416 BELL SYSTEM TECHNICAL JOURNAL 



in which C/ is a universal constant equal to lirGk^-me/h^ =120 

 amps. /cm. ^ °K.-; h (Planck's constant), m, e and k have the customary 

 significance ; G is the statistical weight which is equal to 2 for electrons ; 

 a = exp {Sop/k) ; 5op is the entropy per atom of a metal whose surface 

 has a charge density p at 7" = ; Lo is the heat of vaporization per 

 electron at constant pressure at 7" = ; 



Cpp is the specific heat per atom at constant pressure when the metal 

 surface has a charge density p while Cpm is the specific heat for the 

 uncharged metal. In the derivation it is assumed that the entropy of 

 the uncharged metal at T = is zero in accordance with the third 

 law of thermodynamics; it is also assumed that the electron vapor 

 acts like a perfect gas. The value of U follows from the value of the 

 entropy constant of a perfect gas deduced from quantum statistics. 

 Up to the present time neither theory nor experiment has yielded 

 numerical values for a or (p{T). If, however, it is assumed that 

 a = 1, <p{T) = and r = then equation (6a) reduces to 



i= UT'exp. (- Lo/kT), (6b) 



which is the equation derived by Dushman ^^ in 1923. It predicts 

 that all Richardson lines should have the same intercept on the y axis, 

 namely, log U. Since this prediction is not fulfilled by experiment 

 it would appear that the assumptions made in obtaining equation 

 (6b) are not valid. It may be well to point out also that adsorbed 

 particles on the surface probably contribute additional terms to the 

 expression for the specific heats and entropy at absolute zero. These 

 have not been taken into account. 



We are now in a position to show why the exponent of T in equation 

 (la) should be 2. To do this we consider h in equation (5) or L„ in 

 equation (3). The heat of vaporization Lp is defined as the heat 

 energy that must be added to the system in order to evaporate one 

 g. mole of electrons at constant pressure. We have seen that {5/2)RT 

 ergs must be added to account for the specific heat of the vaporized 

 electrons and work done against the external pressure. The remainder, 

 Rh, which includes all other energies can be put equal to P — i^ 

 — T{dP/dT) where P is the increase in potential energy of the elec- 

 trons, and K is the mean kinetic energy which the electrons had in 

 the metal. P includes work done against the image force or any 

 other electrical forces. So little is known about the exact nature of P 



