Two moles of an ideal gas are cooled isochorically and then expanded isobarically to lower the gas t

Question

Two moles of an ideal gas are cooled isochorically and then expanded isobarically to lower the gas temperature back to the initial value. If in this process the gas pressure changed $n$ times ($n>1$), the entropy increment of the gas is:

Professor PC Thomas Classes · Answer

Initial state $(P_0, V_0, T_0)$. Process 1 (Isochoric): $P$ drops to $P_0/n$. Process 2 (Isobaric): $T$ returns to $T_0$. Final state $(P_0/n, nV_0, T_0)$. Since $T_f = T_i$, overall process is effectively isothermal. $\Delta S = 2 R \ln(V_f/V_i) = 2 R \ln n = 2R \ln n$.