EQUILIBRIA AND THEIR DISPLACEMENT 269 



ideal and limiting cases of transformations where there 

 is no increase in entropy. The most famous case is 

 known as the Carnot cycle which is typical of heat 

 engines or internal combustion engines. The conclu- 

 sion reached by Carnot and by Clausius is that the 

 maximum efficiency of such a cycle is independent of 

 the working substance, e.g. water, or air, and depends 

 only upon the extremes of temperature to which the 

 substance is subjected. The efficiency will be much 

 less than this in all but the ideal case. 



