132 Starkweather — Thermodynamic delations for /Steam. 



equation will not hold for much smaller volumes. The larger 

 deviations near 323°'T are not due to the form chosen for the 

 equation, for at such large volumes the gas deviates only 

 slightly from the law of Boyle and Charles. A sufficient 

 explanation for these deviations lies in the values of p and 



dv) 



-|-, Regnault's formula for which is incorrect at low pressures, 

 at 



due to the fact that he did not recognize the sudden change in 



clii) 



-4- at 0°. This matter will be considered later. 

 dt 



p and T being given, the formula is not convenient for 



obtaining v, but if an approximate value of v be found from 



Boyle and Charles' law, p obtained, and then v corrected by 



the assumption 



Blogp = — 8 log v, 



a second correction will generally be sufficient. 



1 " 3 1 



If the factor — is correct, the term v»(v^+y) must be sen- 

 sibly so, for it satisfies the volumes on the saturation line and 

 approaches the value v* for large values of v. To justify the 



factor — recourse would naturally be had to volumetric 



experiments on superheated steam. Since it has been shown 

 in the previous paper, however, that such experiments do not 

 appear reliable, a more roundabout method is necessitated to 

 justify the factor. 



We now proceed to obtain the equations for entropy, ??, and 

 energy, e. The equations for energy formed by previous 

 writers have all been based on the assumption that either the 

 specific heat at constant pressure or that at constant volume is 

 constant, or on another assumption equally unjustifiable, which 

 will be mentioned later. There will be needed the quantity 



$ = €— T77, 

 and since 



de = Tdrj — pdv, 

 we have 



dxp = —7)dT —pdv. 



From this equation follow 



g] r =-p and .&], = ■-!• 



Substituting the value of p from our equation of condition in 

 the first of these, and integrating, there results 



