Pathria 7.4. This problem gets you more comfortable with the Bose-Einstein functions. For the last part, you need a nontrivial result which is obtained in the previous problem (7.3). In your solution you may use that result as given in the statement of problem 7.3 without deriving it.

Pathria 7.20. This is a good problem for improving your understanding of blackbody radiation.

Pathria 7.34. Changing the dimensionality is another way to change the density of states. In this problem, you find the effect of this change on the phonon contribution to specific heat of solids.