﻿610 Prof. 0. W. Richardson : Some Applications 

 volume is increased by dv the heat abstracted is 



dQ = 0dS = dv(n^ + vR6y . . . (34) 



The value of ^- which we require is the limiting value 



which obtains when v is infinitesimal compared with t, the 

 volume of the conductor. We have 



f , , coe-^dr f coe-^dr+^we-^dr 

 t _ Jr + ov Jr Jov 



"i; 



f (oe'^^dr + Bvco^' 





■w / 



E0 



Thus 



and from (3) 



«U=vK-J} (35) 



By comparison with (10), the loss of heat which accompanies 

 the escape of one electron is 



-^ = Wo -J + R0. . . . (36) 



vdv 



Moreover, since S is a perfect differential, 



i bvXd0)v--d0\'dv)o' 



and by using (9), 



Hence 



i d 



„ = Ae + ^ dd = Ae -^ + ke^- J)d6 , . . (38 ) 



where A is a quantity, characteristic of the material, which 

 does not involve 6. 



To determine the Peltier effect P we only need to consider 

 a reversible isothermal cycle involving two different con- 

 ductors. Let the suffixes 1 and 2 be used to distinguish the 

 various physical quantities which relate to the separate 

 materials, the notation being otherwise as before. Let eV 2 

 be > eVi. Surround the first conductor by a potential filter, 



