A gas consisting of rigid diatomic molecules was expanded in a polytropic process so that the rate o — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Rate of collision against the wall per unit area $Z_w \propto \frac{\sqrt{T}}{V}$. For $Z_w$ to remain constant, $T^{1/2}V^{-1} = \text{const} \implies TV^{-2} = \text{const}$. This implies a polytropic process $TV^{n-1} = \text{const}$ where $n-1 = -2 \implies n = -1$. The molar heat capacity $C = C_V + \frac{R}{1-n} = \frac{5}{2}R + \frac{R}{1 - (-1)} = \frac{5}{2}R + \frac{1}{2}R = 3R$. Using $R = 2\text{ cal/K-mol}$, $C = 3 \times 2 = 6\text{ cal/K-mol}$.