32 WILSON 



ART. C 



As the whole complex consisting of the system and the engines 

 is cyclic, the total work done, which is 



Q1 + 7Q2 + 7Q3 + 7Q4+...., 



t2 t3 h 



must be negative or zero as we cannot obtain work by a cyclic 

 process without creating a perpetual motion machine. Hence 

 dividing by ti, which is positive, we have 



«! + e^ + Q' + «' + ....=s«so, or /-so, 



tl ti ts 14 t 



r-f 



the equality sign holding only when the system is reversible. 



Now let s be any state of reference of the body for which we 

 take 1? = 0; then any states 1 and 2 which can be reached from s 

 by a reversible process will have the entropies 



- r 



dQ 

 t' 



and the difference between the entropies will be 



where there is obviously one reversible way to go from 1 to 2, 

 namely, that via s reversing the path from 1 to s above and 

 following the path from s to 2. For example, if we have a satu- 

 rated solution in equilibrium with some crystals, the application 

 of heat will dissolve the crystals maintaining a saturated solu- 

 tion until such point as the crystals are all dissolved and the 

 further application of heat will render the solution unsaturated. 

 Next, if heat be withdrawn the solution will become saturated 

 and then possibly somewhat supersaturated rather than crystal- 

 lizing. This process is reversible ; if the solution were supersatu- 

 rated appUcation of heat would render it unsaturated. The 

 transition from the state of saturation in the presence of crystals 

 to an unsaturated state through the application of heat is how- 

 ever not necessarily reversible because of the phenomenon of 

 supersaturation; but there is generally some way to induce 



