220 J. W. Gibbs — Equilibrium, of Heterogeneous Substances. 



are the same, (whether these gas-masses are entirely different gases, 

 or gas-mixtures differing only in the proportion of their components,) 

 the condition just mentioned can only be satisfied when the tempera- 

 ture of the resultant gas-mixture is also the same. In such com- 

 binations, therefore, the final temperature will be the same as the 

 initial. 



If we consider a vertical column of an ideal gas-mixture which is 

 in equilibrium, and denote the densities of one of its components at 

 two different points by y^ and ;//, we shall have by (275) and (234) 



i ^i-/"/ g[h'-h) 

 ^=e "'* =e ""'* . (284) 



From this equation, in which we may regard the quantities distin- 

 guished by accents as constant, it appears that the relation between 

 the density of any one of the components and the height is not 

 affected by the presence of the other components. 



The work obtained or expended in any reversible process of com- 

 bination or separation of ideal gas-mixtures at constant temperature, 

 or when the temperatures of the initial and final gas-masses and of 

 the only external source of heat or cold which is used are all the same, 

 will be found by taking the difference of the sums of the values of ip 

 for the initial, and for the final gas-raasses. (See pages 145, 146). 

 It is evident from the form of equation (279) that this work is equal 

 to the sum of the quantities of work which would be obtained or 

 expended in producing in each different component existing separately 

 the same changes of density which that component experiences in 

 the actual process for which the w^ork is sought.* 



We will now return to the consideration of the equilibrium of a 

 liquid with the gas which it emits as affected by the presence of 

 difterent gases, when the gaseous mass in contact with the liquid may 

 be regarded as an ideal gas-mixture. 



It may first be observed, that the density of the gas which is 

 emitted by the liquid will not be affected by the presence of other 

 gases which are not absorbed by the liquid, when the liquid is pro- 

 tected in any way from the pressure due to these additional gases. 

 This may be accomplished by separating the liquid and gaseous 



* This result has been given by Lord Rayleigh, (Phil. Mag., vol. xlix, 1875, p. 311). 

 It will be observed that equation (279) might be deduced immediately from this 

 principle in connection with equation (260) which expresses the properties ordinarily 

 assumed for perfect gases. 



