Problem 7.2. A system consists of N noninteracting, distinguishable two-level atoms. Each atom can exist in one of two energy states, Eo = 0 or E = . The number of atoms in energy level, Eo, is no and the number of atoms in energy level, E, is n. The internal energy of this system is U = noEo + nE.

(a) Compute the entropy of this system as a function of internal energy.

(b) Compute the temperature of this system. Under what conditions can it be negative?

(c) Compute the heat capacity for a fixed number of atoms, N.