(Evaluating reversibility of a composite two-step path)
(a) An ideal monatomic gas initially at 300 K and 1.0 atm undergoes the following two-step path:
Step A: Free expansion into vacuum doubling its volume; no heat is exchanged with the surroundings.
Step B: The gas is then compressed quasi-statically and isothermally at 300 K back to its original volume by placing it in contact with a large reservoir at 300 K.
(b) (i) Determine the sign of the entropy change of the gas, of the surroundings, and of the universe for each step separately.
(c) (ii) Compute the net entropy change of the universe for the complete two-step path.
(d) (iii) Classify each individual step and the overall path as reversible or irreversible, giving clear reasons.
(e) (iv) Explain whether it is possible to restore both the gas and the surroundings to their original states without leaving any additional change in the universe.