Consider two systems, A and B, both consisting of 105 independent, indistinguishable particles. System A consists of 3 energy levels of energy 0, , 2, and corresponding degeneracies of 1, 10, 100, while system B consists of 5 energy levels of energy 0, , 2, 4, 5, and corresponding degeneracies of 1, 5, 10, 30, 80.

1.Provide the molecular partition functions for the two systems as the function of T.

2. How many particles are in each level at the temperatures where the populations at respective levels 2 and 3 are equal?

3. Determine the entropies of the systems as a function of T.

4. At which temperature (in terms of /k) are the two systems in thermal equilibrium?