DIFFUSION. 645 



are mixed so as to occupy a volume Vi + v a at the same temperature and 

 pressure, the entropy of the system increases during the process by the quantity 



Since in this case the temperature does not change during the process, we 

 may calculate the quantity of energy dissipated by multiplying the gain of 

 entropy by the temperature, and we thus find for the dissipation 



or the sum of the work which would be done by the two portions of gas if 

 each expanded under constant temperature to the volume v 1 + v i . 



It is greatest when the two volumes are equal, in which case it is 

 l'386jw, where p is the pressure and v the volume of one of the portions. 



Let us now suppose that we have in a vessel two separate portions of 

 gas of equal volume, and at the same pressure and temperature, with a 

 movable partition between them. If we remove the partition the agitation of 

 the molecules will carry them from one side of the partition to the other in 

 an irregular manner, till ultimately the two portions of gas will be thoroughly and 

 uniformly mixed together. This motion of the molecules will take place whether 

 the two gases are the same or different, that is to say, whether we can 

 distinguish between the properties of the two gases or not. 



If the two gases are such that we can separate them by a reversible 

 process, then, as we have just shewn, we might gain a definite amount of 

 work by allowing them to mix under certain conditions ; and if we allow them 

 to mix by ordinary diffusion, this amount of Work is no longer available, but 

 is dissipated for ever. If, on the other hand, the two portions of gas are 

 the same, then no work can be gained by mixing them, and no work is 

 dissipated by allowing them to diffuse into each other. 



It appears, therefore, that the process of diffusion does not involve dis- 

 sipation of energy if the two gases are the same, but that it does if they can 

 be separated from each other by a reversible process. 



Now, when we say that two gases are the same, we mean that we cannot 

 distinguish the one from the other by any known reaction. It is not probable, 

 but it is possible, that two gases derived from different sources, but hitherto 

 supposed to be the same, may hereafter be found to be different, and that a 



