To obtain equation (9-42), we calculated a total number of fermions N as a function of EF,...

To obtain equation (9-42), we calculated a total number of fermions N as a function of EF, assuming T=0, starting with equation (9-41). But note that (9-41) is the denominator of our model for calculating average particle energy, equation (9-26). Its numerator is the total (as opposed to average particle) energy, which we'll call Utotal here. (In other words, the total system energy U is the average particle energy  times the total number of particles N.) Calculate Utotal, as a function of EF? and use this to show that the minimum (T = 0) energy of a gas of spin ½ fermions may be written