314 Lord Rayleigh on the Work that may be 



In like manner the work that can be gained during the mix- 

 ing of any number of pure and different gases, which press in- 

 dependently, is the sum of those due to the expansions of the 

 several gases from their original to their final volumes, where the 

 volume of a gas is understood to mean the space in which the gas 

 is confined. 



The next problem which presents itself is that of finding the 

 work that may be done during the mixture of two quantities 

 of mixed gases — for example, oxygen and hydrogen. Suppose 

 the two mixtures to be contained in a cylinder, and separated 

 from one another by a piston which moves freely. The rule is that 

 the work required to be estimated is that which would be gained 

 during the equalization of the oxygen-pressures if the hydrogen 

 were annihilated, together with that which would be gained du- 

 ring the equalization of the hydrogen-pressures if the oxygen 

 were annihilated. 



If the proportions of the gases are the same in the two 

 mixtures, and also the total pressures, there is, of course, no 

 possibility of doing work. If, on the other hand, the gas on the 

 one side of the piston be pure oxygen, and on the other side pure 

 hydrogen, the more general rule reduces to that already given 

 for pure gases. 



I now pass to another proof of the fundamental rule, depend- 

 ing on the possibility of separating two gases of different densi- 

 ties by means of gravity. In a vertical column maintained at a 

 uniform temperature, two gases which press independently will 

 arrange themselves each as if the other were absent. Conse- 

 quently, if there be any difference in density, the percentage 

 composition will vary at different heights, and a partial separation 

 of the gases is thus effected. 



Imagine now a large reservoir containing gas at sensibly con- 

 stant pressure, on which is mounted a tall narrow vertical tube ; 

 and first, in order to understand the operation more easily, let there 

 be only one kind of gas present. If/? be the pressure and p the 

 density, p — kp, since the temperature is constant; and if z be 

 the height measured from the reservoir in which the pressure is P, 



dp=—gpdz — —fipdz, if jj,=g-r-k; 



whence, by integration, 



p = p«""* a) 



expresses the law of variation of pressure with height. Suppose 

 now that a small quantity of gas of volume v is (1) removed from 

 the top of the tube, (2) compressed to volume v Q until it is of 

 the same pressure as the gas in the reservoir, (3) allowed to fall 

 through the height z to the level of the reservoir, and (4) forced 



