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

💡 Solution & Explanation

Molar heat capacity $C = \frac{dq}{dT} = \frac{dU + dW}{dT}$. Since $dU = C_v dT = \frac{R}{\gamma-1}dT$ and $dW = R(1-\alpha)dT$, adding them gives $C = \frac{R}{\gamma-1} + R(1-\alpha)$.