumNEET2025

A container has two chambers of volumes V_1=2 litres and V_2=3 litres separated by a partition made of a thermal insulator. The chambers contain n_1=5 and n_2=4 moles of ideal gas at pressures p_1=1 \mathrm{~atm} and p_2=2 \mathrm{~atm}, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

Options:

A) 1.4 atm

B) 1.8 atm

C) 1.3 atm

D) 1.6 atm

910

MediumNEET2025

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressures at temperature 27^{\circ} \mathrm{C}. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, R=\frac{100}{12} \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, and molecular mass of \mathrm{O}_2=32,1 atm pressure =1.01 \times 10^5 \mathrm{~N} / \mathrm{m}]

Options:

A) 0.116 kg

B) 0.156 kg

C) 0.125 kg

D) 0.144 kg

911

HardNEET2025

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius r_A and r_B, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by 16 cm and 9 cm , respectively. If the change in their internal energy is the same, then the ratio \frac{r_A}{r_B} is equal to

Options:

A) \frac{2}{\sqrt{3}}

B) \frac{\sqrt{3}}{2}

C) \frac{4}{3}

D) \frac{3}{4}

912

MediumNEET2024

Given below are two statements: One is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$. Assertion A: Houses made of concrete roofs overlaid with foam keep the room hotter during summer. Reason R: The layer of foam insulation prohibits heat transfer, as it contains air pockets. In the light of the above statements, choose the correct answer from the options given below.

Options:

A) A is true but R is false.

B) A is false but R is true.

C) Both A and R are true and R is the correct explanation of A.

D) Both A and R true but R is NOT the correct explanation of A.

913

MediumNEET2024

The equilibrium state of a thermodynamic system is described by A. Pressure B. Total heat C. Temperature D. Volume E. Work done Choose the most appropriate answer from the options given below.

Options:

A) A, B and E only

B) B, C and D only

C) A, B and C only

D) A, C and D only

914

MediumNEET2024

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $\gamma=\frac{C_p}{C_v} is (C_P where C_V$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):

Options:

A) \frac{4+3 \gamma}{\gamma-1}

B) \frac{3+4 \gamma}{\gamma-1}

C) \frac{4-3 \gamma}{\gamma-1}

D) \frac{3-4 \gamma}{\gamma-1}

915

MediumNEET2024

A thermodynamic system is taken through the cycle $abcda. The work done by the gas along the path b c$ is:

Options:

A) Zero

B) 30 J

C) -$90 J

D) -$60 J

916

MediumNEET2024

The following graph represents the $T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P_1, P_2 and P_3$ compared with those of Charles's law represented as dotted lines. Then the correct relation is :

Options:

A) P_3>P_2>P_1

B) P_1>P_3>P_2

C) P_2>P_1>P_3

D) P_1>P_2>P_3

917

MediumNEET2023

For the given cycle, the work done during isobaric process is:

Options:

A) 200 J

B) Zero

C) 400 J

D) 600 J

918

MediumNEET2023

A container of volume $200 \mathrm{~cm}^3 contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature 200 \mathrm{~K} (\mathrm{R}=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$) will be :-

Options:

A) 6.15 \times 10^5 \mathrm{~Pa}

B) 6.15 \times 10^4 \mathrm{~Pa}

C) 4.15 \times 10^5 \mathrm{~Pa}

D) 4.15 \times 10^6 \mathrm{~Pa}

919

MediumNEET2023

The temperature of a gas is $-50^{\circ} \mathrm{C}. To what temperature the gas should be heated so that the rms speed is increased by 3$ times?

