THERMIONIC ELECTRON EMISSION 415 



ing the mechanism by which the electrons evaporate from the metal, 

 we can arrive at some conclusions regarding the temperature depend- 

 ence of Lp. Since in the derivation of equation (3) it was assumed 

 that the electron vapor acts like a perfect gas, it follows that when 

 1 g. mole of electrons is vaporized at constant pressure an amount 

 of work RT must be done against the external pressure and an amount 

 of heat {3/2)RT must be provided to furnish the known mean kinetic 

 energy of the vaporized electrons. It then becomes desirable to define 

 a new quantity h by the equation, 



h = (Lp/R) - (5/2) r. (4) 



Since h plays an important role in the final formula, it will be con- 

 venient to give it the name " heat function." * The product kh, 

 where k is Boltzmann's constant, represents the average heat of 

 vaporization per electron less {5/2)kT. Substituting equation (4) in 

 equation (3), 



logi = log ir' + log [(1 - r)/{l - /)] - 2 log T' 



+ 2\ogT-\-{\/2.3)f{h/r~)dT. (5) 



J T' 



Thermodynamics alone cannot tell us how the heat function h varies 

 with T and we cannot perform the indicated integration until this is 

 known. However, we can deduce an important theorem even without 

 performing the integration : // the experimental value of log i — 2 log T 

 is plotted versus 1/T, the slope of the tangent at any value of T is — ^/2.3.f 

 Hence for those surfaces for which the Richardson lines are straight, 

 h is independent of T in the experimental range. For these surfaces, 

 equation (5) reduces to 



log i = log iT'/{l - r'){T'y -f h/2.?>r -f log (1 - r) 



+ 2 log r - h/2.2>T = log //(I - r) + 2 log T - h/2.3T, (6) 



where 



log H = log ir'/(l - r'){T'y + h/2.3T'. 



Log ^(1 — r) is the intercept of the Richardson line on the y axis. 



An alternative derivation of the thermodynamic emission equation 

 uses the absolute zero of temperature as the lower limit in the various 

 integrals. In this way Bridgman derives the equation,! 



i = Uail - r)T^ exp. [- U/kT ■\- <p(r)], (6a) 



* This is of course not the heat function used in thermodynamics. The heat 

 function defined here has the dimensions of temperature. It is often given in volts 

 V = khje. Later h will also be used for Planck's constant but we believe no con- 

 fusion will arise. 



t For the proof see Becker and Brattain.* In the proof it is assumed that drjdT 

 is zero or very small. This assumption is justifiable. 



% See Eq. IV, 33 on page 99 of his book named in References.' 



