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Asymptotic expansions of the expressions for the partition function and the rotational specific heat of a rigid polyatomic molecule for high temperatures

Published online by Cambridge University Press:  24 October 2008

Irene E. Viney
Irene E. Viney
Affiliation:
Newnham College, Fellow of the University of Wales
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Extract

The partition function F(θ) is of fundamental importance in the theory of the specific heat of gases. Once it is known, the rotational specific heat of a perfect gas is given by

where R is the gram-molecular gas constant, and θ bears the relation

to the absolute temperature T, k being Boltzmann's constant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 1 , January 1933 , pp. 142 - 148
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

* Fowler, , Statistical Mechanics, p. 34 (1929).Google Scholar

† Statistical Mechanics, p. 37.

* Proc. Camb. Phil. Soc. 24, p. 280 (1928).Google Scholar

† Proc. Camb. Phil. Soc. 26, p. 402 (1930).

‡ Bieberbach, L., Lehrbuch der Funktionentheorie, vol. 1, p. 308 (1931)Google Scholar; Knopp, K., Theory and Application of Infinite Series, ch. xiv (Engl. Ed. 1928).Google Scholar

* The differentiations involved in the calculation of the Bernoulli summations are in each case long and tedious to calculate, but the actual working is quite straightforward so that only the results of it will be given in the text.

* Notice also that |P 2k| < B k/(2k)!, so that the remainder could also be expressed in terms of Bernoulli numbers.

* Cf. Borel, E., Leçons sur les séries divergentes, p. 32 (1928)Google Scholar; K. Knopp, loc. cit. p. 547.

* Tannery, and Molk, , Fonctions elliptiques, vol. 2, p. 48 (1896).Google Scholar