Question: EXERCISE 7.1. An Einstein solid consists of a lattice in three- dimensional space with N lattice sites. Each lattice site contains three harmonic oscillators (one

EXERCISE 7.1. An Einstein solid consists of a lattice in three- dimensional space with N lattice sites. Each lattice site contains three harmonic oscillators (one for each direction in space), each of which has frequency w. Neither the lattice sites nor the harmonic oscillators are coupled to one another. The total energy of the lattice is H = hwnit Nhw=E, where n, is the number of quanta of energy on the ith harmonic oscillator. The total number of quanta on the lattice is fixed at M = ni. Assume that M and N are very large.

(a) What is the total number of microscopic states with energy E?

(b) Compute the entropy as a function of temperature, T, and number of lattice sites, N.

(c) Compute the heat capacity of this solid. 3N

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