Starkweather — Thermodynamic Relations for Steam. 133 



2A 2A v% + 7 



*« -BTlog«(»-a)-— ^ + — log, ^ + F(T) 



where F(T) is some unknown function of T. It should be 

 observed that differences of ^ at constant temperature formed 

 by means of this equation are more accurate than the value of 

 p found by the equation of condition, for an integral cannot 

 have a greater percentage of error than the integrand. 

 Making use of the equation 



there is obtained 



2A 2A ^^ «i + y 



It is at once evident that here the factor — in the equation for^> 



plays an important role, and this equation, together with the 

 one to be obtained presently for the energy, may have a great 



error at small volumes, unless the factor — is justified. 



From the equation 



e = if/ -f Tyj 



we find 



, = R log, (v -a) -— + — log . —^1 -F'(T) 



where 



4A 4A . v$ +v 



— i + — l °ge—T 

 yTu Y y T V? 



^=-—, + -^og s -^+f(T) 



/(T) =F(T)-TF(T). 



y(T), except for an additive constant, is the kinetic energy, or 

 rather such part of it as depends on the temperature alone. 



A number of writers have performed this same integration 

 with their p-v-T equation, and have immediately assumed 

 that/(T) is linear in the temperature. We are now in position 

 to show that this assumption is contrary to the experimental 

 data at hand by determining f(T) within certain limits. For, 

 from the equation for e, we have 



/(T)= , + _f_ + 4 1(B ,.^ 



where, if e is expressed in kilogrammeters and v in cubic meters 

 per kilogram, the constants are given by 



log a — 6-286713 y = 1*20484 . 



log b— 6*567998 



