EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 95 



Also in the case of a body of variable composition, when all the 

 quantities of the components except one vanish, the potential for 

 that one will be equal to the value of f for one unit of the body. 

 We may make this occur for any given composition of the body by 

 choosing as one of the components the matter constituting the body 

 itself, so that the value of f for one unit of a body may always be 

 considered as a potential. Hence the relations between the values 

 of f for contiguous masses given on page 91 may be regarded as 

 relations between potentials. 



The two following propositions afford definitions of a potential 

 which may sometimes be convenient. 



The potential for any substance in any homogeneous mass is equal 

 to the amount of mechanical work required to bring a unit of the 

 substance by a reversible process from the state in which its energy 

 and entropy are both zero into combination with the homogeneous 

 mass, which at the close of the process must have its original volume, 

 and which is supposed so large as not to be sensibly altered in any 

 part. All other bodies used in the process must by its close be 

 restored to their original state, except those used to supply the 

 work, which must be used only as the source of the work. For, in 

 a reversible process, when the entropies of other bodies are not 

 altered, the entropy of the substance and mass taken together will 

 not be altered. But the original entropy of the substance is zero; 

 therefore the entropy of the mass is not altered by the addition of 

 the substance. Again, the work expended will be equal to the 

 increment of the energy of the mass and substance taken together, 

 and therefore equal, as the original energy of the substance is zero, 

 to the increment of energy of the mass due to the addition of the 

 substance, which by the definition on page 93 is equal to the potential 

 in question. 



The potential for any substance in any homogeneous mass is equal 

 to the work required to bring a unit of the substance by a reversible 

 process from a state in which \[s = and the temperature is the same 

 as that of the given mass into combination with this mass, which at 

 the close of the process must have the same volume and temperature 

 as at first, and which is supposed so large as not to be sensibly 

 altered in any part. A source of heat or cold of the temperature 

 of the given mass is allowed, with this exception other bodies are 

 to be used only on the same conditions as before. This may be 

 shown by applying equation (109) to the mass and substance taken 

 together. 



The last proposition enables us to see very easily how the value 

 of the potential is affected by the arbitrary constants involved in 

 the definition of the energy and the entropy of each elementary 



