POSSIBLE EFFICIENCY OF HEAT-ENGINES. 837 



Since no heat can enter, the temperature will fall to t, and the pressure 

 to A a. It is easy to show that, during this reverse cycle, an amount 

 of mechanical energy represented by A BCD has been expended, 

 and it is seen that heat equal to h has been taken from the refrigerator, 

 and heat equal to II given to the source. The engine is, therefore, a 

 perfectly reversible engine in the sense before defined, and it has al- 

 ready been seen that no other heat-engine of whatever construction, 

 steam, gas, hot air, thermo-electric, or whatever it may be, working 

 between the same temperatures, could develop more mechanical effect 

 from the heat II taken from the source. In other words, any heat-en- 

 gine working between the temperatures J 1 and t, and taking from the 

 source the amount II of heat, must transfer to the refrigerator an 

 amount of heat at least equal to /1, the amount given up by our rever- 

 sible engine under the same conditions. It remains to be seen what 

 relation this bears to the heat taken from the source. 



Experiment proves that the lower the temperature the smaller is h, 

 and it is evident that if the temperature of the refrigerator had been 

 lower the isotherm A D would have been N. The area A B C D 

 would then be greater, and, since this represents the work done by the 

 engine in one revolution, it is seen that this is greater the lower the 

 temperature of the refrigerator. It appears, then, that the propor- 

 tion of the heat taken from the source which can be converted into 

 mechanical effect, is greater as the temperature of the refrigerator is 

 lower, and the question arises, how low must this temperature be in 

 order that the whole of the heat may be so converted. Perhaps the 

 best way of approaching this question is by Sir TV. Thomson's abso- 

 lute scale of temperature. This may be defined as a scale upon which 

 the temperatures of any two bodies are to each other as the heat, re- 

 ceived is to the heat rejected by a reversible heat-engine using one of 

 the bodies as a source and the other as a refrigerator. That is, if T 

 and t are the temperatures upon the absolute scale of our source and 

 refrigerator, T : t :: II : h, or T-t : T=II-h : H. 



Let T be the temperature of boiling water, and t that of melting 

 ice, and let Tt = 180, as in the Fahrenheit scale. ' From the prop- 

 erties of air we know that if it is used as the working substance of a 

 reversible engine, with a source at the temperature of boiling water and 

 a refrigerator at the temperature of melting ice, II h : II :: 100 : 373 



nearly. Hence 



180 : T:: 100 : 373 



T= 671-4 



and t 491-4. 



Any other temperatures may be easily determined. Suppose B C 

 (Fig. 2) be the isotherm corresponding to the temperature of boiling 

 water, A D that corresponding to that of melting ice, and m n an 

 isotherm corresponding to some intermediate temperature, that marked 

 100 on the Fahrenheit scale, for instance, whose temperature t' upon 



