The temperature variation of the work function of clean and of thoriated tungsten

It is well known that the relation between the electron emission i from a hot body and its absolute temperature T may be expressed empirically by the equation i = AT2e-ψ/kT, in which A and ψ are constants characteristic of the emitting surface, and k is Boltzmann’s constant. This is of the same form as the theoretical equation i = A0D-T2e-x/kT, in which A0 is a universal constant having the numerical value of 120 amp. cm. -2 degree-2, D- is the mean transmission coefficient, and X is the work function of the emitter. This quantity is not necessarily constant with temperature, and if we assume its temperature variation to be linear, as we may do within a sufficiently restricted range of temperatures, setting X = ω+αKT, Where ω and α are Constants, we may rewrite(2) thus: i = A0D-T2e-ω/kT. It may be shown (cf. Reimann 1934a, p. 265) that in such cases as occur in nature D- probably never varies appreciably with temperature, and so, assuming this, and comparing (1) with (4), we may write A = A0D-e-α, ψ = ψ .