6o 4 SCIENCE PROGRESS 



and evaporated, and heated until each occupies volume 2v, and 

 is at the original temperature of the mixture. It is assumed 

 (i) that the volumes of the liquids are negligible in comparison 

 with their vapours ; (2) that the specific heats are constant ; 

 (3) that the latent heat of evaporation of either component is 

 unaffected by the presence or absence of the other. On these 

 assumptions Bryan concludes that the process is reversible. 

 Therefore entropy is the same at the end, when each gas has a 

 volume 2v to itself, as at the beginning, when they had one 

 volume 2v in common, cceteris paribus. 



(/) The entropy of a gas in volume v increases, cceteris 

 paribus, when v increases. This follows from the definition (a). 



For S denoting entropy, 8S = ~± ; therefore -^=y ~^, and -^ 



is always positive by the Carnot cycle. 



11. We may now compare two states of a system : state A, 

 two gases occupying each a volume v, separated by a partition, 

 and each at pressure p, and temperature T ; state B, the same 

 two gases mixed in volume 2v, cceteris paribus. Each gas has in 

 state A entropy n<£ (T, v), and by (e) it has in state B entropy 

 n$ (T, 2v), which by (/) is greater than n<£ (T,v) — that is, each has 

 greater entropy, and therefore the system has greater entropy 

 in B than in A. Therefore the system has less available energy in 

 B than in A, or available energy is lost in the process of mixing, 

 no energy passing in that process from or to external bodies. 



12. Evidently the amount of available energy that each gas 

 loses in the process of mixing is measured by the entropy 

 that it gains — that is, the difference of entropy between the gas 

 occupying volume v, and the same gas cceteris paribus 

 occupying volume 2v — that is, the available energy lost by the 

 process is for each gas the available energy it would lose by 

 expanding into vacuum from volume v to volume 2v, the 

 temperature being constant. The Rayleigh-Bryan law is thus 

 formally and completely proved in the sense of Bryan's definition 

 of available energy, whatever that may be. 



13. I note that Bryan's process of separating the gases 

 (p. 124) involves no expenditure of work. If, therefore, the 

 gases when separated have more available energy than when 

 mixed, it is not because work has been spent in their separation 

 which can be regained in their mixture, in which Bryan seems 

 to differ from Rayleigh. 



