Generalized Theory of Condensing Systems
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概要
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The theory in the previous paper II, which has dealt with the two-phase separation in condensing systems on the basis of the "cluster " concept and by means of a mathematically rigorous method, is generalized to the case of systems with volume-dependent cluster integrals. The cluster integrals are assumed to satisfy several mathematical conditions, which are considered to represent the essential features of the real systems. One of these conditions is concerned with the effects of the volume dependence of the cluster integrals composed of a comparatively small number of molecules. Another essential condition is that the contribution, per molecule, to a cluster integral in which the number i of the constituent molecules is infinitely large and of the same order as the volume V of the system, should be definite, finite, and independent of the volume per molecule, V / l, in a certain range. By means of a function l(N) which satisfies certain conditions, the sizes of clusters are classified into "large" [l>l(N)] and "small" [l≦l(N)]. The "small" cluster part of the system in consideration and that of the "(0)-system" (i. e. a system with volume-independent cluster integrals) are proved to be practically equivalent. Then, after some discussions of the "large" clusters, it is proved that, in a certain range of the specific volume, the isotherm is horizontal and a "huge" cluster (i. e. a cluster of size comparable to the volume of the system) coexists with the saturated set of" small" clusters. This corresponds to the liquid-vapour coexistence range. And it is proved that, in the gas range. the system is thermo-dynamically equivalent to the (0)-system and has practically no "large" clusters. A remark is given on the analytical properties of the singularity representing the condensation. It is noted that the present theory applies to both the cases of "analytical" singularity and of "non-analytical" singularity. A non-rigorous treatment which leads to the same results as those in the text, is given in the Appendix.
- 理論物理学刊行会の論文
- 1966-07-31
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関連論文
- Cluster Theory of Condensing Systems
- Generalized Theory of Condensing Systems
- Some Remarks on the Born-Green-Rodriguez Theory of Condensation
- Generalized Theory of Condensing Systems
- On the Theory of Condensation