Gibbs' Theory of Statistical Mechanics as a Physicochemical Theory

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  • ギブスの熱力学と統計力学 : 物理化学の視点から
  • ギブス ノ ネツリキガク ト トウケイ リキガク ブツリカガク ノ シテン カラ

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Abstract

This paper reveals that Josiah Willard Gibbs (1839-1903) attempted to explain certain chemical properties of matter, such as osmotic pressure of "diaphragms" (semi-permeable membranes) and electromotive force of chemical cells, from his theory of statistical mechanics, i.e., Elementary Principles in Statistical Mechanics (1902; EPSM). To begin with, I examine his thermodynamical theory developed in "On the Equilibrium of Heterogeneous Substances" (1876/78; EHS). Later, I attempt to support the above claim by analyzing his theory of statistical mechanics. In EHS and his later discussions on thermodynamics, Gibbs used thermodynamics to derive various properties of matter in equilibrium. Among others, "the fundamental equations" of thermodynamics and different "conditions of equilibrium," for both of which temperature, pressure and chemical potentials were essential, played a pivotal role in explaining these properties. With these two means, Gibbs explained a wide range of physicochemical phenomena such as diaphragms and chemical cells. In EPSM, Gibbs argued that some properties of ensembles corresponding to those of thermodynamical systems can be derived. I focus, in particular, on the properties of grand canonical ensembles, because he used them to deduce a formula analogical to one of the fundamental equations of thermodynamics, and to construct an analog of a diaphragm with corresponding conditions of equilibrium. Further, he included problems of chemical cells in the scope of statistical mechanics. Therefore, Gibbs' theory of statistical mechanics can be considered as a theory that attempted to explain the physicochemical domain.

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