26 PROCEEDINGS OP THE AMERICAN ACADEMY. 



The agreement is satisfactory and within the limits of experimental 

 error. 



2. The Vapor Pressitre Curve. — The change with changing temper- 

 ature of the equilibrium between a vapor and its liquid or solid phase 

 may be obtained from equation (20) ; for if we consider the vapor to 

 obey with sufficient exactness the laws of perfect gases, the system under 

 consideration is one for which equation (20) was developed, since it con- 

 tains only a gaseous phase and a condensed phase of definite composition. 



From equation (20), — ^- = -^^ . 



In K = In V — In ?/, 



where v is the molecular volume of the vapor, v' that of the solid or 



,. ., din v' . ^ . ^ d\n v 



liquid. „ is entirely negligible compared with , and equa- 



tion (20) becomes d\nv U 



~dT ^ 'RT^ ' 



hince V =^ , where p is the vapor pressure, 



In y = — In JO + In ^ + In T, 



and dlnv = — d\np + — d T. 



^ , . . d\np U 1 -U+ RT 

 Substituting, -j-^' ^ — -^-^ + 7^ ^ iej-^ — • 



As on page 22, let — U + R T = L, 



din p L 



then __ = __, 



which is the familiar expression for the vapor pressure curve. 



A complete expression for the vapor pressure in the case of liquids 

 to which equation (36) applies, if the vapor approximates a perfect gas, 

 may be derived as follows : 



1 '^' — ^ 

 V^^'~R~T' 



R T 



Substitute for v, and 



V 



RT L RT (±\ 



In :^ . or z;: aXR T/ 



^"^(y'-Z,') i?r °^ p{v'-b') ^ 



RT 

 whence p 



(y' - b') e(^) 



