A rigid, thermally insulated container is divided into two equal compartments by a thin partition. One compartment contains an ideal gas at pressure P0 and temperature T0; the other compartment is a vacuum. The partition is suddenly removed, allowing the gas to expand freely and fill the entire container. No heat is exchanged with the surroundings, and the container does no external work.
Answer the following questions.
(a) During the expansion, does the gas do macroscopic work on the surroundings? Explain.
(b) State the sign (positive, negative, or zero) of the entropy change ΔSgas of the gas and provide qualitative reasoning for your answer.
(c) State the sign of the entropy change ΔSsurroundings outside the container and justify your answer.
(d) Determine the sign of the entropy change ΔSuniverse for the entire process, and explain how your result is consistent with the second law.