ABSTRACT

So far we have been considering only the occupation numbers of the various energy levels at equilibrium. From this we have been able to deduce information about the thermal energy and heat capacity of a simple model. Now however we will return to some more general properties with a view to interpreting the entropy of an assembly in terms of these distribution numbers. Before considering the entropy, however, let us examine the parameter /3 (in equations (59) and (60)) more carefully and convince ourselves that it must be closely related to the temperature. To do this, we shall consider briefly what happens if two different assemblies (of localised elements) are allowed to exchange energy with each other. Let assembly A have N molecules, each of which may have energy cl, .s2, &3 etc., and let assembly B have M molecules, each of which may have energies ql, n2, n3 etc. Consider now a typical distribution in which in assembly A

nl molecules have energy cl n2 molecules have energy ~2 . . .