'234 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



From equations (312) and (234) it follows that if there is a phase 

 of dissipated energy at any point in an ideal gas-mixture in equili- 

 In-iuni under the iutiuence of gravity, the whole gas-mixture must 

 consist of such phases. 



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

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

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



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



equal quantities of the two components under the same conditions of 

 temperature and pressure), we shall have 



log ^ = -^- H log t - — -, (319) 



3—1 a, cto «2 ^ 



m^ V d ^ <£ 



log i-^^i — — 1 lost- — : ; (-3^^) 



/ , V /3— 1 «2 «P «2 ^ 



where 



^ = c, -C2, i?' = Ci — Cg +«j — rtg, (322) 



C=iE^~E^. (323) 



Gas-mixtures with Convertible Gom,ponents. 



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

 tures 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 pi-essure. 

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

 ponents. The very general considerations adduced on pages 197-203, 

 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. 



