A sample of ideal gas initially at temperature T expands from volume V1 to V2>V1 by two different paths.
• Path A: a slow, reversible, isothermal expansion.
• Path B: a rapid, adiabatic free expansion into a vacuum so that the temperature afterward is also T.
Which of the following correctly compares the entropy changes for the two paths?
(a) The system entropy increase is larger for Path B, and the total entropy increase of the universe is larger for Path A.
(b) The system entropy increase is larger for Path A, while the total entropy increase of the universe is the same for both paths.
(c) The system entropy increase is the same for both paths, but the total entropy increase of the universe is larger for Path B.
(d) The system entropy increase is zero for both paths because the temperature is the same, and the total entropy increase of the universe is zero as well.