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 B C D has been expended, and it is seen that heat equal to h has been taken from the refrigerator, and heat equal to H given to the source. The engine is, therefore, a perfectly reversible engine in the sense before defined, and it has already 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 H taken from the source. In other words, any heat-engine working between the temperatures T and t, and taking from the source the amount H of heat, must transfer to the refrigerator an amount of heat at least equal to h, the amount given up by our reversible 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 O X. 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 proportion 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 W. Thomson's absolute 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, received 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:: H: h, or Tt: THh: H.
Let T be the temperature of boiling water, and t that of melting ice, and let Tt180°, as in the Fahrenheit scale. From the properties 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, Hh : H :: 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
