EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 167 



of the same kind stands on a different footing from the mixture of 

 gas-masses of different kinds, the fact is not less significant that the 

 increase of entropy due to the mixture of gases of different kinds, 

 in such a case as we have supposed, is independent of the nature of 

 the gases. 



Now we may without violence to the general laws of gases which 

 are embodied in our equations suppose other gases to exist than such 

 as actually do exist, and there does not appear to be any limit to the 

 resemblance which there might be between two such kinds of gas. 

 But the increase of entropy due to the mixing of given volumes of the 

 gases at a given temperature and pressure would be independent of 

 the degree of similarity or dissimilarity between them. We might also 

 imagine the case of two gases which should be absolutely identical 

 in all the properties (sensible and molecular) which come into play 

 while they exist as gases either pure or mixed with each other, 

 but which should differ in respect to the attractions between their 

 atoms and the atoms of some other substances, and therefore in their 

 tendency to combine with such substances. In the mixture of such 

 gases by diffusion an increase of entropy would take place, although 

 the process of mixture, dynamically considered, might be absolutely 

 identical in its minutest details (even with respect to the precise 

 path of each atom) with processes which might take place without 

 any increase of entropy. In such respects, entropy stands strongly 

 contrasted with energy. Again, when such gases have been mixed, 

 there is no more impossibility of the separation of the two kinds 

 of molecules in virtue of their ordinary motions in the gaseous mass 

 without any especial external influence, than there is of the separation 

 of a homogeneous gas into the same two parts into which it has once 

 been divided, after these have once been mixed. In other words, the 

 impossibility of an uncompensated decrease of entropy seems to be 

 reduced to improbability. 



There is perhaps no fact in the molecular theory of gases so well 

 established as that the number of molecules in a given volume at a 

 given temperature and pressure is the same for every kind of gas 

 when in a state to which the laws of ideal gases apply. Hence the 



quantity *y- in (297) must be entirely determined by the number of 



L 



molecules which are mixed. And the increase of entropy is therefore 

 determined by the number of these molecules and is independent of 

 their dynamical condition and of the degree of difference between 

 them. 



The result is of the same nature when the volumes of the gases 

 which are mixed are not equal, and when more than two kinds of 

 gas are mixed. If we denote by v lf v 2 , etc., the initial volumes of the 



