Q 11-11-101JEE MainJEE Main 2022 (24 Jun, Shift 2)Medium
A monoatomic gas performs a work of $\dfrac Q4$ where $Q$ is the heat supplied to it. The molar heat capacity of the gas will be ______ $R$ during this transformation, where $R$ is the gas constant.
Numerical value type. Enter your answer.
Answer: 2
$\Delta U = Q - W = \dfrac{3Q}{4}$. For a monoatomic gas $\Delta U = n\cdot\dfrac32R\,\Delta T$:
$$\frac{3Q}{4} = \frac32 nR\Delta T\ \Rightarrow\ Q = 2nR\Delta T$$
$$C = \frac{Q}{n\Delta T} = 2R$$
Solution by Sreeraj P, M.Sc Physics