340 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



Lord Rayleigh,* to the work which may be gained by allowing each 

 gas separately to expand at constant temperature from its initial 

 volume to the volume occupied by the two gases together. The 

 same work is equal, as appears from equations (278), (279) on page 

 156 (see also page 159), to the increase of the entropy of the system 

 multiplied by the temperature. 



It is possible to vary the construction of the cell in such a way 

 that nitrogen or other neutral gas will not be necessary. Let the 

 cell consist of a U-shaped tube of sufficient height, and have pure 

 hydrogen at each pole under very unequal pressures (as of one and two 

 atmospheres respectively) which are maintained constant by properly 

 weighted pistons, sliding in the arms of the tube. The difference of 

 the pressures in the gas-masses at the two electrodes must of course 

 be balanced by the difference in the height of the two columns of 

 acidulated water. It will hardly be doubted that such an apparatus 

 would have an electromotive force acting in the direction of a current 

 which would carry the hydrogen from the denser to the rarer mass. 

 Certainly the gas could not be carried in the opposite direction by 

 an external electromotive force without the expenditure of as much 

 (electromotive) work as is equal to the mechanical work necessary 

 to pump the gas from the one arm of the tube to the other. - And 

 if by any modification of the metallic electrodes (which remain 

 unchanged by the passage of electricity) we could reduce the passive 

 resistances to zero, so that the hydrogen could be carried reversibly 

 from one mass to the other without finite variation of the electro- 

 motive force, the only possible value of the electromotive force would 



be represented by the expression t -J, as a very close approximation. 



It will be observed that although gravity plays an essential part 

 in a cell of this kind by maintaining the difference of pressure in 

 the masses of hydrogen, the electromotive force cannot possibly be 

 ascribed to gravity, since the work done by gravity, when hydrogen 

 passes from the denser to the rarer mass, is negative. 



Again, it is entirely improbable that the electrical currents caused 

 by differences in the concentration of solutions of salts (as in a cell 

 containing sulphate of zinc between zinc electrodes, or sulphate of 

 copper between copper electrodes, the solution of the salt being of 

 unequal strength at the two electrodes), which have recently been 

 investigated theoretically and experimentally by MM. Helmholtz and 

 Moser,t are confined to cases in which the mixture of solutions of 

 different degrees of concentration will produce heat. Yet in cases in 

 which the mixture of more and less concentrated solutions is not 



* Philosophical Magazine, vol. xlix, p. 311. 



t Annalen der Phyeik und Chemie, Neue Folge, Band iii, February, 1878. 



