422 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



If T is the absolute temperature, p the external pressure, v the 

 specific volume, k the coefficient of compressibility at constant temp- 

 erature, and e the coefficient of expansion at constant pressure, then 

 /■ and e have by definition the following meanings. 



k = 



e = 



V \9j) 



do 



9T 



If, according to the van 

 der Waals equation, we 

 plot on the 7^ r-plane, 

 as in Figure 1, the iso- 

 thermals of the liquid, /■ 

 and e each have a geo- 

 metric interpretation ; /• 

 is the reciprocal of the 

 slope of the isothermal 

 divided by v; and e is 

 the distance between 

 twoisothermals measured 

 parallel to the r-axis, 

 divided by the difference 

 of temperature between 



the isothermals and di- 



^ vided also by v. 



The purpose of this re- 

 search may now be made 

 somewhat clearer by an examination of Figure 1, where we will suppose 

 that we have plotted two of the isothermals of either ethyl ether or 

 ethyl alcohol. Suppose the temperatures for which these isothermals 

 are plotted differ from each other only by two or three degrees. To be 

 specific, consider the isothermal A F H J. On this isothermal the 

 point D represents the liquid when it is under a pressure equal to its 

 vapor-pressure. The part D F of this isothermal represents the liquid 

 in the superheated state. We are to determine the slope of such an 

 isothermal, (1) at B and C, where the external pressure exceeds the 

 vapor-pressure by about one atmosphere, (2) at D, where the external 

 pressure is equal to the vapor-pressure, (3) at E, where the external 

 pressure is less than the vapor-pressure. Furthermore, the distance 

 B L between any two neighboring isothermals, when p is equal to one 



Figure 1. 