Options:

A) 3295^{\circ} \mathrm{C}

B) 3097 \mathrm{~K}

C) 223 \mathrm{~K}

D) 669^{\circ} \mathrm{C}

920

MediumNEET2023

A Carnot engine has an efficiency of $50 \% when its source is at a temperature 327^{\circ} \mathrm{C}$. The temperature of the sink is :-

Options:

A) 15^{\circ} \mathrm{C}

B) 100^{\circ} \mathrm{C}

C) 200^{\circ} \mathrm{C}

D) 27^{\circ} \mathrm{C}

921

MediumNEET2022

An ideal gas follows a process described by the equation $P{V^2} = C from the initial ({P_1},\,{V_1},\,{T_1}) to final ({P_2},\,{V_2},\,{T_2})$ thermodynamic states, where C is a constant. Then

Options:

A) If ${P_1} > {P_2} then {V_1} > {V_2}

B) If ${P_1} > {P_2} then {T_1} < {T_2}

C) If ${V_2} > {V_1} then {T_2} > {T_1}

D) If ${V_2} > {V_1} then {T_2} < {T_1}

922

MediumNEET2022

Two rods one made of copper and other made of steel of same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s $-1 K -1 m -1 and 50 J s -1 K -1 m -1 respectively. The free ends of copper and steel are held at 100^\circC and 0^\circ$C respectively. The temperature at the junction is, nearly :

Options:

A) 88.5^\circ C

B) 12^\circ C

C) 50^\circ C

D) 73^\circ C

923

MediumNEET2022

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is :

Options:

A) The root mean square speed of sulfur hexafluoride is the largest

B) All vessels contain unequal number of respective molecules

C) The root mean square speed of molecules is same in all three cases

D) The root mean square speed of helium is the largest

924

MediumNEET2022

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is

Options:

A) 1

B) 2

C) 3

D) 4

925

MediumNEET2022

The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is

Options:

A) 5.6 $\times$ 10 6 m 3

B) 5.6 $\times$ 10 3 m 3

C) 5.6 $\times 10 -$3 m 3

D) 5.6 m 3

926

MediumNEET2021

A cup of coffee cools from 90$^\circC to 80^\circC in t minutes, when the room temperature is 20^\circC. The time taken by a similar cup of coffee to cool from 80^\circC to 60^\circC at a room temperature same at 20^\circ$C is :

Options:

A) {5 \over {13}}$t

B) {13 \over {10}}$t

C) {13 \over {5}}$t

D) {10 \over {13}}$t

927

MediumNEET2021

Match Column - I and Column - II and choose the correct match from the given choices. Column - I Column - II (A) Root mean square speed of gas molecules (P) ${1 \over 3}nm{\overline v ^2} (B) Pressure exerted by ideal gas (Q) \sqrt {{{3RT} \over M}} (C) Average kinetic energy of a molecule (R) {5 \over 2}RT (D) Total internal energy of 1 mole of a diatomic gas (S) {3 \over 2}{k_B}T

Options:

A) (A) - (R), (B) - (Q), (C) - (P), (D) - (S)

B) (A) - (R), (B) - (P), (C) - (S), (D) - (Q)

C) (A) - (Q), (B) - (R), (C) - (S), (D) - (P)

D) (A) - (Q), (B) - (P), (C) - (S), (D) - (R)

928

MediumNEET2020

The average thermal energy for a mono-atomic gas is : (k B is Boltzmann constant and T absolute temperature)

Options:

A) {3 \over 2}{k_B}T

B) {5 \over 2}{k_B}T

C) {7 \over 2}{k_B}T

D) {1 \over 2}{k_B}T

929

MediumNEET2020

The mean free path for a gas, with molecular diameter d and number density n can be expressed as :

Options:

A) {1 \over {\sqrt 2 n\pi {d^2}}}

B) {1 \over {\sqrt 2 {n^2}\pi {d^2}}}

C) {1 \over {\sqrt 2 {n^2}{\pi ^2}{d^2}}}

D) {1 \over {\sqrt 2 n\pi d}}

930

MediumNEET2020

A cylinder contains hydrogen gas at pressure 249 kPa and temperature 27$^\circ $C Its density is : (R = 8.3 J mol -1 K -1 )

Options:

A) 0.2 kg/m 3

B) 0.1 kg/m 3

C) 0.02 kg/m 3

D) 0.5 kg/m 3

931

MediumNEET2020

The quantities of heat required to raise the temperature of two solid copper spheres of radii r 1 and r 2 (r 1 = 1.5r 2 ) through 1 K are in the ratio :

Options:

A) {9 \over 4}

B) {3 \over 2}

C) {5 \over 3}

D) {27 \over 8}

932

MediumNEET2020

Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire systems is thermally insulated. The stop cock is suddenly opened. The Process is :

Options:

A) adiabatic

B) isochoric

C) isobaric

D) isothermal

933

MediumNEET2019

In which of the following processes, heat is neither absorbed nor released by a system?

