An ideal gas with the adiabatic exponent goes through a process: , where and are positive constants — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

For maximum entropy, $dS = \frac{C_V dT + P dV}{T} = 0$. Using $T = \frac{P_o V - \alpha V^2}{R}$, $dT = \frac{P_o - 2\alpha V}{R} dV$. Substituting yields $C_V(P_o - 2\alpha V) + R(P_o - \alpha V) = 0$. Since $R = C_P - C_V$, divide by $C_V$ to get $(P_o - 2\alpha V) + (\gamma - 1)(P_o - \alpha V) = 0 \implies \gamma P_o - (\gamma + 1)\alpha V = 0 \implies V = \frac{\gamma P_o}{\alpha (\gamma + 1)}$.