The energy levels of a localized particle are 0, epsilon , and 2 epsilon . The middle level is doubly degenerate and the other levels are nondegenerate.

A) Write and simplify the partition function.

B) Find the total energy, the heat capacity, and the entropy of a system of these particles. Sketch these properties as a function of the temperature and compare them with the corresponding properties of the spin -1/2 system.