JEE Main 2024 — Kinetic Theory of Gases Question with Solution

$\begin{aligned} & \mathrm{dQ}=\mathrm{du}+\mathrm{dW} \\ & \mathrm{CdT}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}+\mathrm{PdV} \\ & \therefore \mathrm{PV}^2=\mathrm{RT} \\ & \mathrm{P}=\text { constant } \\ & \mathrm{P}(2 \mathrm{VdV})=\mathrm{RdT} \\ & \mathrm{PdV}=\frac{\mathrm{RdT}}{2 \mathrm{~V}} \\ & \end{aligned}$
Put in equation (1) $\mathrm{C}={\mathrm{C}}_{\mathrm{V}}+\frac{\mathrm{R}}{2\mathrm{V}}$