442 Mr. J. H. Shaxby on Vapour Pressures 



Thus U 2 =n x e~ & =TLM 2 . 



d\ 



But a fundamental relation connecting Ili and n 2 is 



n i (r 1 -6) = RT = n 2 (r 2 -6), 



where i\ and r 2 are the volumes of unit mass in the liquid 

 and in the vapour. 



S ° — -fi 



d 2 2 _i\ — b_d l 



d Y 2 " v^-L> " T~ ' 



e/ 2 



whence b — 



d l + 6? 2 ' 



The quantity (^1 + ^2) diminishes linearly, and fairly 

 slowly, with rise of temperature : this fact is well known and 

 is embodied in the so-called Cailletet-Mathias rule. The 

 rule is nearly exact for substances which are not associated, 

 but does not hold for such substances as water, for which 

 the changes in (d x -f d 2 ) are less regular. For most substances 

 the rate of decrease of (d 1 + d 2 ) is of the order of *001 per 

 1° C. Hence b is not a true constant, and this is known to 

 be the case from comparison of Dietericfs equation with 

 experimental data. 



lat 



We find, then, that 







i\ — b d 2 



and 



b 



v x d 1 + d 2 



i'i 



tiilc v 2 -b_ d, 



and 



b 



v 2 d l -t d 2 



«2 



di + d 2 ' 



d. 



di + d 2 . 



That is to say, the "free" space per unit volume in a 

 liquid at any temperature is equal to the " occupied " space 

 per unit volume in its saturated vapour, and conversely. 

 Equal volumes of liquid and vapour are, as it were, comple- 

 mentary in this respect. 



§ 2. We may write Dieterici's equation in the form 

 p{v~b) -4- 

 KT 



Thus for a liquid and its saturated vapour at temperature 

 T, if p is the saturation pressure, 



p(vi-b) _ ^ 



, p(Vo-b) _^ 



and J v " J = e r,RT m 



