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Dissociative Equilibrium in an External Field of Force

Published online by Cambridge University Press:  24 October 2008

E. A. Milne
E. A. Milne
Affiliation:
Trinity College.
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Extract

(1) The conditions of dissociative equilibrium in an external gravitational field have been given by Willard Gibbs, as follows: If the state of a system is such that it is in (mechanical and thermodynamic) equilibrium when the constituents are taken to be independent, and if a condition of dissociative equilibrium is satisfied at one point, then the same condition is satisfied at all points, and the state is one of equilibrium if the constituents are actually capable of dissociating.

(2) In particular, the constituents of a column of dissociating gas under gravity settle out according to Dalton's law; if the condition of dissociative equilibrium is satisfied at one height it is satisfied at all heights.

(3) The conditions of equilibrium are generalised so as to take account of external electric fields and of the possibility of the products of dissociation being charged. Result (1) is shown to be unaffected.

(4) The theory is applied to the equilibrium of an ionized gas such as a stellar atmosphere under gravity. Whatever the charge on the star, the tendency of the light electrons to diffuse away from the heavy ions is almost entirely prevented by the electrostatic forces between them, and the result is the production of a field in the interior capable of supporting half the weight of the positiveions (Pannekoek, Rosseland). For the purposes of this statement the “interior” may be taken to commence at a pressure of 10−24 atmos. It is only above the level corresponding to 10−34 atmos. that electrons and ions separate out according to Dalton's law.

(5) The theory is applied to the equilibrium of an ionized gas under an external electric field. An external applied field of the order of 40,000 volt cm.−1 cannot give rise to potential differences exceeding about 1 volt under the conditions of a typical stellar atmosphere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 4 , March 1925 , pp. 493 - 509
Copyright
Copyright © Cambridge Philosophical Society 1925

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References

* Trans. Connecticut Acad. 3, 108 (1875)Google Scholar. Sci. Papers, 1, 144, 171.Google Scholar

* B.A.N. 1, 110, No. 19 (1922).Google Scholar

† Monthly Notices, 84, 720 (1924).CrossRefGoogle Scholar

‡ In this form the principle has been used by the author in a paper in Monthly Notices, 12, 1924, in considering the equilibrium of an ionized atmosphere under radiation pressure.Google Scholar

* Camb. Phil. Trans. 26, 512 (1923).Google Scholar

† If the sun has evolved from a giant star, it may have retained the charge it possessed in the giant stage. In that case the ratio of electrostatic force to gravity will be the same in the dwarf and giant stages.

* The problem has analogies with that considered by SirThomson, J. J., “Conduction of Electricity through Gases” (1906), 84. In his problem, however, there is a steady current and a steady production of ions due to an outside agency.Google Scholar