Q 11-11-065JEE MainJEE Main 2024 (6 Apr, Shift 1)Hard
The specific heat at constant pressure of a real gas obeying the equation $PV^2 = RT$ is
Answer: (C) $C_V + \dfrac{R}{2V}$
At constant pressure, $C_P = C_V + P\left(\dfrac{\partial V}{\partial T}\right)_P$ (per mole, with the internal energy depending only on $T$).
From $PV^2 = RT$: $2PV\,dV = R\,dT \Rightarrow P\dfrac{dV}{dT} = \dfrac{R}{2V}$.
$$C_P = C_V + \frac{R}{2V}$$
Solution by Sreeraj P, M.Sc Physics