ELECTROMOTIVE FORCE OF A THERMOELECTRIC COUPLE. 273 



282. ELECTROMOTIVE FORCE OF A THERMOELECTRIC COUPLE. 

 This being admitted, let us consider a circuit (Fig. 69) formed 

 of any number of metals A lf A 2 , . . . A n . Let H 15 H 2 , . . . H n be the 

 sudden variations corresponding to the electromotive forces of con- 

 tact; o- 15 cr 2 , . . . o- n the specific heats of electricity of the metals A lf 



A! H! A., H. ? A B H tt A 1 



t o-i t t <r a t 2 ar n t n o-j. t 



Fig. 69. 



A 2 , . . . A n ; finally, let f lt / 2 , . . . t n be the temperatures of the junc- 

 tions, and f Q the constant temperature of the external wire. The 

 expression for the electromotive force of the circuit is 



f*i f a rtn rt 



[ 2 ..+H n + 0y#+ <r. 2 dt. . + <r n dt + cr^df, 



Jt Jti Jtn-l Jt n 



or, combining the two extreme integrals, 



ft. rt a rt n 



/ _ \ "p ^/ T-T -I- I rr /// I I /// | _\__ I JA 



\O/ <4M * 2 ^^ t \^ l .**' 



}u ft J^.v 



Suppose that the circuit only consists of two metals A and A', 

 the electromotive forces of contact H x and H 2 are in general of 

 opposite signs. Taking these signs into account, we shall have 



(4) 



PV- 

 A 



If the difference of temperature of the two junctions is infinitely 

 small, we have / 2 - / t = dt> and the equation becomes 



(5) -+cr'-<r= 



at at 



We have seen that for an infinitely weak current the circuit may 

 be regarded as a reversible heat engine; we may therefore apply 

 Carnot's theorem, and state that the algebraical sum of the quotients 

 obtained by dividing the quantity of heat absorbed at a point, by the 

 corresponding absolute temperature, is equal to zero. 



