228 ./ W. Gihhs — Equilibrhim of Heterogeneous Substances. 



of different kinds. If we should bring into contact two masses of the 

 same kind of gas, they would also mix, but there would be no in- 

 crease of entropy. But in regard to the relation which this case 

 bears to the preceding, we must bear in mind the following considera- 

 tions. When we say that when two different gases mix by diffusion, 

 as we have supposed, the energy of the whole remains constant, and 

 the entropy receives a certain increase, we mean that the gases could 

 be separated and brought to the same volume and temperature which 

 they had at first by means of certain changes in external bodies, for 

 example, by the passage of a certain amount of heat from a warmer 

 to a colder body. But when we say that when two gas-masses of the 

 same kind are mixed under similar circumstances there is no change 

 of energy or entropy, we do not mean that the gases which have been 

 mixed can be separated without change to external bodies. On the 

 contrary, the separation of the gases is entirely impossible. We call 

 the energy and entropy of the gas-masses when mixed the same as 

 when they were unmixed, because we do not recognize any difference 

 in the si\bstance of the two masses. So when gases of different kinds 

 are mixed, if we ask what changes in external bodies are necessary to 

 bring the system to its original state, we do not mean a state in 

 which each particle shall occupy more or less exactly the same posi- 

 tion as at some previous epoch, but only a state which shall be 

 undistinguishable from the previous one in its sensible properties. 

 It is to states of systems thus incompletely defined tliat the problems 

 of thermodynamics relate. 



But if such considerations explain why the mixture of gas-masses 

 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 indej^endent 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 imaoine the case of two gases which should be absolutely identi- 

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

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



