The Theory of Thermionics

Abstract

Thermodynamical theory of electron emission from metals.—By means of a reversible cycle similar to that first used by O. W. Richardson, an accurate expression for the thermionic emission is obtained and it is shown that the constant in the equation for the vapor pressure of the electrons is equal to the chemical constant for electron gas. It is shown that if all the internal heat of evaporation of the electrons is due to electrical forces then Richardson's original equation $I=A{\theta }^{\frac{1}{2}}{\epsilon }^{\frac{-b}{\theta }}$ must be correct and the specific heat of the negative electricity in the metal must be the same as for a monatomic gas at constant volume, but that if this specific heat is small, as is known to be the case, then all the internal heat of evaporation cannot be due to electrical forces and Richardson's second equation $I=A{\theta }^2{\epsilon }^{\frac{-b}{\theta }}$ is a better first approximation to the exact relation. It is shown that the equation $L=\frac{R{\theta }_{2}d\left(logp\right)}{d\theta }$ where $L$ is the heat of evaporation of a liquid at pressure $p$ and temperature $\theta$ is not exactly true for the evaporation of electrons. It is pointed out that the thermodynamical theory of evaporation was applied to electron emission by the writer in 1903 and that O. W. Richardson in 1912, M. V. Laue in 1918, R. C. Tolman in 1921 and S. Dushman in 1923 have made further applications of it to the same question.