Calculating the entropy change

Question

Response to the following problem:

Suppose that we have 1mol of a monatomic gas B₁, whose nuclei are in their lowest energy state, and 1mol of a monatomic gas B₂ consisting of exactly the same atoms as B₁, except that the nuclei are in an excited state whose energy ? is much larger than k_T and whose lifetime is much larger than the time for diffusion to occur. Both gases are at the same pressure and are maintained at the same temperature T by a heat reservoir.

(a) Immediately after the nuclei of gas B₂ have been excited, diffusion takes place. Calculate the entropy change of the universe.

(b) After the nuclei of gas B₂ have been excited, a time much larger than the lifetime of the excited state is allowed to elapse, and then diffusion takes place. Calculate the entropy change of the universe.

(c) Show that the answer to part (b) is larger than that to part (a).