Question 193: Thermodynamics & KTG

Question

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 :

Accepted Answer

In an adiabatic process, the key characteristics for a monoatomic gas are:
No Heat Exchange
: The adiabatic process occurs without heat transfer, meaning $ Q = 0 $.
Work Done and Internal Energy Change
: The work done on or by the system is equal to the change in internal energy. Mathematically, this is expressed as:
$    \Delta U = -W    $
where $\Delta U$ is the change in internal energy and $W$ is the work done.
Work and Temperature Relationship
: The work done when changing the temperature from $ T_1 $ to $ T_2 $ is proportional to the difference between these temperatures. This relationship can be expressed as:
$    |	ext{Work Done}| = nC_v \Delta T \propto (T_2 - T_1)    $
Here, $ n $ is the number of moles, $ C_v $ is the molar heat capacity at constant volume, and $\Delta T$ is the change in temperature.
From these characteristics, the correct features of an adiabatic process in a monoatomic gas relate to the relationships involving work done and temperature change, specifically options (B) and (E).

Answer

(B), (D) only

Answer

(B), (E) only

Answer

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

Answer

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

Thermodynamics & KTG

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