Chemistry 2720 Practice Problems on Statistical Thermodynamics

1. Suppose that a system has a ground state with degeneracy W and that there are no accessible higher-energy states. Show that the entropy of this system is just . (This is the Boltzmann formula for the entropy. In addition to the simple system described here, the Boltzmann formula gives the entropy of a system of known total energy and volume. In that case, W is the number of different ways of rearranging the system without changing the energy or volume.)
2. 1. Consider a two-level system in which neither energy level is degenerate. Let the upper level have an energy relative to the lower level. At what temperature does the population in the upper level become significant relative to that of the lower level?
   2. Work out the internal energy and entropy of this system.