A Critical Thermodynamic Discussion of the Volta, Thermo-electric and Thermionic Effects

Abstract

In this paper the various relations between the Volta effect, thermo-electric effects, and thermionic effects are critically discussed from the general view point of thermodynamics, avoiding assumptions involving special mechanisms. The ordinary concept of an impressed E.M.F. is found inadequate, and a general definition is proposed, competent to include systems in which the force driving electricity has not the character of a spatially distributed field of force. A thermodynamic proof, dispensing with all special assumptions, is given for a formula for the temperature coefficient of the Volta effect originally given by Lorentz and Kelvin. This temperature coefficient involves a surface heat, the existence of which has not yet been established experimentally, and the possibility of which is usually overlooked. It is shown that Richardson has neglected this surface heat, and that the formula of Lorentz and Kelvin may be deduced also from the phenomena of thermionic emission when the surface heat is taken into account. Formulas are deduced connecting the latent heat of vaporization of electrons, surface heat, surface E.M.F., surface potential jump, Thomson heat, E.M.F. and potential gradient. It is shown that in general local heat, potential difference, and E.M.F. cannot be equal to each other. An expression is found from thermionic considerations for the Volta difference of potential between two parts of the same unequally heated metal, and the possibility suggested of using this effect in determining the hypothetical surface heat. It is shown that it is almost certain that in an unequally heated metal there are currents continuously flowing in closed circuits through the metal and the surrounding electron gas. It is shown that the Volta law of tensions must be capable of extension to include the local potential jumps and E.M.F.'s, although these are not susceptible of direct measurement. Finally, expressions are deduced for the effects of pressure and change of state on the Volta contact difference of potential. These involve the change of volume with surface charge and the effect of surface charge on melting pressure; effects for which no search has been made yet experimentally.