In the preceding chapter it was proven that the introduction of probability considerations into the mechanical and electrodynamical theory of heat is justifiable and necessary, and from the general connection between entropy and probability , as expressed in equation [eqn:(164)] (164), a method was derived for calculating the entropy of a physical system in a given state.
Before we apply this method to the determination of the entropy of radiant heat we shall in this chapter make use of it for calculating the entropy of an ideal monatomic gas in an arbitrarily given state.
The essential parts of this calculation are already contained in the investigations of L. BoltzmannL. Boltzmann, Sitzungsber. d. Akad. d. Wissensch. zu Wien (II) 76, p. 373, 1877. Compare also Gastheorie, 1, p. 38, 1896. on the mechanical theory of heat; it will, however, be advisable to discuss this simple case in full, firstly to enable us to compare more readily the method of calculation and physical significance of mechanical entropy with that of radiation entropy, and secondly, what is more important, to set forth clearly the differences as compared with Boltzmann's treatment, that is, to discuss the meaning of the universal constant and of the finite region elements . For this purpose the treatment of a special case is sufficient.