344 EEPOKT— 1888. 



pose the cell brought back to its original condition by some reversible chemical 

 process, involving a certain expenditure (positive or negative) of work and heat, 

 but involving no electrical current nor any permanent changes in other bodies 

 except the supply of this work and heat. 



Now the first law of thermo-dynamics requires that the algebraic sum of all the 

 •work and heat (measured in ' equivalent ' units) supplied by external bodies during 

 the passage of the electricity through the cell, and the subsequent processes by 

 ■which the cell is restored to its original condition, shall be zero. 



And the second law requires that the algebraic sum of all the heat received 

 from external bodies, divided, each portion thereof, by the absolute temperature at 

 ■which it is received, shall be zero. 



Let us write W for the work and Q for the heat supplied by external bodies 

 during the passage of the electricity, and [W], [Q] for the work and heat supplied 

 in the subsequent processes. 



Then W + Q + [W] + [Q]=0 (1) 



and 



?,.j^ = 0, (2) 



where t under the integral sign denotes the temperature at which the element of 

 heat d [Q] is supplied, and t' the temperature of the cell, which we may suppose 

 constant. 



Now the work W includes that required to carry a unit of electricity from the 

 cathode having the potential V" to the anode having the potential V. (These 

 potentials are to be measured in masses of the same kind of metal attached to the 

 electrodes.) "When there is any change of volume, a part of the work will be 

 done by the atmosphere or other body enclosing the cell. Let this part be denoted 

 by Wp. In some cases it may be necessary to add a term relating to gravity, but 

 as such considerations are somewhat foreign to the essential nature of the problem 

 which we are considering, we may set such cases aside. We have then 



W = V'-V" + Wp (3) 



Combining these equations we obtain 



Y"_V' = AVp + [W] + [Q]-rffi] . . . . (4) 



It will be observed that this equation gives the electromotive force in terms of 

 quantities which may be determined without, seftinr/ vp the cell. 



Now [W] + [Q] represents the increase of the intrinsic energy of the substances 



in the cell during the processes to which the brackets relate, and AtLl represents 



their increase of entropy during the same processes. The same expressions, there- 

 fore, with the contrary signs, will represent the increase of energy and entropy in 

 the cell during the passage of the current. W'q may therefore write 



Y"_V'=-Ae + rA'; + Wp . . . . (6) 



where Af and A7 denote respectively the increase of energy and entropy in the 

 cell during the passage of a unit of electricity. This equation is identical in meaning, 

 and nearly so in form, with equation ((394:) of the paper cited in my former letter, 

 except that the latter contains the term relating to gravity. See ' Trans. Connect. 

 Acad.' III. (1878), p. 509. The matter is thus reduced to a question of energy 

 and entropy. Thus, if we knew the energy and entropy of oxygen and hydrogen 

 at the temperature and pressure at which they are disengaged in an electrolytic 

 cell, and also the energy and entropy of the acidulated water from which they are 

 set free (the latter, in strictness, as functions of the degree of concentration of the 

 acid), we could at once determine the electromotive force for a reversible cell. 

 This would be a limit below which the electromotive force required in an actual 

 cell used electrolytically could not fall, and above which the electromotive force 

 of any such cell used to produce a current {s,a in a Grove's gas battery) could not 

 reach. 



