268 HEAT. 



temperature of the final refrigerator, the efficiency is evidently propor- 

 tional to the number of engines or steps down, and we may write 



Efficiency = A(0 S - K ) 



where A does not depend on R , but is a function of O s alone. 



Let us now suppose that it is possible to continue the steps down so 

 far that all the heat put in is converted to work, and that none remains 

 over to put into the lowest refrigerator. The temperature of this 

 refrigerator is the lowest conceivable consistent with the First Law of 

 Thermodynamics, for a still lower temperature would enable us to get 

 more work out of a given quantity of heat than its mechanical equiva- 

 lent. We choose this temperature, then, as the zero of the new scale, 

 and shall term it the absolute zero. 



If the refrigerator is at the absolute zero R = 0, and the efficiency is 

 1, or all the heat put in at O s is converted to work. Then we have 



A= 



With any other temperature of refrigerator the efficiency is 



This efficiency has been obtained from a peculiar compound engine ; but 

 since that engine is reversible, its efficiency equals that of any other 

 reversible engine working between the same temperatures and the 

 result is therefore general. 



If Q s is the heat taken in at the source and Q R that given out to the 

 refrigerator by a reversible engine, then, equating the temperature ex- 

 pression to the work expression for the efficiency, we have 



Efficiency = %^R = ^B 

 Vis PS 



whence 5 = 5 



- 



PS #B 



We may put this result into the following form. If any quantity of 

 heat is allowed to go down a temperature slope, some of it being inter- 

 cepted and transformed, then if the transformations are reversible, so 

 that by exact reversal the original quantity of heat could be returned 



to the source, the quantity -^ remains constant down the slope. We 



may here mention that this quantity, ^, is termed the Entropy put in GO 

 the system. We shall return to the subject of Entropy later. 



