THERMODYNAMICAL SYSTEM OF GIBBS 69 



where dQ is the element of heat absorbed at temperature t. 

 This heat must come from surrounding bodies, and the process 

 can only be perfectly reversible when each element of heat is 

 absorbed from a body which has the same temperature as the 



system itself. Therefore — / dQ/t represents the entropy 



Jin 

 change of the surrounding bodies, so that when a reversible 



change takes place the sum of the changes of entropy of the 



system and its surroundings is zero. 



On the other hand, if the change of the system is irreversible, 



its entropy change is still 77" — rj^, since this quantity depends 



solely on the initial and final states and not on the way in 



which the change occurs, but it is no longer equal to / dQ/t. 



JU) 

 Since less work is obtained from the system in an irreversible 



change than in a reversible change, the heat absorbed is also 



less, and therefore: 



dQ/t {system) < 7?" " 1?'^ 



in 

 or 



Jc 



nil) 



77" — TJ^ — / dQ/t (system) > 0. 



J {n 



The decrease in entropy of the surroundings cannot be greater 



than/ dQ/t (,y,tem), since an element of heat c?Q can only be 



Jin 

 absorbed from a body having a temperature equal to or greater 



than the momentary temperature t of the system. The total 



entropy change of the system and its surroundings is therefore 



positive, i.e. when an irreversible change takes place, the entropy 



of the universe is increased. We have seen that irreversible 



changes may take place spontaneously in the universe or in 



any isolated system which is not in a state of equilibrium, so 



that we arrive at Clausius' statement of the second law of 



thermodynamics; "The entropy of the universe tends to a 



maximum." 



It is evident that the second law of thermodynamics affords a 