Options:

A) adiabatic

B) isobaric

C) isochoric

D) isothermal

934

MediumNEET2019

Increase in tempertaure of a gas filled in a container would lead to :

Options:

A) increase in its kinetic energy

B) decrease in intermolecular distance

C) decrease in its pressure

D) increase in its mass

935

MediumNEET2018

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given : Mass of oxygen molecule (m) = 2.76 × 10 –26 kg, Boltzmann’s constant k B = 1.38 × 10 –23 J K –1 )

Options:

A) 2.508 × 10 4 K

B) 8.360 × 10 4 K

C) 5.016 × 10 4 K

D) 1.254 × 10 4 K

936

MediumNEET2018

A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 10 5 N m –2 ) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is

Options:

A) 104.3 J

B) 208.7 J

C) 42.2 J

D) 84.5 J

937

MediumNEET2018

The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is

Options:

A) 26.8%

B) 20%

C) 6.25%

D) 12.5%

938

MediumNEET2018

The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

Options:

A) {2 \over 5}

B) {2 \over 3}

C) {1 \over 3}

D) {2 \over 7}

939

MediumNEET2017

Thermodynamic processes are indicated in the following diagram. Match the following Column-1 Column-2 P. Process I A. Adiabatic Q. Process II B. Isobaric R. Process III C. Isochoric S. Process IV D. Isothermal

Options:

A) P $ \to C, Q \to A, R \to D, S \to $ B

B) P $ \to C, Q \to D, R \to B, S \to $ A

C) P $ \to D, Q \to B, R \to A, S \to $ C

D) P $ \to A, Q \to C, R \to D, S \to $ B

940

MediumNEET2017

A gas mixture consists of 2 moles of O 2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

Options:

A) 15 RT

B) 9 RT

C) 11 RT

D) 4 RT

941

MediumNEET2017

A carnot engine having an efficiency of ${1 \over {10}}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Options:

A) 90 J

B) 99 J

C) 100 J

D) 1 J

942

MediumNEET2016

One mole of an ideal monatomic gas undergoes a process described by the equation PV 3 = constant. The heat capacity of the gas during this process is

Options:

A) {3 \over 2}$ R

B) {5 \over 2}$ R

C) 2R

D) R

943

MediumNEET2016

The temperature inside a refrigerator is t 2 o C. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be

Options:

A) {{{t_1}} \over {{t_1} - {t_2}}}

B) {{{t_1} + 273} \over {{t_1} - {t_2}}}

C) {{{t_2} + 273} \over {{t_1} - {t_2}}}

D) {{{t_1} + {t_2}} \over {{t_1} + 273}}

944

MediumNEET2016

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?

Options:

A) P/(kT)

B) Pm/(kT)

C) P/(KTV)

D) mkT

945

MediumNEET2016

A refrigerator works between 4 o C and 30 o C. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is (Take 1 cal = 4.2 Joules)

Options:

A) 236.5 W

B) 2365 W

C) 2.365 W

D) 23.65 W

946

MediumNEET2016

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then

Options:

A) Compressing the gas isothermally or adiabatically will require the same amount of work.

B) Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

C) Compressing the gas isothermally will require more work to be done.

D) Compressing the gas through adiabatic process will require more work to be done.

947

MediumNEET2016

The molecules of a given mass of a gas have r.m.s. velocity of 2000 m s $-1 at 27 o C and 1.0 \times 10 5 N m -2 pressure. When the temperature and pressure of the gas are respectively, 127 o C and 0.05 \times 10 5 N m -2 , the r.m.s. velocity of its molecules in m s -$1 is

Options:

A) {{100\sqrt 2 } \over 3}

B) {{100} \over 3}

C) 100\sqrt 2

D) {{400} \over {\sqrt 3 }}

948

MediumNEET2015

An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas ?

