Serway & Jewett — Heat Engines, Entropy, and the Second Law of Thermodynamics: Problem 38

A system consisting of $n$ moles of an ideal gas with molar specific heat at constant pressure $C_P$ undergoes two reversible processes. It starts with pressure $P_i$ and volume $V_i$, expands isothermally, and then contracts adiabatically to reach a final state with pressure $P_i$ and volume $3V_i$. (a) Find its change in entropy in the isothermal process. (The entropy does not change in the adiabatic process.) (b) What If? Explain why the answer to part (a) must be the same as the answer to Problem 46. (You do not need to solve Problem 46 to answer this question.)