134 /Starkweather — Thermodynamic Relations for Steam. 



Now e and v are known on the saturation line for values of T 

 from 273°-7 to 473°-7. For there 



e = JH— p(v—w) 



where H is the total heat, J the mechanical equivalent, and w 

 the volume of water at the pressure and temperature under 

 consideration. Consequently f(T) is found for this range. 



The values given for the energy on the saturation line by 

 the last equation are untrustworthy at low temperatures, since 

 there v is rather uncertain owing to the error in Regnault's 

 formula for corresponding saturation pressures and tempera- 

 tures. But from the equation for^>, since for the region below 

 100° C. w is constantly 0*001, there is obtained 



p(v-r-w) 



RT(?;--001) A(v--001) 



•0008 Tv?(vt + y) 



In the first term of the second member, since v is large, any 

 error in v cancels out. The last term is so small for the region 

 where serious errors in v may occur that the volumes calcula- 

 ted from the latent heats may be used. This also is true con- 

 cerning the values of the potential energy ; any slight errors 

 in the volumes at low temperatures will not affect things. 



In this manner e has been calculated for the saturation line, 

 then f /(T), and the following table obtained. In the first 

 column is given the absolute temperature, in the second the 

 corresponding value of f{T), and in the third, under /"(T), the 

 average rate of increase of f(T) for each ten degrees. 



T 



/(T) 



/'(T) 



T 



/(T) 



/'(T) 



T 



/(T) 



/'(T) 



273-7 



242870 



141-5 



343*7 



252135 



126-4 



413-7 



261362 



146-6 



283-7 



244285 



137-3 



353-7 



253399 



127-0 



423-7 



262828 



151-2 



293-7 



245658 



133-4 



363-7 



254669 



127-1 



433-7 



264340 



155-7 



303-7 



246992 



131-4 



373-7 



255940 



128-5 



443-7 



265897 



159-5 



313-7 



248306 



128-7 



383-7 



257225 



133-4 



453-7 



267492 



163-3 



323-7 



249593 



128-0 



393-7 



258559 



137-3 



463-7 



269125 



165-2 



333-7 



250873 



126-2 



403-7 



259932 



143-0 



473-7 



270777 





Leaving out the lowest temperatures, which will be con- 

 sidered presently, we have the very remarkable fact thaty'(T), 

 instead of being constant, as is generally supposed, is an 



