The abnormal kinetic energy of an ion in a gas

Abstract

1. In a paper on "The Charges on Ions in Gases, and the Effect of Water Vapour on the Motion of Negative Ions," Townsend showed that when a stream of ions is moving in an electric field the extent to which it spreads out as it advances depends on the dryness of the gas as well as on the electric force, indicating that the rate of diffusion in dry air is abnormally great in comparison with the velocity under an electric force. It was suggested ( loc. cit ., p. 469) that this could be explained on the supposition that the ions were not in "thermal equilibrium" with the molecules of the gas, but that their mean kinetic energy exceeded that of an equal number of gas molecules in the ratio k to unit), where k depends on the pressure and the electric force. Townsend mentioned a possible means by which this abnormal energy might arise, namely, that the extra velocity acquired by an ion in an interval between collisions was nod all lost by collision with a gas molecule, 80 that energy might accumulate for some time. The effect has been further studied by Haselfoot, both observers showing that k is, at any rate approximately, a function of X/ p only, where X is the electric forces and p the pressure of the gas. It seemed to the author that it would be desirable to investigate tbs matter quantitatively on the basis of the kinetic theory of gases, sines we are here dealing with the validity or non-validity oh the law of equipartition of energy. It is shown in this paper that it is easy enough to obtain theoretical support for the assumption of abnormal kinetic energy; in fact, the values of k predicted by pure theory are considerably in excess of those actually observed. In order to prevent misunderstanding, it may be stated that the law of equipartition of energy in the kinetic theory is only proved to be true when the molecules are left to themselves in tile absence of external forces.