DIFFUSION AND ENTROPY OF GASES 599 



are supposed to be both at the same pressure, p, and the same 

 temperature, and each initially occupying volume v. Also the 

 temperature is maintained constant notwithstanding the conver- 

 sion of heat into work during expansion of either gas. The 

 piston being fixed, hydrogen escapes through it, until it is of the 

 same density throughout the cylinder, oxygen behaving as a 



vacuum to it. This being done, the pressure is ^ on the oxygen 



side, and-E- on the hydrogen side. The piston being now set 



free, the oxygen expands, and if its expansion takes place very 

 slowly, the hydrogen, as it can pass through, will be throughout 

 the process at the same pressure on either side of the piston. 

 The work done by expansion of the oxygen is then the same as 

 if the hydrogen were absent, and is 



V 



y—^~ dx = pv log 2. 



o 



It is therefore exactly half the work required by the Rayleigh- 

 Bryan law. At the end of the process the two gases are 

 uniformly mixed throughout the volume 2V of the cylinder. No 

 further work can be obtained from the system while it is in that 

 state. If the piston, instead of being impermeable to oxygen, 

 were permeable by it, only in less degree than by hydrogen, the 

 work obtained would be less — that is, less than half the work 

 required by the law. 



4. We must now consider Rayleigh's arguments. They 

 seem designed to show that the separation of mixed gases 

 generally involves the expenditure of work, and that this 

 work may be regained in their mixture. In his first example 

 a mixture of steam and hydrogen under a piston in a cylinder 

 of volume v is compressed, the temperature being main- 

 tained constant, until at volume Vi, the saturation point of 

 the steam is reached, and it begins to liquefy, and is all liquefied 

 at volume v . I understand Rayleigh to say that at this 

 point all the hydrogen exists as gas between the water and 

 the piston, none being held in solution by the water. The water 

 is then put in a separate vessel, and is evaporated and expanded 

 to its original volume and temperature. The hydrogen also 

 expands to its original volume and temperature. The work 

 gained in expansion is, he says, equal to that spent in compres- 