Options:

A) Isochoric

B) Isothermal

C) Adiabatic

D) Isobaric

949

MediumNEET2015

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is

Options:

A) 2

B) {1 \over 2}

C) {2 \over 3}

D) {3 \over 4}

950

MediumNEET2015

The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is $-$20 o C, the temperature of the surroundings to which it rejects heat is

Options:

A) 11 o C

B) 21 o C

C) 31 o C

D) 41 o C

951

MediumNEET2015

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is

Options:

A) 20 J

B) -$ 12 kJ

C) 20 kJ

D) -$ 20 kJ

952

MediumNEET2015

A Carnot engine, having an efficiency of as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Options:

A) 90 J

B) 1 J

C) 100 J

D) 99 J

953

MediumNEET2015

The ratio of the specific heats ${{{C_p}} \over {{C_v}}} = \gamma $ in terms of degrees of freedom (n) is given by

Options:

A) \left( {1 + {2 \over n}} \right)

B) \left( {1 + {n \over 2}} \right)

C) \left( {1 + {1 \over n}} \right)

D) \left( {1 + {n \over 3}} \right)

954

MediumNEET2015

Figure below shows two paths that may be taken by a gas to go from a state A to a state C. In process AB, 400 J of heat is added to the system and in process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process AC will be

Options:

A) 460 J

B) 300 J

C) 380 J

D) 500 J

955

MediumNEET2014

A monatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is (Take $\gamma $ = 5/3)

Options:

A) 64P

B) 32P

C) P/64

D) 16P

956

MediumNEET2014

A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system in the cycle is

Options:

A) P 0 V 0

B) 2P 0 V 0

C) {{{P_0}{V_0}} \over 2}

D) zero

957

MediumNEET2014

The mean free path of molecules of a gas, (radius r) is inversely proportional to

Options:

A) r 3

B) r 2

C) r

D) \sqrt r

958

MediumNEET2013

A system is taken from state a to state c by two paths adc and abc as shown in the figure. The internal energy at a is ${U_a} = 10\,J. Along the path adc the amount of heat absorbed dQ 1 = 50 J and the work obtained dW 1 =$ 20 J whereas along the path abc the heat absorbed dQ 2 = 36 J. The amount of work allong the path abc is

Options:

A) 10 J

B) 12 J

C) 36 J

D) 6 J

959

MediumNEET2013

In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

Options:

A) 2P

B) P

C) P/2

D) 4P

960

MediumNEET2013

Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T 1 and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T 2 . For what values of T the efficiencies of the two engines are equal

Options:

A) {{{T_1} - {T_2}} \over 2}

B) {T_1}{T_2}

C) \sqrt {{T_1}{T_2}}

D) {{{T_1} + {T_2}} \over 2}

961

MediumNEET2013

Which of the following relations does not give the equation of an adiabatic process, where terms have their usual meaning?

Options:

A) P 1$-\gamma T \gamma $ = constant

B) PV $\gamma $ = constant

C) TV $\gamma -$1 = constant

D) P $\gamma T 1-\gamma $ = constant

962

MediumNEET2013

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of ${{{C_p}} \over {{C_p}}}$ for the gas is

Options:

A) {5 \over 3}

B) {3 \over 2}

C) {4 \over 3}

D) 2

963

MediumNEET2013

A gas is taken through the cycle A $ \to B \to C \to $ A, as shown. what is the net work done by the gas?

Options:

A) Zero

B) -$ 2000 J

C) 2000 J

D) 1000 J

964

MediumNEET2013

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T 1 K to T 2 K is

Options:

A) {3 \over 4}{N_a}{k_B}\left( {{T_2} - {T_1}} \right)

B) {3 \over 4}{N_a}{k_B}\left( {{{{T_2}} \over {{T_1}}}} \right)

C) {3 \over 8}{N_a}{k_B}\left( {{T_2} - {T_1}} \right)

D) {3 \over 2}{N_a}{k_B}\left( {{T_2} - {T_1}} \right)

965

MediumNEET2013

In the given (V $-$ T) diagram, what is the relation between pressure P 1 and P 2 ?

