Partition function problems

The partition function is used to calculate the average number of occupied energy levels in a system. It is a normalization factor for statistical calculations. It is temperature dpendent. At T = 0 K the partition function is equal to the degeneracy of the ground state. At infinite temperature the partition function is equal to the total number of energy levels. One can use the partition function to calculated averaged properties, such as energy, pressure etc. If the number of energy levels is infinite then the high temperature limit of the average energy is kT.