XII. The kinetic theory of a gas constituted of spherically symmetrical molecules

Abstract

The principal kinetic theories of a gas proceed either on the hypothesis that the molecules are rigid elastic spheres, or that they are point centres of forces which vary inversely as the fifth power of the distance. Maxwell has worked out the consequences of the letter hypothesis in his well-known theory, which is unrivalled in its high degree of accuracy and (after some improvements by Boltzmann) in its perfection of mathematical form. All the quantities not taken account of in the theory (such as the time occupied by molecular encounters, and the effect of collisions in which more than two molecules take part) are properly negligible under ordinary conditions. The theory has the disadvantage, however, that the underlying hypothesis is highly artificial (being chosen chiefly on account of mathematical simplifications connected with it, rather than from any physical reasons), and does not represent the real facts at all adequately. The other hypothesis referred to seems to be much more in agreement with fact, but its consequences have been worked out less accurately. The method which has almost always been used is the one originally devised by Clausius and Maxwell; Maxwell abandoned it later, however, as it had “led him at times into grave error.” In spite of its apparent simplicity, numerical errors of large amount may undoubtedly creep in in a very subtle way. Hence the theory of a gas whose molecules are elastic spheres remains in a rather unsatisfactory state. As a “descriptive” theory (to use Meyer’s apt term) it has, however, served a useful purpose; the general laws of gaseous phenomena have been developed by its aid in an elementary way, which has conduced to a wider diffusion of knowledge of the kinetic theory than would have been possible if the sole line of development had been by the more mathematical and accurate methods used by Maxwell and Boltzmann.