ABSTRACT
These are just some of the more important kinds of energy that molecules can have. We shall now see how some of these forms of energy, possessed by individual atoms or molecules, affect the thermodynamic properties (e.g. heat capacity or entropy) of systems formed from enormously large numbers of such molecules. (In referring to collections of molecules in large numbers I shall usually use the word ‘assembly’ to emphasise that it is made up of large numbers of individual molecules. This is in contrast to the word ‘system’ used in discussing thermodynamic properties where the emphasis was on the singleness of the entity.) We shall assume from the beginning - and this is a very important but very reasonable assumption - that the thermodynamic quantity U, i.e. the internal energy of a system, is just the total mechanical energy, potential and kinetic, of all the atoms and molecules composing it. (In the statistical treatment which follows I shall denote this energy by E simply to conform to the usage common in other books.)
A specific example
As our first introduction to the methods of statistical mechanics let us consider a specific and simple example. (This follows the lines of one given by Boltzmann in a paper of 1877 in which he explains very clearly his statistical interpretation of entropy.)*
Consider an assembly of seven identical atoms and suppose that each atom can take on only certain definite energies: 0, E, 2&, 3c, 4~ etc. This limitation on the possible values of the energy of atoms or molecules is characteristic of quantum mechanics; in classical mechanics, of course, a particle would have a continuous range of energies.
