Consider a container with a partition in the middle. The container is thermally isolated from the environment. Initially one half of the container is filled with gas A (N molecules) and the other half with gas B (also N molecules). Both gases are kept at the same pressure and the same temperature: pA = pB = p0; TA = TB = T0. Then the partition is removed and the gases are allowed to mix.
(a) Assuming that the temperature of the container does not change upon mixing, calculate the entropy of the container before and after the removal of the partition.
(b) What is the entropy of mixing, ?S = SAfter – SBefore? [HINT: ?S should be positive.]
(c) The increase in entropy must mean that the volume of phase space available to each molecule has increased. Is this increase due to the volume of the “position” subspace, the volume of the “momentum” subspace, or both? Concisely explain your answer.
(d) Is this a reversible or an irreversible process? Why?