266 



HEAT. 



FIG. 152. 



lose nor gain heat, for B restores what A takes. But after each cycle 

 which B goes through, a balance of work W - W remains over. This 

 can only come from the refrigerator, which must give up to B more heat 

 than it receives from A. Allowing the process to continue indefinitely 

 we should obtain any quantity of work by abstracting heat from the 

 refrigerator. Now the refrigerator may be arranged to be the coldest 



body in the system, so that we should 

 be obtaining work by merely extracting 

 heat from the already coldest body. 

 For the working substances are at the 

 end of each cycle in their initial con- 

 dition in every respect. This is con- 

 trary to the experience embodied in 

 the Second Law of Thermodynamics. 



Hence we conclude that A cannot 

 be more efficient than B, or that the 

 two reversible engines are equally 

 efficient. 



We may further prove that the 

 efficiency of a reversible engine working 

 between given temperatures is the same 

 whatever quantity of heat is put in at 



the higher temperature. That is, if on an indicator diagram (Fig. 152) 

 ABCD represents a Carnot cycle for a reversible engine, the area ABCD 

 is proportional to the heat taken in along BO, so long as BO and AD 

 are given isothermals. For suppose that in a second case double the 

 heat is taken in, the working substance at the higher temperature 

 moving to E along the BO isothermal, and suppose that BEFA now 

 represents the cycle. We may imagine a second engine exactly like the 

 first working round the cycle ODFE. Then from the preceding proposition 

 it has the same efficiency 

 for the same quantity of 

 heat taken in. But the 

 heat given along CE equals 

 the heat given along BO 

 by supposition. Hence the 

 area CDFE equals the area 

 BADC. Or, if the heat 

 given along BE is double 

 the heat given along BO, 

 the work BF is double the 



work BD. That is, the efficiency is the same whatever quantity of heat 

 is taken in. 



Absolute or Work Scale of Temperature. We may express the 

 equal efficiency of all reversible engines between given temperatures, 

 and its independence of the quantity of heat put in, by saying that the 

 efficiency between given temperatures depends only on those tempera- 

 tures, and not on the nature or conditions of the particular substance 

 used. This independence of the working substance suggested to Lord 

 Kelvin that the efficiency might be used to indicate the temperature on 

 an absolute scale i.e. one in which the given intervals would have 



1'iG. 153. Equal Temperature Intervals 

 on the Work Scale. 



