An ideal monoatomic gas undergoes the following two-step cyclic process:
Step 1: Starting at state A with pressure PA, volume VA, and temperature TA, the gas is compressed quasistatically and isothermally to state B with volume VB (VB<VA).
Step 2: From state B, the gas is allowed to expand adiabatically and irreversibly back to its original volume VA by suddenly reducing the external pressure to zero (a free expansion against vacuum). At the end of this expansion the gas returns to its initial pressure PA and volume VA, but its temperature is now TC.
Assume ideal-gas behavior and neglect any heat exchange with the surroundings during Step 2.
(1) Derive an expression for the entropy change of the gas during Step 1 in terms of VA and VB.
(2) Determine the sign of the entropy change of the gas during Step 2. Explain your reasoning qualitatively, citing appropriate thermodynamic principles.
(3) Calculate the total entropy change of the universe over the complete cycle (Steps 1 and 2 combined).
(4) Based on your result in part (c), discuss whether this two-step cycle could serve as the working cycle of a reversible heat engine. Support your answer with thermodynamic arguments.