Options:

A) P 2 < P 1

B) Carnot be predicted

C) P 2 = P 1

D) P 2 > P 1

966

MediumNEET2012

An ideal gas goes from state A to state B via three different processes as indicated in the P-V diagram. If Q 1 , Q 2 , Q 3 indicate the heat absorbed by the gas along the three processes and $\Delta U 1 , \Delta U 2 , \Delta $U 3 indicate the change in internal energy along the three processes respectively, then

Options:

A) Q 1 > Q 2 > Q 3 and $\Delta U 1 = \Delta U 2 = \Delta $U 3

B) Q 3 > Q 2 > Q 1 and $\Delta U 1 = \Delta U 2 = \Delta $U 3

C) Q 1 = Q 2 = Q 3 and $\Delta U 1 > \Delta U 2 > \Delta $U 3

D) Q 3 = Q 2 = Q 1 and $\Delta U 1 > \Delta U 2 > \Delta $U 3

967

MediumNEET2012

One mole of an ideal gas goes from an initial state A to final state B via two processes : It first undergoes isothermal expansion from volume V to 3V and then its volume is reduced from 3V to V at constant pressure. The correct P-V diagram representing the two process is

Options:

968

MediumNEET2012

A thermodynamic system is taken through the cycle ABCD as shown in figure. Heat rejected by the gas during the cycle is

Options:

A) 2PV

B) 4PV

C) {1 \over 2}$ PV

D) PV

969

MediumNEET2011

A mass of diatomic gas $(\gamma = 1.4)$ at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27 o C to 927 o C. The pressure of the gas in the final state is

Options:

A) 8 atm

B) 28 atm

C) 68.7 atm

D) 256 atm

970

MediumNEET2011

When 1 kg of ice at 0 o C melts to water at 0 o C, the resulting change in its entropy, taking latent heat of ice to be 80 cal/ o C, is

Options:

A) 273 cal/K

B) 8 $ \times $ 10 4 cal/K

C) 80 cal/K

D) 293 cal/K

971

MediumNEET2011

During an isothermal expansion, a confined ideal gas does $-$ 150 J of work against its surroundings. This implies that

Options:

A) 150 J of heat has been removed from the gas

B) 300 J of heat has been added to the gas

C) no heat is transferred because the process is isothermal

D) 150 J of heat has been added to the gas

972

MediumNEET2010

A monatomic gas at pressure P 1 and volume V 1 is compressed adiabatically to ${{1 \over 8}^{th}}$ of its original volume. What is the final pressure of the gas?

Options:

A) 64P 1

B) P 1

C) 16P 1

D) 32P 1

973

MediumNEET2010

If c p and c v denote the specific heats (per unit mass of an ideal gas of molecular weight M, then

Options:

A) c p $-$ c v = R/M 2

B) c p $-$ c v = R

C) c p $-$ c v = R/M

D) c p $-$ c v = MR

974

MediumNEET2010

If $\Delta U and \Delta $W represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true ?

Options:

A) \Delta U = -\Delta $W, in an adiabtic process

B) \Delta U = \Delta $W, in an isothermal process

C) \Delta U = \Delta $W, in an adiabatic process

D) \Delta U = - \Delta $W, in an isothermal process

975

MediumNEET2009

The internal energy change in a system that has absorbed 2 kcal of heat and done 500 J of work is

Options:

A) 6400 J

B) 5400 J

C) 7900 J

D) 8900 J

976

MediumNEET2009

In thermodynamic processes which of the following statements is not true ?

Options:

A) In an isochoric process pressure remains constant.

B) In an isothermal process the temperature remains constant.

C) In an adiabatic process PV $\gamma $ = constant.

D) In an adiabatic process the system is insulated from the surroundings.

977

MediumNEET2008

At 10 o C the value of the density of a fixed mass of an ideal gas divided by it pressure is x. At 110 o C this ratio is

Options:

A) {{10} \over {110}}x

B) {{283} \over {383}}x

C) x

D) {{383} \over {283}}x

978

MediumNEET2008

If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closed cyclic process, then

Options:

A) E = 0

B) Q = 0

C) W = 0

D) Q = W = 0

979

MediumNEET2007

An engine has an efficiency of 1/6. When the temperature of sink is reduced by 62 o C, its efficiency is doubled. Temperatures of the source is

Options:

A) 37 o C

B) 62 o C

C) 99 o C

D) 124 o C.

