The entropy change of 2.0 moles of an ideal gas whose adiabatic exponent , if as a result of a certa — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

$\gamma = 1.5 \implies C_V = 2R$. Temperature ratio $\frac{T_2}{T_1} = \frac{P_2 V_2}{P_1 V_1} = \left(\frac{1}{4}\right) \times 2 = \frac{1}{2}$. $\Delta S = n C_V \ln\left(\frac{T_2}{T_1}\right) + n R \ln\left(\frac{V_2}{V_1}\right) = 2(2R) \ln(0.5) + 2R \ln(2) = -4R \ln 2 + 2R \ln 2 = -2R \ln 2 = -2(8.314)(0.7) \approx -11.64 \text{ J/K}$.