Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant.…

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 charge 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 :
  1. (A), (C), (D) only
  2. (A), (C), (E) only
  3. (B), (E) only
  4. (B), (D) only

Solution

$\begin{aligned} & \mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}=0 \Rightarrow-\Delta \mathrm{U}=\mathrm{W} \\ & \mathrm{WD}=-\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T} \Rightarrow|\mathrm{WD}|=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T} \propto \mathrm{T}_2-\mathrm{T}_1\end{aligned}$
$\therefore \mathrm{B} \& \mathrm{E}$ [Only possibility]

Asked in: JEE Main 2025 (02 Apr Shift 2)

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