270 HEAT. 



Then the efficiency 



_ABGD. 



" BONM. 



KBGL 



~BONM 



BK + OL 



xMN 



BM + CN 

 = x 



2 



BK + GL 

 "BM+CN 



Now BM and KM are the pressures at constant volume correspond- 

 ing to t' and t, and are therefore proportional to t' and t, this being really 

 the definition of t' and t with the air thermometer. 



. KM t 



BK t'-t 



and SM r 



CL t'-t 



Similarly 



.". efficiency = 



CN~ t 



BK + CL t-i 



BM+CN" H 



If 6 & are the temperatures on the absolute scale corresponding to 

 t and t' 



ff-e t'-t 



& t 



0=1 



Or the temperatures on the one scale are approximately proportional 

 to those on the other, and we may conveniently choose the degrees so 

 that 0C. shall be - 273 on either scale, or, more exactly, that the interval 

 between C. and 100 C. shall be 100 degrees on either scale. 



This is only an approximate result, for it assumes that in Joule's 

 experiment (p. 120) there was no change of temperature, an assumption 

 not quite exact, as we know by later experiments. It also assumes that 

 the air scale for the volume OM is proportional to that for ON, an 

 assumption exceedingly near the truth, but still probably slightly inexact. 



Non-Reversible Cyclical Engine. The foregoing propositions 

 relate to reversible engines only, but if we have an engine not reversible, 

 say one in which the working substance is at a lower temperature than 

 the source when it takes in heat and is at a higher temperature than the 

 refrigerator when it gives out heat, and yet goes through a cycle so that 

 it recurs to its initial condition, it is easy to show that 



No cyclical non-reversible engine working between given temperatures is 

 more efficient tJian a reversible engine. For let the non-reversible engine 



