ELECTROCHEMICAL THERMODYNAMICS. 409 



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 W P . 

 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" + W P (3) 



Combining these equations we obtain 



V" - V = W P + [ W] + [Q] - if . (4) 



J * 



It will be observed that this equation gives the electromotive force 

 in terms of quantities which may be determined without setting up 

 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 *-/** represents their increase of entropy during the 



same processes. The same expressions, therefore, with the contrary 

 signs, will represent the increase of energy and entropy in the cell 

 during the passage of the current. We may therefore write 



V- V'= - Ae+f Afl + Wp, (5) 



where Ae and A^ 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 

 (694) of the paper cited in my former letter, except that the latter 

 contains the term relating to gravity. See Trans. Conn. 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 (as in a 

 Grove's gas battery) could not reach. 



* [This volume, p. 338.] 



