Problem 7 (14 marks) The partition function of a simple harmonic oscillator in equilibrium with a Man -1 thermal bath of temperature Tis Z = Zoe kr = (1-e- KT . Use this result to find the partition function Z(N, T), and then the entropy S(N, T) of an Einstein solid of N oscillators, all of frequency w. For simplicity, consider only the high-temperature limit. Then, express the entropy as a function of the average energy E of the solid, i.e. find S(N, E). Compare with the entropy obtained as a logarithm of the multiplicity function Inn(N, q) = (N-1+q)! (N-1)!4! low = NIn, where q is the total number of quanta of the Einstein solid. Are you surprised by the result? Explain