716 HARMED ART. M 



original state. Since by the first law of thermodynamics the 

 algebraic sum of the work and heat effects in a cycle is zero, 



W + Q + [W] + [Q] = 0. (18) ([1] p. 408) 



By the second law the algebraic sum of the entropy changes 

 throughout such a cycle is zero. Hence, we obtain 



P + I 7 = 0, (19) ([2] p. 408) 



where t' is the temperature at which the cell charges or dis- 

 charges. In the reverse process, the heat is supplied or with- 

 drawn throughout a range of temperatures. 



If we neglect the term due to gravity, the reversible work 

 during cell discharge involving the passage of one unit of elec- 

 tricity is 



W = (V - V") + Wp. (20) ([3] p. 409) 

 From equations (18), (19), and (20) we readily obtain 



7" -v' = Wp+ [W] + [Q] - ^' / 7 • (21) ([4] p. 409) 



[W] + [Q] is the increase in energy Ac, supplied in bringing the 

 cell back to its original condition, and this by the first law is 

 equal numerically, but opposite in sign to the decrease in 



f dQ . ^ 

 energy, — Ae, during cell discharge. Further, / — is the 



entropy change during the reverse process, and is equal, but 

 opposite in sign, to the entropy change At/ during discharge. 

 Therefore, 



V" -V = -Ae + t'Ar, + Wp. (22) ([5] p. 409) 



Since the variables of equation (15) are all extensive, it may be 

 integrated term by term to give equation (22). 

 Let us now define a temperature t", such that 



[Q] 

 t' 



P = J ^' (23) ([7] p. 410) 



