DAVIS. 



CERTAIN THERMAL PROPERTIES OF STEAM. 



295 



Bd. Planck's equation : — There remains the most interesting of all 

 the indirect attacks on C p at ordinary temperatures. In 1897 Planck 

 published in his thermodynamics the equation 



dff 





<lt 



L L 



f + u 



[(if] 



Ul (wat J 



This equation holds only along the saturation curve. For its deriva- 

 tion the reader is referred to the English translation of Planck's 

 book 43 or to Griessmann's paper. 44 The two partial derivatives must 

 be such as to describe the behavior of superheated steam and of water, 

 both close to the steam dome, not of steam within the steam dome. 

 In practise, the second of these derivatives is always negligible in 

 comparison with the first. 



Two sorts of experimental material are necessary for computations 

 with this equation, a set of total heat values (those proposed in this 

 paper will be used), and a set of values of (dv/dt) p for superheated 

 steam close to saturation. The latter can be based on the volume 

 measurements of Knoblauch, Linde and Klebe, 45 or on those on Ram- 

 say and Young, 46 or on those of Battelli. 47 

 These three sources will be considered in 

 turn. 



In the experiments of Knoblauch, Linde, 

 and Klebe, the volume was held constant 

 while the pressure and temperature were 

 varied. Their results, when plotted on the 

 p t plane, gave isochors or lines of constant 

 volume. These turned out to be straight 

 lines within the limit of error of the meas- 

 urements. Their slopes are entered with 

 other data in the main table of the original 

 paper. These slopes are values of {dp/dt) v 

 and some manipulation is necessary to get 

 from them the desired values of {dv/di) p . 

 Let Figure 11 represent a portion of the 



p t plane drawn, like an analytical geometry figure, with the same unit 

 of length along each axis. Then 



43 Treatise on Thermodynamics, 1903, 147. 



44 Forschungsarb., 1904, 13, 8. 



45 Forschungsarb., 1905, 21, 33. « Phil. Trans., 1893, 183 A, 107. 

 47 Mem. di Torino, 1893, 43, 63; condensed in Ann. Chim. et Phys., 1894, 



3, 408. 



Figure 11 



