172 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



The equations of the phases of dissipated energy of a binary gas- 

 mixture, the components of which are identical in substance, are 

 comparatively simple in form. In this case the two components have 



the same potential, and if we write /3 for (the ratio of the volumes 



& 2 



of equal quantities of the two components under the same conditions 

 of temperature and pressure), we shall have 



mJ* A B , , G /QIQ\ 



log- -1-^ = -\ lost -- T, (319) 



& ra 2 t>0- a 2 a 2 a 2 t' 



m^p?- 1 A , B' C /Qom 



log -r- xft-i= H lg -- ;5 (320) 



& p- 



where A = H 1 H 2 q + Cg a^a^ (321) 



^ = c x c 2 , B / = c 1 -c 2 -\-a l a 2 , (322) 



C=E l -E 2 . (323) 



Gas-mixtures with Convertible Components. 



The equations of the phases of dissipated energy of ideal gas-mixtures 

 which have components of which some are identical in ultimate 

 analysis to others have an especial interest in relation to the theory of 

 gas-mixtures in which the components are not only thus equivalent, 

 but are actually transformed into each other within the gas-mixture 

 on variations of temperature and pressure, so that quantities of these 

 (proximate) components are entirely determined, at least in any per- 

 manent phase of the gas-mixture, by the quantities of a smaller 

 number of ultimate components, with the temperature and pressure. 

 Such gas-mixtures may be distinguished as having convertible com- 

 ponents. The very general considerations adduced on pages 138-144, 

 which are not limited in their application to gaseous bodies, suggest 

 the hypothesis that the equations of the phases of dissipated energy 

 of ideal gas-mixtures may apply to such gas-mixtures as have been 

 described. It will, however, be desirable to consider the matter more 

 in detail. 



In the first place, if we consider the case of a gas-mixture which 

 only differs from an ordinary ideal gas-mixture for which some of the 

 components are equivalent in that there is perfect freedom in regard 

 to the transformation of these components, it follows at once from the 

 general formula of equilibrium (1) or (2) that equilibrium is only 

 possible for such phases as we have called phases of dissipated energy, 

 for which some of the characteristic equations have been deduced in 

 the preceding pages. 



If it should be urged, that regarding a gas-mixture which has con- 

 vertible components as an ideal gas-mixture of which, for some reason, 



