DIFFUSION AND ENTROPY OF GASES 605 



14. The argument (Bryan's) seems to prove too much, if I 

 am right in {(f) above. For if so, the argument applies equally 

 to two portions of any single gas. Therefore, we could increase 

 the available energy of a single gas by dividing it into two parts 

 by a partition. Even if (d) be not accepted, does not the same 

 thing follow from Bryan's proof (e) applied to two portions 

 of the same gas ? It is true that this process, although it 

 separates two gases having different temperatures of lique- 

 faction, cannot separate two portions of the same gas. But we 

 may separate the two portions, and put them in separate vessels, 

 immediately after or before liquefaction, and then evaporate 

 them separately, till each attains its original temperature and 

 original volume 2v. If the process is reversible for two gases, 

 is it not equally reversible for two portions of the same gas ? 

 If so, then two portions of the same gas, each at the same 

 temperature and pressure, mixed in one volume 2v, have more 

 entropy than they would have if they each occupied volume v, 

 and were separated by a partition. 



15. Subject to the doubt raised in 14, the argument of arts. 

 ID and II seems logically conclusive, that two separated gases 

 lose available energy, whatever that may mean, when allowed 

 to mix by diffusion, and that the amount of available energy 

 lost is that stated in the Rayleigh-Bryan law, 



16. Nevertheless, it does not necessarily follow that the 

 available energy lost is t/ie practical possibility of transforming 

 heat into work. For the only definition of available energy 

 which we have used in the argument is that it diminishes 

 with increase of entropy. In fact, if the entropy is a function 

 of T and v, and independent of any conditions, the available 

 energy must be a function of T and v, and independent of 

 any conditions. It does not, therefore, follow that because a 

 system loses available energy in passing from state A to state 

 B, therefore we can actually transform heat into work given 

 the system in state A. It may be that in state A work is 

 theoretically^ but owing to the external conditions not practically, 

 derivable from the system. In Bryan's definition of available 

 energy (p. 43) "work theoretically derivable " must mean " work 

 which under suitable external conditions might be derived." If 

 two separated gases (state A) are each at pressure p, and are 

 surrounded by infinite air at pressure p and at the same tem- 

 perature as the gases, no part of the heat of either gas can 



39 



