THERMODYNAMICS. 



269 



Comparison of the Absolute with the Air Thermometer Scale. 



To make the formula just found of practical importance, it is necessary 

 to show what relation the absolute bears to known scales. Fortunately 

 it can easily be shown that it nearly coincides with the air thermometer 

 scale. Since all gases give nearly the same temperature indications if 

 far above their condensing points, and the gas scale is therefore nearly 

 independent of the particular gas used, we might perhaps be led to 

 expect this. 



Let us work a mass of air in a reversible engine between two tem- 

 peratures expressed on the air scale. Our knowledge of the properties 

 of air enables us to determine the efficiency of the engine in terms of 



FIG. 155. Air Scale and Absolute Scale. 



the air temperatures, and we may compare the efficiency so found with 

 its expression in terms of the absolute temperatures. 



Let AD, BO (Fig. 155) be two neighbouring isothermals of the air, 

 the temperatures measured from - 273 C. being t and t' respectively. 

 Let AB, DC be adiabatics, and let AD and t' t be so small that ABCD 

 is sensibly a parallelogram. Working round the cycle reversibly, heat 

 is taken in along BO and given out along DA, the difference being 

 converted into work represented by the area ABCD. 



The Efficiency = 



Area ABOD 



Mechanical Equivalent of Heat taken in along BC. 



But by Joule's experiment on the expansion of gases, a gas expanding 

 and doing no external work remains very nearly at the same temperature 

 without any supply of heat. If it does work and still remains at the 

 same temperature, the heat supplied must be equivalent to the work 

 done. But this is the condition of the air along BC, and the work done 

 is represented by BCNM, which is therefore the mechanical equivalent of 

 the heat taken in along BC. 



