What is the molar heat capacity of the gas in the process? — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

The process follows $P \propto V \implies PV^{-1} = \text{const}$, which represents a polytropic process with index $n = -1$. The heat capacity is $C = C_v + \frac{R}{1 - n} = \frac{R}{\gamma - 1} + \frac{R}{1 - (-1)} = \frac{R}{\gamma - 1} + \frac{R}{2} = \frac{2R + R(\gamma - 1)}{2(\gamma - 1)} = \frac{R(\gamma + 1)}{2(\gamma - 1)}$.