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

💡 Solution & Explanation

Molar heat capacity $C = \frac{q}{n\Delta T}$. Given $\Delta U = n C_v \Delta T = \frac{nR}{\gamma-1}\Delta T$, we can substitute $n\Delta T = \frac{\gamma-1}{R}\Delta U$. Then $C = \frac{\Delta U (1 + \frac{\gamma-1}{\alpha})}{\frac{\gamma-1}{R}\Delta U} = \frac{R}{\gamma-1} \left(1 + \frac{\gamma-1}{\alpha}\right) = \frac{R}{\gamma-1} + \frac{R}{\alpha}$.