Question 340: Thermodynamics & KTG

Question

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 :

Accepted Answer

From P-V diagram,
Given PV
1/2
= constant ...... (1)
We know that
PV = nRT
$$P \propto \left( {{T \over V}} \right)$$
Put in equation (1)
$$\left( {{T \over V}} \right){(V)^{1/2}}$$ = constant
$$T \propto {V^{1/2}}$$
$$ \Rightarrow $$ $${{{T_2}} \over {{T_1}}} = \sqrt {{{{V_2}} \over {{V_1}}}} $$
$$ \Rightarrow $$ $${{{T_2}} \over {{T_1}}} = \sqrt {{{2{V_1}} \over {{V_1}}}} $$ [As V
2
= 2V
1
]
$$ \Rightarrow $$ $${{{T_2}} \over {{T_1}}} = \sqrt 2 $$

Answer

$$\sqrt 2 $$

Answer

$${1 \over {\sqrt 2 }}$$

Answer

$${1 \over 2}$$

Answer

2

Thermodynamics & KTG

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 :

Choose the correct answer: