92 EQUILIBEIUM OF HETEROGENEOUS SUBSTANCES. 



and b parts of a salt which is in contact with vapor of water and 

 crystals of the salt, it is necessary that the value of f for the quantity 

 a+b of the solution should be equal to the sum of the values of f for 

 the quantities a of the vapor and 6 of the salt. Similar propositions 

 will hold true in more complicated cases. The reader will easily 

 deduce these conditions from the particular conditions of equilibrium 

 given on page 74. 



In like manner we may extend the definition of x t any mass or 

 combination of masses in which the pressure is everywhere the same, 

 using e for the energy and v for the volume of the whole and setting 

 as before 



(118) 



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 



'-'O = Q. (H9) 



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 x remains unchanged. 



Potentials. 



In the definition of the potentials yu p /x 2 , 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 

 differential 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 considered 

 as composed. For example, if we have a solution obtained by dis- 

 solving in water a certain salt containing water of crystallization, 

 we may consider the liquid as composed of m s weight-units of the 

 hydrate and m w of water, or as composed of m a of the anhydrous 

 salt and m w of water. It will be observed that the values of m s and 



