312 Lord Rayleigh on the Work that may be 



The result at which I have arrived is extremely simple. It 

 appears that the work that may be done during the mixing of 

 the volumes v x and v 2 of two different gases is the same as that 

 which would be gained during the expansion of the first gas 

 from volume v x to volume v l + v%, together with the work 

 gained during the expansion of the second gas from v 2 to v l + v <i , 

 the expansions being supposed to be made into vacuum. Now 

 these expansions may be considered actually to take place; and 

 thus the rule is brought under Dalton's principle that each gas 

 behaves to the other as a vacuum. It is understood that the 

 gases follow the common law of independent pressures, so that 

 the total pressure is always the sum of those which would be 

 exerted by each gas in the absence of the other. 



We will take first the case when one gas is condensable, and 

 estimate how much work must be done in order to separate the 

 components of a mixture. Suppose, then, that a long cylinder, 

 closed at the bottom, contains a uniform mixture of (for example) 

 hydrogen and steam confined under a piston, and that the walls 

 of the cylinder are maintained at a constant temperature. When 

 the piston descends, heat will be generated ; but the operation is 

 supposed to proceed so slowly, that not only is the temperature 

 rigorously constant throughout, but also the mixture is at any 

 time in that condition which it would finally attain were the 

 descent of the piston arrested. The pressure on the piston re- 

 sisting the descent is by hypothesis the sum of those which it 

 would experience from the hydrogen and steam separately*. 

 When the space under the piston is reduced to that which the 

 given quantity of steam is capable of saturating at the given 

 temperature, condensation commences and continues as the steam - 

 space is gradually diminished. 



By carrying this process sufficiently far, the condensation of the 

 steam may be effected with any desired degree of completeness, 

 and thus the water and hydrogen separated. A second movable 

 piston may now be inserted immediately over the condensed 

 water, and a very gradual expansion allowed until the original 

 total volume is recovered. If the second piston be allowed free 

 motion, the constituents of the original mixture are now separated, 

 under equal pressures, and occupying the same total volume as 

 before ; and the question is, how much work has been expended 

 in arriving at this state of things ? 



In view of the fact that during the first part of the operation 

 the hydrogen and steam press independently, it is clear that the 

 total work done is the same as that which would be required to 



* For the sake of simplicity we may suppose a vacuum on the other side 

 of the piston, though, of course, any constant pressure would give finally 

 no result. 



