Generalized Theory of Condensing Systems. III : Uniform Convergence of Thermodynamic Functions
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概要
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The uniform convergence with respect to ν (the volume per molecule) is discussed for the thermodynamic functions-especially N^<-1> 1nΩN, ΩN being the configurational partition function-when N (the number of molecules) tends to infinity, with a view to obtaining the physical reasonableness and the mathematical completeness of the convergence arguments in the previous papers^<1), 2), 3)> on the theory of condensing systems. The discussion yields also a basis for the commutability of the two operations N→∞ and ∂ / ∂υ in calculating the limiling pressure for an infinite system. The systems that are treated are the (0)-system, whose cluster integrals are volume-independent, and the G-system, whose cluster integrals are volume-dependent and satisfy the G-condition introduced in the previous paper.^<3)> Several lemmas and theorems (concerning the cluster integrals bτ^<(0)> and bτ(V)) proved in the previous papers for the (0)- and the G-system are altered into lemmas and theorems containing the statements of the uniform convergence. The following conclusions are obtained: In the region (υ≦υ_s) of two-phase coexistence for the (0)-system, N^<-1> 1n ΩN converges to Συbτ^<(0)>z^τ_s-1nz_s uniformly for υ'≦υ≦υ_s, υ' being any positive real number. In the gaseous state (υ≧υ_s) of the (0)-system, N^<-1> 1nΩN converges to Συb_τ^(0)z^τ-1nz uniformly for υ_s≦υ≦υ_2, υ_2 being any positive real number. Thus, for the (0)-system, N^<-1> 1nΩN converges uniformly in the wider sense for 0<υ<+∞. In the region I(υ^<υ<υcond) of two-phase coexistence for the G-system, N^<-1> 1nΩN converges to Συb_τ^<(0)>z^τcond-1n zcond uniformly in the wider sense for υ<υ<υcond. In the gaseous state (υ≧υcond) of the G-system, N^<-1> 1nΩN converges to Συb_ι^<(0)>z^ι-1nz uniformly for υcond≦υ≦υ_2, υ_2 being any positive real number. The present paper also contains a method of treating the gaseous state (for the (0)- and the G-system) different from the methods in the previous papers.
- 理論物理学刊行会の論文
- 1966-07-31
著者
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Nakazawa Teruko
Department Of Electronics Faculty Of Engineering Kyusyu University Hukuoka.
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Ikeda Kazuyosi
Department Of Applied Physics Faculty Of Engineering Osaka University
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Kawasima Teruko
Department Of Electronics Faculty Of Engineering Kyusyu University Hukuoka.
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Kawasima Teruko
Department of Electronics, Faculty of Engineering, Kyusyu University, Hukuoka.
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Ikeda K.
Department of Applied Physics, Faculty of Engineering, Osaka University
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Ikeda K.
Department of Applied Physics, Faculty of Engineering Osaka University
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