THERMIONIC ELECTRON EMISSION ' 425 



or 



(^ = (Po + a{k/e)T; {2>2>) 



where a — div/dt is a constant independent of T; its units are degrees 

 per degree. The slope of a Richardson Hne is now — Wo/2.3 so that 



^ = Wo = Wa/k = ^p^e/k 

 while 



log A = \ogU - a/2.3. (34) 



Since the slope is constant, the Richardson line is straight. This line 

 is determined either by the empirical constants A and h or by the 

 values of w and dw/dT in theoretical equations. 



If w is a general function of T, the Richardson line will be curved. 

 If a tangent is drawn at a point corresponding to any temperature, 

 the slope of the tangent is — (1/2.3) (w — Tdw/dT) and its intercept 

 is log U — {l/2.3)dw/dT; w and dw/dT are to be taken at the point 

 of tangency. Hence 



b = w — Tdw/dT 

 and 



log A ^ \ogU - {l/2.3)dw/dT. (35) 



In a previous section it was shown that the slope of the Richardson 

 line is always equal to — h/2.3. Hence 



- h/2.3 = - (1/2.3) (w - Tdw/dT) 

 or 



h = w - T{dw/dT). (36) 



This important equation gives the relation between the heat function 

 and the work function. It is similar in form to the relation between 

 the total energy E and the free energy F, viz., 



E= F - T{dF/dT). (37) 



The distinction between the heat function h and the work function 

 w is strikingly brought out in Fig. 2. The slope of the Richardson 

 line is — h/2.3, while the slope of a straight line connecting any point 

 on the Richardson line with the intercept log Z7(l — r) \s — w/2.3. 



The theory that the work function is indeed a function of tempera- 

 ture has been championed in recent times by R. Suhrmann and his 

 collaborators. A good account of this work can be found in Volume 4 

 of Miiller-Pouillets Lehrhuch der Physik. One method by which Suhr- 

 mann has shown the temperature dependence of the work function is 



