592 Mr. L. Vegard : Contributions to 



According to the second law o£ thermodynamics P is a 

 quantity that, for all processes which can arise in the system 

 of their own accord, can never be negative. 



If our system is considered in the neighbourhood of the 

 point of equilibrium the vis viva can be left out of consideration, 

 and in accordance with the First Law of Thermodynamics 



Q=I„-I 1+ A, 



the heat being measured in work units. I is the internal 

 energy, and A the external work done by the forces o£ the 

 system. 



By a combination of both these equations: 



TP=(I -TS )-(I 1 -T8 1 )+A. 



Here I and S are functions of the variables of the system. 

 We put 



where ^ is the so-called thermodynamic potential. I£ the 

 system suffers an infinitely slight change : 



TSP=-g^ + SA. 



The condition which is necessary, in order that a system 

 left to itself at constant temperature, shall be in equilibrium, is 

 that SP = for every small change that the system may suffer*. 

 If the system depends on r independent variables a 1? u 2 ...a r , 

 the system can suffer r independent variations. The equi- 

 librium condition may therefore be expressed as follows : 



(HU = (SA) aa I (3 , } 



Here (<ty) ar and (£A) a „ mean the changes respectively of 

 yfr and A for the same variation of a r , when the other variables 

 are kept invariable. 



The change that must come into consideration here is a 

 relative displacement of both components in a volume element. 

 This variation will generally cause a small volume change. 

 The pressure on the element will, however, not be changed 

 by it. If the external pressure is kept constant during the 



* Duhem, Mecanique Chimique, tome i. livre i. p. 89. 



