From heat capacity data one can calculate a set of energy moments for any system. Using the maximum-entropy method, these energy moments can be used to construct an approximate energy probability distribution which, in turn, can be used to calculate the density of states as a function of energy. The density of states is a temperature independent function from which the free energy, internal energy, entropy, and heat capacity for the system can be obtained plus the energy probability distribution and its potential at any temperature. We compare the behavior of the density of states for various substances in a single phase and as one goes through different types of phase transition.