4. Einstein Solid. In this problem we revisit the Einstein solid discussed in the first problem set. The Einstein model of a solid composed of N atoms consists of 3N independent quantum harmonic oscillators, all with the same frequency w (3N oscillators because every atom can oscillate along three independent axes). Recall that the energy of a single harmonic oscillator in a state with n oscillator quanta is En = ( n + 1/1) hw a) Find the partition function of the Einstein solid. b) Find the average energy. c) Find the heat capacity Cy. (2) d) Show that at high temperatures, the Einsten model correctly predicts the Dulong-Petit law for the heat capacity of a solid, Cy=3NkB Where N is the number of oscillators/atoms.