One can show that for an Einstein solid containing N oscillators and q energy units, the multiplicity is approximately: 2(N,q) {(q+N)/q}{(q+N)/N}N. a) Starting with this formula, find an expression for the entropy of an Einstein solid as a function of N and q. b) Use the result of part (a) to calculate the temperature of an Einstein solid as a function of its energy. (The energy is U = q ɛ, where & is a constant.) Simplify your answer as much as possible. c) Invert the relation you found in part (b) to find the energy as a function of temperature, then differentiate to find a formula for the heat capacity. d) Show that, in the limit Too, the heat capacity is C = N KB. (Hint: when x is very small then ex1+x.) Is this the result you would expect? Explain.