VI. On the law of distribution of molecular velocities, and on the theory of viscosity and thermal conduction, in a non-uniform simple monatomic gas

Abstract

The kinetic theory of gases can be developed accurately only after the distribution of the molecular velocities has been determined. This was done by Maxwell in the case of a uniform gas, and by means of his well-known law of distribution the pressure and temperature can be precisely expressed in terms of the molecular data. His law does not suffice, however, for the investigation of diffusion, viscosity, or thermal conduction, since these occur only when the gas is not uniform in composition, mean velocity, or energy. An accurate theory of these phenomena must be based on the evaluation of the modified velocity-distribution function, a task which for many decades has constituted one of the classical unsolved problems of the kinetic theory. In one special case, as Maxwell found, the actual determination of this function proves to be unnecessary for the purpose mentioned; this is the case of a gas composed of molecules which are point centres of force varying inversely as the fifth power of the distance. The reasons for the peculiarity in this instance are analytical and not physical, and unfortunately for the simplicity of the mathematical theory of gases, Maxwell’s results for such a gas do not accord with the observed data of actual gases. This particular molecular model is therefore interesting chiefly on theoretical grounds, and it is important to develop the theory for molecules of other types, which may better represent the behaviour of real molecules.