148 J. W. Gibbs — Eqidlibrium of Heterogeneous Substances. 



If we denote by Q the heat received by the combined masses from 

 external sources in any process in which the pressure is not varied, 

 and distinguish the initial and final states of the system by accents 



we have 



/' - / = 6" - 6' +p {v" - v') = Q. (119) 



This function may therefore be called the heat function for constant 

 pressure (just as the energy might be called the heat function for 

 constant volume), the diminution of the function representing in all 

 cases in which the pressure is not varied the heat given out by the 

 system. In all cases of chemical action in which no heat is allowed 

 to escape the value of j remains unchanged. 



POTENTIALS. 



In the definition of the potentials /i^, /Yg, etc., the energy of a 

 homogeneous mass was considered as a function of its entropy, its 

 volume, and the quantities of the various substances composing it. 

 Then the potential for one of these substances was defined as the dif- 

 ferential coefficient of the energy taken with respect to the variable 

 expressing the quantity of that substance. Now, as the manner in 

 which we consider the given mass as composed of various substances 

 is in some degree arbitrary, so that the energy may be considered as 

 a function of various different sets of variables expressing quantities 

 of component substances, it might seem that the above definition 

 does not fix the value of the potential of any substance in the given 

 mass, until we have fixed the manner in which the mass is to be con- 

 sidered as composed. For example, if we have a solution obtained 

 by dissolving in water a certain salt containing water of crystalliza- 

 tion, we may consider the liqviid as composed of nig weight-units of the 

 hydrate and myy of water, or as composed of m, of the anhydrous 

 salt and w„, of water. It will be observed that the vahies of m,, and 

 m, are not the same, nor those of m„- and m,,,, and hence it might 

 seem that the potential for water in the given liquid considered as 

 composed of the hydrate and water, viz., 



(^\ 



\d»ijy/fi, V, ms 



would be different from the potential for water in the same liquid con- 

 sidered as composed of anhydrous salt and water, viz., 



