Starkweather — Thermodynamic Relations for Steam. 129 



Akt. XIY. — The Thermodynamic Relations for Steam; by 

 G\ P. Starkweather. 



Among the various thermodynamic relations for a gas that 

 between pressure, volume and temperature, the 'equation of 

 condition ' is one of the most important. To apply to the 

 case of steam such equations, either empirical, or based on 

 assumptions hardly justifiable, have been formed by Zeuner,* 

 Schmidt,f Ritter,J and Antoine.§ Of these Zeuner's and 

 Schmidt's satisfied the saturation line well, but they, as well as 

 Antoine's, had the fatal defect that the constant which deter- 



pv 

 mines the limiting value of j— for very great volumes was 



assumed incorrectly. 



Van der Waals' celebrated pamphlet in 1873 gave a rational 

 form to the equation of condition, and Clausius' generalization | 

 of the same, 



RT /(T) 



p v-a (v+py 



has been for the most part adopted for various substances. 

 Equations based upon this generally have the aim of satisfying 

 not only the gaseous state but also the liquid. A relation 

 between a and /3, and also the value of f(T) at the critical 

 point, follow from the fact that at that point not only does this 

 equation hold, but also its first and second partial derivatives 

 with respect to v. B. is fixed by the chemical composition of 

 the substance, while f(T) is so determined as to satisfy the 

 corresponding saturation pressures and temperatures by 

 Clausius' method. Tf The value of a (hence fi, from the rela- 

 tion mentioned above) is so chosen as to satisfy the water line 

 at some point. 



The best application of this method to steam has been given 

 by Van Laar,** who has taken for f(T) the form adopted by 

 Sarrauff for carbonic acid, /cy~ T ^ k and 7 being constants. On 

 applying Clausius' method of determining the corresponding 

 saturation pressures and temperatures to the equation he has 

 found a good agreement. 



* Zeitschr. des Yer. Deutsch. Ingen., xi, p. 42, 1867. 



f Zeitschr. des Ver. Deutsch. Ingen., xi, pp. 649, 771, 1867, and Prag Abhandl., 

 i, 1868. 



JWied. Ann., iii, p. 447, 1878. 



gComptes Rendus, ex. p. 632, 1890. 



fWied. Ann, xiv, pp. 279, 692, 1881. 



IfWied. Ann., xiv, p. 692, 1881. 



** Zeitschr. fur Phys. Chem., xi, p. 438, 1893. 



ffComptes Rendus, -ci, pp. 941, 994, 1145, 1885. 



Am. Jour. Sci.— Fourth Series, Yol. YII, No. 38.— February, 1899. 



