Q 11-11-126JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
$1$ mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{xR}{8}$. The value of $x$ is [$R$ universal gas constant]
Numerical value type. Enter your answer.
Answer: 25
First law: $\Delta U = Q - W = \dfrac{4Q}{5}$.
For a rigid diatomic gas, $\Delta U = \dfrac{5}{2}R\,\Delta T$ (1 mole), so $\Delta T = \dfrac{8Q}{25R}$.
$$C = \frac{Q}{\Delta T} = \frac{25R}{8} \Rightarrow x = 25$$
Solution by Sreeraj P, M.Sc Physics