Page:Text-book of Electrochemistry.djvu/223

 2o8 ELECTROMOTIVE FORCE. chap.

The completely reversible elemeDt has now retiimed to its initial condition, leaving the temperature out of account, for the same quantity of electricity has passed through it in 'both directions. Practically no work has to be done to raise its temperature by dT.

Let the quantity of electricity q be 96,500 coulombs, and the heat evolved in the chemical process be W, then at the

— W} cal. is taken from the element (and therefore from the surrounding medium which keeps the temperature of the element constant). At the temperature 2^ the. quantity of heat (P X 23,070 — W) cal. is introduced into the element, whilst the quantity 23,070. dP is transformed into work. Now, if a quantity of heat, Q cal., passes from the temperature T + dT to T, and if the work done thereby is dA cal., then, according to the second law of thermodynamics —

dA ^dT Q T

— W. Therefore —

23,070rfP ^ dT 23,070P - W ~T

dP If -— = 0, i.e. if the electromotive force of the element dT

does not change with the temperature —

��P =

��and in this case Thomson's rule is correct. As a matter of fact, the electromotive force of a series of elements is almost independent of the temperature, for instance, the Daniell element, and for these Thomson's rule is applicable.

Elements are known which, when functionating, absorb heat — their electromotive force increases with rising

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