DIFFUSION AND ENTROPY OF GASES 



By S. H. BURBURY, F.R.S. 



i. This subject has been treated by Lord Rayleigh in Phil. Mag. 

 January — June 1875, under the title " On the Work that may 

 be gained by the Mixture of Gases," pp. 311, 318, and by Prof. 

 Bryan in his recent work on Thermodynamics (Leipzig: Teubner). 

 Each writer's work presents some difficulties, which I propose 

 to consider in the present paper. Rayleigh's argument is based 

 on the fact that hydrogen escapes through fine apertures more 

 rapidly than air, even at greater pressure, enters to supply its 

 place. His conclusion is that " the work that may be done in 

 the mixing of volumes Vj and v 2 of two different gases is the 

 same as would be gained in the expansion into vacuum of the 

 first gas from volume Vi to v x + v 2 , together with that which 

 would be gained by the expansion into vacuum of the second 

 gas from volume v 2 to v x + v 2 ." It is understood that the gases 

 follow the law of independent pressures, each behaving as a 

 vacuum to the other. The law is thus stated with complete 

 generality, and without qualification as to the nature of the con- 

 taining materials or otherwise. Bryan states the law in 

 substantially the same form at p. 125 of his work. I therefore 

 call it the Rayleigh-Bryan law. 



2. The thing to be proved, as I understand it, is this: that two 

 physically different gases, if separated, can be made to do 

 mechanical work, at the expense, of course, of their heat, in 

 mixing ; on the other hand, if they mix by diffusion, no work is 

 done. Therefore by allowing them to mix by diffusion, we lose 

 the opportunity of converting heat into work, i.e. we lose the 

 " available energy " which they had by virtue of their sepa- 

 ration. 



3. Before discussing the arguments in detail, it will be well to 

 calculate the work that can be done in case of two gases, one of 

 which is hydrogen, in a cylinder of volume 2V, separated, as 

 Rayleigh suggests, by a piston porous to the hydrogen, but 

 hypothetically impermeable to the other gas, say oxygen. They 



598 