980

MediumNEET2006

A Carnot engine whose sink is at 300 K has an efficiency of 40%. By how much should the temperature of source be increased so as to increase its efficiency by 50% of original efficiency ?

Options:

A) 380 K

B) 275 K

C) 325 K

D) 250 K

981

MediumNEET2006

The molar specific heat at constant pressure of an ideal gas is (7/2) R. The ratio of specific heat at constant pressure to that at constant volume is

Options:

A) 9/7

B) 7/5

C) 8/7

D) 5/7

982

MediumNEET2005

Which of the following processes is reversible?

Options:

A) Transfer of heat by conduction

B) Transfer of heat by radiation

C) Isothermal compression

D) Electrical heating of a nichrome wire.

983

MediumNEET2005

An ideal gas heat engine operates in Carnot cycle between 227 o C and 127 o C. It absorbs 6 $ \times $ 10 4 cal of heat at higher temperature. Amount of heat converted to work is

Options:

A) 4.8 $ \times $ 10 4 cal

B) 6 $ \times $ 10 4 cal

C) 2.4 $ \times $ 10 4 cal

D) 1.2 $ \times $ 10 4 cal.

984

MediumNEET2004

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be (where R is the gas constant)

Options:

A) PV = (5/32)RT

B) PV = 5RT

C) PV = (5/2)RT

D) PV = (5/16) RT

985

MediumNEET2004

One mole of an ideal gas at an initial temperature of T K does 6R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be

Options:

A) (T + 2.4) K

B) (T $-$ 2.4) K

C) (T + 4) K

D) (T $-$ 4) K

986

MediumNEET2003

An ideal gas heat engine operates in a Carnot cycle between 227 o C and 127 o C. It absorbs 6 kcal at the height temperature. The amount of heat (in kcal) converted into work is equal to

Options:

A) 4.8

B) 3.5

C) 1.6

D) 1.2

987

MediumNEET2002

The efficiency of Carnot engine is 50% and temperature of sink is 500 K. If temperature of source is kept constant and its efficiency raised to 60%, then the required temperature of sink will be

Options:

A) 100 K

B) 600 K

C) 400 K

D) 500 K

988

MediumNEET2001

A scientist says that the efficiency of his heat engine which work at source temperature 127 o C and sink temperature 27 o C is 26%, then

Options:

A) it is impossible

B) it is possible but less probable

C) it is quite probable

D) data are incomplete.

989

MediumNEET2000

To find out degree of freedom, the expansion is

Options:

A) f = {2 \over {\gamma - 1}}

B) f = {{\gamma + 1} \over 2}

C) f = {2 \over {\gamma + 1}}

D) f = {1 \over {\gamma + 1}}

990

MediumNEET2000

The (W/Q) of a Carnot engine is 1/6, now the temperature of sink is reduced by 62 o C, then this ratio becomes twice, therefore the initial temperature of the sink and source are respectively

Options:

A) 33 o C, 67 o C

B) 37 o C, 99 o C

C) 67 o C, 33 o C

D) 97 K, 37 K

991

MediumVITEEE2025

When the ideal monoatomic gas is heated at constant pressure fraction of heat energy supplied which increases the internal energy of gas is

Options:

A) \frac{2}{5}

B) \frac{3}{5}

C) \frac{3}{7}

D) \frac{3}{4}

992

MediumVITEEE2025

Two identical long solid cylinders are used to conduct heat from temperature T_1 to temperature T_2. Originally, the cylinders are connected in series and the rate of heat transfer is H. If the cylinders are connected in parallel, then the rate of heat transfer will be

Options:

A) \frac{\mathrm{H}}{4}

B) 2 H

C) 4 H

D) 8 H

993

MediumVITEEE2025

A flask contains argon and chlorine in the ratio of 2: 1 by mass, the temperature of mixture is 27^{\circ} \mathrm{C}, the ratio of root mean square ( U_{\mathrm{rms}} ) of the molecule of two gases (Given, Atomic mass of argon =39.9 v, Molecular mass of chlorine =70.9 u )

