More fun with the Ideal Fermi gas in two dimensions
Consider the same two-dimensional, ideal Fermi gas that you dealt with in the previous assignment. You will need the result of that assignment to do this one.
1. Calculate the average number of particles as a function of μ exactly. (This is one of the few problems for which this can be done.)
2. Calculate μ as a function of N and T. Then find the high- and low-temperature behavior of μ.