Viewing smoke under high magnification we see that smoke in fact consists of individual particles in motion. We cannot see individual particles in a gas but they also consist of atoms or molecules in motion. What makes this motion unusual to us is that we cannot identify a cause for the motion as we could when we studied the mechanics of macroscopic bodies. Because of the daunting number of atoms in even the smallest volume of gas it is essentially meaningless and uninteresting to identify the cause of any specific event or motion which occurs. We must be satisfies to say that because there is internal energy in the system there is motion and then proceed to develop a statistical description of this motion. The main accomplishments of our version of this statistical analysis shall be the derivation of expressions for the heat capacity of the ideal gas and also solids and liquids in a certain high temperature limit