The Classical Ideal Gas: Energy Dependence of Entropy

The energy-dependence of the entropy of the configurational contributions is derived by considering the exchange if energy is exchanged between two or more systems. The argument is analogous to that given in Chapter 5 for the configurational contributions to the entropy. The derivation requires evaluating the area and volume of an $n$-dimensional sphere, which is carried out explicitly. The entropy is calculated within the approximation that the width of the energy distribution is zero. The total entropy is just the sum of the configurational entropy and the energy-dependent terms, as discussed in Section 4.1. The significance of the non-zero width of the true energy distribution will be addressed in Chapter 21.