Options:

A) \frac{2}{3}

B) 0.1

C) \frac{10}{3}

D) 1.33

994

MediumVITEEE2024

Variation of internal energy with density of one mole of monoatomic gas is depicted in the below figure, corresponding variation of pressure with volume can be depicted as (assuming the curve is rectangular hyperbola)

Options:

995

MediumVITEEE2024

Two different ideal diatomic gases A and B are initially in the same state. A and B are then expanded to same final volume through adiabatic and isothermal process, respectively. If p_A, p_B and T_A, T_B represent the final pressures and temperatures at A and B respectively, then

Options:

A) p_A< p_B and T_A< T_B

B) p_A>p_B and T_A>T_B

C) p_A>p_B and T_A< T_B

D) p_A< p_B and T_A>T_B

996

MediumVITEEE2024

A cyclic process for 1 mole of an ideal is shown in the V-T diagram. The work done in A B, B C and C A respectively is

Options:

A) 0, R T_2 \ln \left|\frac{V_1}{V_2}\right|, R\left(T_2-T_1\right)

B) R\left(T_1-T_2\right), O_1 R T_1 \ln \left|\frac{V_1}{V_2}\right|

C) 0, R T_2 \ln \left|\frac{V_1}{V_2}\right|, R\left(T_1-T_2\right)

D) 0, R T_2 \ln \left|\frac{V_2}{V_1}\right|, R\left(T_2-T_1\right)

997

MediumVITEEE2023

A copper sphere cools from $82^{\circ} \mathrm{C} to 50^{\circ} \mathrm{C} in 10 minutes and to 42^{\circ} \mathrm{C} in the next 10 \mathrm{~min}$. Calculate the temperature of the surrounding?

Options:

A) 18.01^{\circ} \mathrm{C}

B) 39.3^{\circ} \mathrm{C}

C) 10.6^{\circ} \mathrm{C}

D) 20^{\circ} \mathrm{C}

998

MediumVITEEE2023

Two gases occupy two containers $A and B. The gas in A of volume 0.20 \mathrm{~m}^3, exerts a pressure of 1.40 \mathrm{~MPa} and that in B, of volume 0.30 \mathrm{~m}^3 exerts a pressure of 0.7 \mathrm{~MPa}$. The two containers and united by a tube of negligible volume and the gases are allowed to exchange. Then, if the temperature remains constants. the final pressure in the container will be (in MPa).

Options:

A) 0.70

B) 0.98

C) 1.40

D) 2.1

999

MediumVITEEE2023

0.5 mole of an ideal gas at constant temperature $27^{\circ} \mathrm{C} kept inside a cylinder of length L and cross-section A closed by a massless piston. The cylinder is attached with a conducting rod of length L_1 cross-section area (1 / 9) \mathrm{m}^2 and thermal conductivity k_1 whose other end is maintained at 0^{\circ} \mathrm{C}. If piston is moved such that rate of heat flow through the conduction rod is constant then velocity of piston when it is at height L / 2$ from the bottom of cylinder is (neglect any kind of heat loss from system)

Options:

A) (\mathrm{k} / R) \mathrm{m} / \mathrm{s}

B) (\mathrm{k} / 10 R) \mathrm{m} / \mathrm{s}

C) (\mathrm{k} / 100 R) \mathrm{m} / \mathrm{s}

D) (\mathrm{k} / 1000 R) \mathrm{m} / \mathrm{s}

1000

MediumVITEEE2022

An electrically heated coil is immersed in a calorimeter containing $360 \mathrm{~g} of water at 10^{\circ} \mathrm{C}. The coil consumes energy at the rate of 90 \mathrm{~W}. The water equivalent of calorimeter and coil is 40 \mathrm{~g}. The temperature of water after 10 \mathrm{~min}$ is

Options:

A) 4.214^{\circ} \mathrm{C}

B) 42.14^{\circ} \mathrm{C}

C) 30^{\circ} \mathrm{C}

D) 45.18^{\circ} \mathrm{C}

1000

Total Questions

163

Easy

835

Medium

Hard

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