v. On the Equilibrium of Heterogeneous Substances. 



By J. WlLLARD GiBBS. 



"Die Energie der Welt ist constant. 

 Die Entropie der Welt strebt elnem Maximum zu." 



Clausius.* 



The comprehension of the hiws which govern any material system 

 is greatly facilitated by considering the energy and entropy of the 

 system in the various states of which it is capable. As the difference 

 of the values of the energy for any two states represents the com- 

 bined amount of work and heat received or yielded by the system 

 when it is brought from one state to the other, and the difference of 



entropy is the limit of all the possible values of the integral I -t'-i 



{dQ denoting the element of the heat received from external sources, 

 and t the temperature of the part of the system receiving it,) the 

 varying values of the energy and entropy characterize in all that is 

 essential the effects producible by the system in passing from one 

 state to another. For by mechanical and thermodynamic con- 

 trivances, supposed theoretically perfect, any supply of work and 

 heat may be transformed into any other which does not differ from 

 it either in the amount of work and heat taken together or in the 



value of the integral / — —. But it is not only in respect to the 



extei'ual relations of a system that its energy and entropy are of 

 predominant importance. As in the case of simply mechanical sys- 

 tems, (such as are discussed in theoretical mechanics,) which are capable 

 of only one kind of action upon external systems, viz., the perform- 

 ance of mechanical work, the function which expresses the capability 

 of the system for this kind of action also plays the leading part in 

 the theory of equilibrium, the condition of equilibrium being that 

 the variation of this function shall vanish, so in a thermodynamic 

 system, (such as all material systems actually are,) which is capable of 

 two different kinds of action upon external systems, the two functions 

 which express the twofold capabilities of the system afford an almost 

 equally simple criterion of equilibrium. 



*Pogg. Ann. Bd. cxxv (1865), S. 400; or Mechanische Warmetheorie, Abhand. ix., S. 44. 



