Conceive a system composed of a very large number N of distinguishable atoms at rest and mutually noninteracting, each of which has only two (nondegenerate) energy levels:0,ε>0 Let E / N be the mean energy per atom in the limit N→∞.

a) What is the maximum probable value of E/N if the system is not necessarily in thermodynamic equilibrium? What is the utmost attainable value of E/N if the system is in equilibrium (at positive temperature)?

b) For thermodynamic equilibrium calculate the entropy per atom S/N as a function of E/N.