At what value of will the heat capacity be negative? — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Set the heat capacity equation less than zero: $\frac{R}{\gamma-1} + R(1-\alpha) < 0$. Factoring out $R$ and rearranging: $\frac{1}{\gamma-1} + 1 < \alpha \implies \frac{1 + \gamma - 1}{\gamma-1} < \alpha \implies \alpha > \frac{\gamma}{\gamma-1}$.