Suppose an Einstein Solid is in equilibrium with a reservoir at some temperature T. Assume the ground state energy is 0, the solid is composed of N oscillators, and the size of an energy "unit" is e. (a) Find the partition function for a single oscillator in the solid, Z1. Hint: use the general series summation formula 1+ x + x? + x³ + ... = 1/ (1- x) (b) Find an expression for , the average energy per oscillator in the solid, in terms of kT and e. (c) Find the total energy of the solid as a function of T, using the expression from part (b).

Suppose an Einstein Solid is in equilibrium with a reservoir at some temperature T. Assume the ground state energy is 0, the solid is composed of N oscillators, and the size of an energy "unit" is e. (a) Find the partition function for a single oscillator in the solid, Z1. Hint: use the general series summation formula 1+ x + x? + x³ + ... = 1/ (1- x) (b) Find an expression for , the average energy per oscillator in the solid, in terms of kT and e. (c) Find the total energy of the solid as a function of T, using the expression from part (b).