THERMODYNAMIC AL SYSTEM OF GIBBS 111 



ate, we shall have 



m/ = mi" = h, and 1712" = W2'" = a, 

 and (102) reduces to 



dp ^ v'" - V - v" ^ _Q_ 



dt v'" -v' - v" t.Av ^ ^ 



where Q is the heat absorbed when a quantity a + 6 of calcium 

 carbonate is dissociated into lime and carbon dioxide at the 

 same temperature and pressure, and Av is the increase of volume 

 in the same change. For rj'" — r\ — r\" is the difference be- 

 tween the entropy of a quantity (a + 6) of calcium carbon- 

 ate, and that of the quantities a of lime and 6 of carbon di- 

 oxide. Q = tij]" — v' — v") is thus the heat absorbed in 

 the dissociation of the calcium carbonate. 



When the number of potentials considered in various parts 

 of the system is n + h, there will be h independent relations 

 between them, by means of which the variations of h of the 

 potentials may be eliminated from the equations of the form of 

 (100) in which they occur. We may thus obtain n + 1 equa- 

 tions between the n potentials of the independently variable 

 components of the system as a whole. 



IS. Cases in Which the Number of Degrees of Freedom is 

 Greater Than One* (a) Systems of Two or More Components 

 in Two Phases. We will consider first the case of two inde- 

 pendent components in two phases. We shall have two equa- 

 tions similar to (100), one for each phase: 



y' dp = T]' dt -\- mi dni + mz dm, 



v"dp = v"dt + mi"dni + m2"dfjL2. (104) 



Eliminating d/x2 from these equations, we obtain: 



(vW - v'W)dp = Wm^" - v"m2')dt 



+ (ini'nh" - mi"rrh')dni, (105) 



* Gibbs, I, 99-100. 



