Open AccessThe kinetic theory of a gas constituted of spherically symmetrical molecules
Author(s) -
Sydney Chapman
Publication year - 1912
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1912.0034
Subject(s) - monatomic gas , thermal conductivity , thermodynamics , kinetic theory , thermal conduction , viscosity , physics , symmetry (geometry) , simple (philosophy) , function (biology) , molecule , polynomial , kinetic energy , mathematical physics , mathematics , classical mechanics , quantum mechanics , mathematical analysis , geometry , philosophy , epistemology , evolutionary biology , biology
In order to extend Maxwell's later method of developing the dynamical theory of a gas to cases other than that which he considered (viz., a gas whose molecules are point centres of repulsive force varying inversely as the fifth power of the distance), a knowledge of the velocity distribution function, in the disturbed state of the gas, is necessary. In this paper the simplest possible form is assumed for the function, consistent with the fulfilment of certain preliminary conditions. This form is (hm /π )3/2 e -hm ∑(u -u 0 )2 {1 + F (u -u 0 ,v -v 0 ,w -w 0 )}, where F is a polynomial, in the three variables indicated, of the third degree. The theory of viscosity and thermal conduction, in simple and mixed gases, is developed without assuming any property of the molecules beyond that of spherical symmetry. Perhaps the most interesting result is the relation between the viscosityμ , the thermal conductivity ϑ, and the specific heat at constant volume, Cv , for a simple monatomic gas, viz., ϑ = 5/2μ Cv .