One mole of an ideal gas undergoes a reversible process: , where and are constants. If its volume in — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

$P = \frac{RT}{V} = R\left(\frac{T_o}{V} + \alpha\right)$. Work $W = \int_{V_1}^{V_2} P dV = R T_o \ln\left(\frac{V_2}{V_1}\right) + R\alpha(V_2 - V_1)$. Internal energy $\Delta U = C_V \alpha(V_2 - V_1)$. Total heat $Q = \Delta U + W = (C_V + R)\alpha(V_2 - V_1) + R T_o \ln\left(\frac{V_2}{V_1}\right) = C_P \alpha(V_2 - V_1) + R T_o \ln\left(\frac{V_2}{V_1}\right)$.