Some Remarks on the Born-Green-Rodriguez Theory of Condensation

概要

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We attempt to clarify the origin of the discrepancy in the singular point between the condensation theory of Born-Green-Rodriguez (BGR) using the integral equation method and that of Mayer using the series expansion method. We interpret the BGR theory as the approximate theory in which Mayer's "frame" is replaced by the "ring" (§2). In the framework of Mayer's theory (§3), it is shown that the maximum point of the BGR isotherm gives the condensation point, and that the characteristic temperature T_m for the BGR gas is absolute zero, and that the singular point of the BGR isotherm is analytically explainable but has no physical meaning (§§4 & 5). By applying the results of the author's previous paper to this case, the two-phase separation (the appearance of a "huge" cluster) and the horizontal line (starting from the maximum point of the isotherm) are deduced (§6). In connection with the present problem, some problems on the condensation theory are discussed : [1) A note on the integral equation method ; 2) the different interpretations of an approximation ; the rule of equal areas; van der Waals' equation ; 3) the analytical properties of the condensation point ; 4) the analytical behaviours of condensing systems ; 5) the ideal Bose-Einstein gas] (§7).
理論物理学刊行会の論文
1960-04-25