With what minimum pressure must a given volume of an ideal gas (), originally at 400 K and 100 kPa, — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Minimum external pressure for an irreversible adiabatic compression equals the final pressure $P_2$. Work $W = -P_2(V_2 - V_1) = n C_V(T_2 - T_1)$. Substituting yields $-P_2(\frac{T_2}{P_2} - \frac{T_1}{P_1}) = \frac{T_2-T_1}{\gamma-1}$. $-700 + 400(P_2/100) = (700-400)/0.4 \implies 4P_2 - 700 = 750 \implies P_2 = 362.5 \text{ kPa}$.