The way to calculate the average energy of a system is to use the
Boltzmann Distribution, which says that the probability of a
system at temperature T being in a state n is just proportional to
the Boltzmann Factor, 
, where 
is the
energy of state n and 
where k is the
Boltzmann constant.
We now show how to use the Boltzmann Distribution to calculate
the average energy of a system. We will begin with two instructive
examples. Then, we shall calculate 
using the Planck
hypothesis, which reproduces the experimental results
perfectly.