Generalized Theory of Condensing Systems. VII : An Imperfect Gas Obeying the Perfect-Gas Law in the Gaseous State
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This paper theoretically discusses an imperfect gas which obeys the perfect-gas law in the gaseous state and begins to condense at a certain specific volume. The gas is defined by the simple expressions for the cluster integrals : b_1≡1, b_l=a^<-l> /V (for l≧2), where l is the number of particles composing a cluster integral (i.e., the size of a cluster), V is the volume of the gas, and a is independent of l and V but may depend on the temperature T. In the limit N(=number of particles in the gas)→∞ with v=V/N fixed, the Helmholtz free energy f per particle, the pressure p and the activity z are obtained from the partition function expressed in terms of the cluster integrals. Not all parts of the theory of systems with volume-dependent cluster integrals, which has been developed in the author's previous papers, are applicable to this gas. It is rigorously proved that, for 0<v<a^<-1>, the p-v isotherm is horizontal, z has a constant value a, and at equilibrium a "huge" (i.e., macroscopic-sized) cluster, representing the liquid phase, coexists with a set of clusters of size one, representing the saturated vapour, and that, for v≧a<-1>, the equation pv=kT holds and at equilibrium the gas contains only clusters of size one. Thus it is deduced that the gas condenses at the "non-analytical" singularity z=a. The uniform convergence (for v) of the thermodynamic functions is discussed. A remark is made on a similar problem in the theory of distribution of zeros of the grand partition function.
- 理論物理学刊行会の論文
- 1978-12-25
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