On the Theory of Isothermal-Isobaric Ensemble. II : Imperfect Gases and Condensation
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概要
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A system (consisting of N molecules) in the isothermal-isobaric ensemble of temperature T and pressure p is discussed from the physical viewpoint on the basis of the results of the mathematical analyses in the preceding paper I. First, for readers who wish to avoid mathematical complications, a non-rigorous, rather concise method of treatment is given which leads to the same results as those obtained by the rigorous method in I. Next, the activity of the system for N→∞ is calculated by maximizing a certain function, h(x;α), obtained in I. Two cases, p<p_s and p=p_s, turn out to be different from each other in character. For p<p_s, the system is proved to contain only "small" clusters at equilibrium (the word "small" being defined in I), and is therefore regarded as being in gaseous state. The equations for the pressure, activity, and average volume in the gaseous state are found to be identical with those in the cases of canonical ensemble grand. Forp=p_s, it is shown that a "huge" cluster [where the word "huge" is defined in a mathematically rigorous manner to mean "of the same order of magnitude as N(→∞)"] exists and may be interpreted as the liquid phase but the number of molecules composing it fluctuates between O and N; and that a set of an indeterminate (or fluctuating) number of "small" clusters coexists with the "huge" cluster and may be regarded as the saturated vopour. The fluctuation in the volume of the system for p=p_s is also deduced. Thus it is concluded that when p=p_s, a condensation occurs and it is characterized by the two-phase separation and the fluctuations in the composition of the two phases and in the volume. The condensation point in the present case is found to be the same as in the cases of canonical ensemble and grand canonical ensenble. Finally, a remark is added on the neglect of the volume dependence of the cluster integrals in the present theory.
- 理論物理学刊行会の論文
- 1967-09-25
著者
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Ikeda Kazuyosi
Department Of Applied Physics Faculty Of Engineering Osaka University
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KAMAKURA Siro
Department of Applied Physics, Faculty of Engineering Osaka University
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Kamakura Siro
Department Of Applied Physics Faculty Of Engineering Osaka University
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