The Heat of Expansion of a Gas of Varying Mass

Abstract

In this paper equations are given for the direct treatment of experiments in which not only heat, but also masses, pass the boundary of the container of the system during the experiment. The theoretical development is correlated with the treatment of Gibbs, and certain difficulties, mentioned by others, in the physical interpretation of his equations, are incidentally removed. It was found possible, within a reasonable time, to cause a gas to expand slowly enough from a calorimeter to simulate a reversible expansion, and the special equation developed for the heat of expansion with the aid of the Beattie-Bridgeman equation of state was verified by the results for the slow expansion of carbon dioxide and ammonia. In the case of carbon dioxide the effect of the deviations from the ideal gas law was to make the heat effect in excess of that calculated for an ideal gas by a sufficient amount so that the excess itself could be calculated within about 7 percent. A series of expansions of carbon dioxide was carried out at varying rates of flow, some as fast as permissible. The results, correlated by means of an empirical relation, serve to show that the results of the slow expansions correspond practically to an infinitely slow expansion. They also indicate that the heat effect for an infinitely rapid expansion is not zero for a real gas, but possibly vanishes with the pressure. In the absence of a perfectly sound method of calculating the heat effect for an infinitely fast expansion, a method is suggested which has at least the merit of agreement with the present experiments. The bearing of the results on variable-pressure calorimetry, as practiced in experiments on the heat of adsorption, is briefly discussed.

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“…In his two-part paper (1875, 1878), Gibbs used the idea of open systems, but only for defining the chemical potential in statistical mechanics [84], [85], [97]. At about the same time as Lotka, also Bauer studied open systems independently [98].…”

A discussion of the first law of thermodynamics for open systems

“…The energies o[ different homogeneous systems o/ the same ] pressure, temperature and constitution are proportional to I (2) the masses o/the systems.…”