138 Starkweather — Thermodynamic Relations for Steam, 



From the relation 



/(T) = F(T)-TF'(T) 

 there follows 



y"(T) = - TF"(T) 



from which F'(T) and F(T) are determined. The formulae for 

 T) and ty on page 133 become accordingly 



, = a'log 1 .(t>-a)-^+^log 1 .^+<riog 1 .T + .'T + K' 



* = ~ ^^ I— >- |i + T l0 «» ^T " 



d'T log Icl T- e"T-^-T + K" 



it 



where if -q is in kilogrammeters per degree, yjr in kilogram- 

 meters, and v in cubic meters per kilogram, 



log a' = 2*035657 

 log c' =6-266968 

 log e' = 1-195875 

 K' = 192-2 



log V = 5-985683 

 logd' = 2-264662 

 loge" = 2-050449 

 K" = 215126. 



These formulae, with that for the energy, have the same lim- 

 itations as to pressure and volume as the^-v-T formula, and 

 in addition can be used only when T is not far above 503 o, 7 or 

 far below 273°-7. 



The value of K! was determined so as to make the entropy 

 correct for the saturation line at 373°*7 ; the remaining quanti- 

 ties follow from others previously determined. How well the 

 formula for rj represents the saturation line is shown by 

 the following table, in the third column of which are given 

 the fractional changes in the latent heats necessary to make 

 the formula for rj correct. These should be the same as those 

 given on page 137, but there are differences, very slight, 

 however. 



T 



V 



273-7 



935-4 



2837 



908-5 



293-7 



883-9 



303-7 



861-4 



313-7 



840-7 



323-7 



821-7 



333-7 



804-3 



d 



T 



0011 



343- 







353- 



0007 



363- 



0011 



373- 



0015 



383' 



0015 



393- 



0013 



403- 



V 



788-2 

 773-1 

 759-2 

 746-3 

 734-2 

 722-9 

 712-4 



d 



— •0011 



— •0010 



— 0006 

 



+ •0005 

 + -0005 

 + •0009 



T 

 413-7 

 423-7 

 433-7 

 443-7 

 453-7 

 463-7 

 473-7 



v 

 702-5 

 693-3 

 684-4 

 676-3 

 668-5 

 661-3 

 654-5 



d 

 + •0010 

 + •0011 

 + •0008 

 + •0008 

 + •0002 



— •0002 



— ♦0005 



It has been remarked that Regnault's formula for correspond- 

 ing pressures and temperatures is incorrect at low temperatures. 

 Also Wiebe* has taken exception to his determinations near 



* Zeitschr. fur Instrumentenk., xiii, p. 329, 1893. 



