To calculate an average property such as the average energy, pressure, heat capacity and so on we need to calculate teh probability for populatio of each energy level in a aystem. The thermodynamic averages are the sum of the thermodynamic value in each level weighted by the population of that level. We have seen how to do this for a two level system. In general, if we have N levels there will be N terms in the denominator of the probabilty. We call the denominator the partition function. One may think of the partition function as the average number of populated levels at a given temperature. The case that is of particular interest for the Planck law is a system of evenly spaced energy levels that extends to infinity. We can call this an energy ladder. We need to consider how to calculate the partition function and the average energy for the energy ladder.
