no 



BUTLER 



ART. D 



There are thus n + 1 Hnear equations between the w + 2 

 quantities dp, dt, dm, . . . dun, by means of which the n 

 quantities, d^y dm, . . . dy.n can be eliminated. We thus obtain, 

 in the notation of determinants: 



v' mi rrii . . . w/ 



v" my" m^" . . . m„'' 



v'" mi'" mi'" . . . mn'" 



dp = 



r\' mi m^' . . . w„' 



■t]" mi" W2" . . . w„" 



7/ mi m% . . . 7/in 



dt. (101) [129] 



As a simple example, we shall work out the application of this 

 equation to a system containing as separate phases, calcium 

 carbonate, lime and carbon dioxide. The two components 

 lime and carbon dioxide are sufficient to express every possible 

 variation of the system. Let the entropies, volume and quan- 

 tities of the phases be specified as follows. 



Volume 



Entropy 



Quantity of carbon dioxide. 

 Quantity of lime 



Solid 



phase 



(calcium 



carbonate) 



nil 

 mi' 



where m"' and m^" are necessarily in the proportion a : 6 in 

 which lime and carbon dioxide unite to form calcium carbonate. 

 Then, by (101), we have the following relation between varia- 

 tions of the temperature and the pressure: 



dt, 



eo that 



dp 

 dt 



II 



II 



II 



7] mi mi — t] mi m^ — t? mi m^ 

 v'" mi' m" - V mi'" ma" - v" mi' m^'"' 



(102) 



If the system consists of a quantity a of lime and h of carbon 

 dioxide, together with a quantity (a + h) of calcium carbon- 



