Posted by
**martin** on
.

Consider a system of N identical particles. Each particle has two energy levels: a ground

state with energy 0, and an upper level with energy . The upper level is four-fold degenerate

(i.e., there are four excited states with the same energy ).

(a) Write down the partition function for a single particle.

(b) Find an expression for the internal energy of the system of N particles.

(c) Calculate the heat capacity at constant volume of this system, and sketch a graph to

show its temperature dependence.

(d) Find an expression for the Helmholtz free energy of the system.

(e) Find an expression for the entropy of the system, as a function of temperature. Verify

that the entropy goes to zero in the limit T ! 0. What is the entropy in the limit

T ! 1? How many microstates are accessible in the high-temperature limit?