2 14 ELECTROMOTIVE FORCE. chap.
In the first place, we force through Ma towards the left (1 — m)dv c.c. of water. This process takes place against an osmotic excess pressure which rises from to dir, because at the beginning the concentration in the middle partition is the same as that to the left, and at the end it is the same as that to the right. The corresponding work is —
(lAi = ^^djT . dr . (1 — m),
or, since the osmotic pressure n- of a copper sulphate solution is regulated by vant HofTs equation (see p. 76) —
wv = iBT or TT = RTd,
therefore —
(lA, = ^-"^^dv . d(RTci\
Now let J/i be removed, and so much water forced from right to left as was contained between Ma and Mi, namely (1 — m) (v — dt^ c.c. This requires the work —
dA2 = (1 - m)(v - dv)d(IiTci),
Since dv can be neglected, on account of its smallness compared with v, the whole work done is expressed by —
dAi -f- dA2 = (1 - m)MT^} = (1 - m)RT [di + i- \
c \ c f
since V = -, c
��Now, dA must be equal to dAi 4- dAz. Consequently —
- ,^ BT ,, .d(ei) ,^
dV = - - - (1 — m) -^^ volts.
/1. 23,070 c
We may imagine a whole series of solutions of only slightly differing concentrations placed side by side, so that between the two end ones there is a finite difference of con- centration. The total electromotive force, V, between these
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