The Classical Ideal Gas: Configurational Entropy

Abstract

This chapter derives the part of the entropy that is generated by the positions of particles, or the configurational entropy. The remaining part of the entropy, which is generated by the momenta of the particles, is derived in Chapter 6. While both derivations are unconventional, they are based directly on an 1877 paper by Boltzmann that discusses the exchange of energy between two or more systems. The dependence of the entropy on the number of particles is derived solely by assuming that the probability of a given particle being in a specified volume is proportional to that volume. No quantum mechanics is required for this derivation, and the result is valid for both distinguishable and indistinguishable particles.