P^djf^ T^dT
��ifr
Braun (5) made a number of observations with ele- ments which do not follow the Thomson rule, which continued to be supported by Fr. Exner. W. Gibbs (6*) proved that with electrodes which can be used at their melt- ing points (bismuth, lead, tin) there is no change of the electromotive force at this point, as there should be according to the Thomson rule.
Helmholtz's Calculation.— In 1882 Helmholtz (7) gave the following simple deduction from the second law of thermodynamics. In the diagram (Fig. 41) V represents the electro- motive force of an element, and the quantity of electricity, q, which passes through the element is chosen as abscissa. The work is measured by the product g'- F. In the first place, let the quantity of
electricity y pass through the ele- l or
ment, which is supposed to be a ^^ ^^
perfectly reversible one, at the
absolute temperature T -^ dT, and so do the greatest possible (maximum) work. If the electromotive force of the element is T at the temperature T, then at T + dT\i is —
dP F+ --.dT= r + dP. dT
The work done by the element at T + dTia therefore —
A+dA^ (p + '^J^dry
The temperature of the element is now allowed to fall to T, and by doing mechanical work (say, by a dynamo) the quantity q is forced through the element in the opposite direction. The electromotive force of the element is now reduced to P, therefore the work expended by the dynamo
is —
A = I\ ii.
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