J. W. Gihbs — EquUihrhDii of Ileteroqeneoun. Substances. 227 



In regard to equations (216), (2lV), (218), we may now observe 

 that by (264) and (276) they are shown to hokl true in ideal gases or 

 gas-mixtures, not only for components which form only a small part 

 of the whole gas-mixture, but without any such limitation, and not 

 only approximately but absolutely. It is noticeable that in this case 

 quantities A and C are functions of the temperature alone, and do 

 not even depend upon the nature of the gaseous mass, except upon 

 the particular component to which they relate. As all gaseous bodies 

 are generally supposed to approximate to the laws of ideal gases when 

 sufficiently rarefied, we may regard these equations as approximately 

 valid for gaseous bodies in general when the density is sufficiently 

 small. When the density of the gaseous mass is very great, but 

 the separate density of the comjionent in question is small, the equa- 

 tions will probably hold true, but the values of A and C may not be 

 entirely independent of the pressure, or of the composition of the mass 

 in respect to its principal components. These equations will also 

 apply, as we have just seen, to the potentials in liquid bodies for com- 

 ponents of which the density iu the liquid is very small, whenever 

 these components exist also in the gaseous state, and conform to the 

 law of Henry. This seems to indicate that the law expressed by 

 these equations has a very general application. 



Considerations relating to the Increase of Entropy due to the 

 Mixture of Gases by Diffusion. 

 From equation (278) we may easily calculate the increase of 

 entropy which takes place when two different gases are mixed by 

 diffusion, at a constant temperature and pressure. Let us suppose 

 that the quantities of the gases are such that each occupies initially 

 one half of the total volume. If we denote this volume by F, the 



increase of entropy will be 



V V 



m , a^ log F-f mg a^ log F- m^ a^ log — - m^ a^ log -^, 



or {7n^ «, + >«2 ^'2) log 2. 



p F -, pV 



Now m^a-^ = ---, and m.^ a^ = — y. 



Therefore the increase of entropy may be represented by the expres- 

 sion 



^- log 2. (297) 



It is noticeable that the value of this expression does not depend 

 upon the kinds of gas which are concerned, if the quantities are such 

 as has been supposed, except that the gases which are mixed must be 



