Starkweather — Thermodynamic delations for Steam. 137 



saturation line, whereas f"(T) refers to any states whatever. 

 The writer has therefore assumed f(T) to be represented in 

 the range considered, so far as the accuracy of the experiments 

 permits us, by the formula 



/(T)=a + £T + cT 2 



Determining a, h and c from the values of f(T) at 273° *7, 

 373°*7 and 503°*7, there are obtained 



a =215126 Log b = 1*902449 log c = 2*894845 



How weliyCT) is represented by this formula is shown by 

 the following set of values calculated from it, which should be 

 compared with those given on page 134. In order to properly 

 represent the inaccuracies of the formula, in the third column 

 are given the fractional deviations in the latent heats which it 

 would be necessary to assume in order to make the formula 

 absolutely correct. 



T 



/(T) 



d 



T 



/(T) 



d 



T 



/(T) 



d 



273-7 



242870 







353-7 



253200 



-•0009 



433-7 



264536 



+ •0009 



283-7 



214107 



— '0008 



363-7 



254562 



— •0004 



443-7 



266023 



+ '0006 



293-7 



245358 



—•0012 



373-7 



255940 







453-7 



267527 



+ •0002 



303-7 



246626 



— •0015 



383-7 



257334 



+ •0005 



463-7 



269045 



— •0004 



313-7 



247910 



— •0017 



393-7 



258743 



+ •0008 



473-7 



270580 



— •0010 



323*7 



249209 



— •0016 



403-7 



260167 



+ •0011 



503-7 



275278 







333-7 



250524 



— •0014 



413-7 



261608 



+ •0011 









343-7 



251854 



— •0013 



423-7 



263064 



+ •0011 









It will be noted that the negative deviations near 313-7 bring 

 the latent heats nearer Griffiths' determinations. It is probable 

 that the latent heats thus calculated from f(T) as expressed by 

 the formula are from 0° C. to 100° C. nearer the truth than 

 those obtained from the formula for H given in the preceding 

 article. 



Theoretically it would be very gratifying if /"(T), which is 

 the specific heat at constant volume for very large volumes, 

 should at low temperatures approach either 3R or J-R. These 

 are respectively 141*44 and 117*37. That the first is not 

 approached is evident from the numbers on page 134. 

 Whether or not the second is, is not conclusively shown ; the 

 total heats are not accurately enough known at low temper- 

 atures to determine this. Since J R would be 165*01, it looks 

 as though in the range say from —50° C. to +200° C. a change 

 in the molecular deportment of the steam occurs, such that the 

 number of degrees of freedom of the molecule increases, and 

 the specific heat at constant volume changes from f R to JR. 

 Such molecular change might explain why a difficulty exists 

 in finding a p-v-T formula to satisfy both water and steam. 



