GIBBS' PAPERS I AND II 33 



crystallization so that we can consider that the state of satura- 

 tion in the presence of crystals may be reached reversibly. If 

 this is the case it is easy enough to define the difference in 

 entropy between a state of supersaturation and the state of 

 saturation in the presence of crystals. 



Consider next a process which goes on within a wholly iso- 

 lated system doing no work and receiving no heat. If that 

 system can exist in two states 1 and 2 such that the path from 1 

 to 2 is irreversible but the path from 2 to 1 is reversible we can 

 represent the difference in entropy at 2 and at 1 as 772 — 171. 

 Then 



r^A+r^A^O and 



7l t J2 t ~ 



irrev. rev. 



^ T72 — 771. 



But if the irreversible process goes on entirely within the system 

 there will be no heat dQ absorbed by the system, dQ = 0, and 

 hence 



^ T72 — Tji or 172 = 171- 



Hence if an isolated system changes from state 1 to state 2, the 

 entropy in state 2 must exceed that in state 1 (except when the 

 change is reversible, when 772 = 171). It is assumed that there is 

 some way to reach both states 1 and 2 reversibly from a third 

 state. Take the case of the supersaturated solution. This may 

 go over of itself into the state of a saturated solution with crys- 

 tals. We have seen that we can reach the supersaturated 

 states reversibly (i.e., we can reach any attainable degree of 

 supersaturation reversibly). We can reach the state of satu- 

 ration in the presence of crystals by merely placing the saturated 

 solution and the crystals in juxtaposition. We have thus the 

 possibility of defining the entropy 772 of the mixture of saturated 

 solution and crystals and the entropy 771 of the supersaturated 

 solution. The difference 772 — 771 will be positive. It is assumed 

 that the mixture of saturated solution and of crystals in all its 

 characteristics is that which would result from the spontaneous 

 crystalhzation of the supersaturated solution in complete iso- 

 lation. 



