374 



(1 ^ e-^Y 



Finally we obtain 



— — p.~^ Inn 1 — — . 



— =r ^ — ^ — e~^ log 

 a n 



(11') 



= ~log\\^eX^ . (12) 



This is, therefore, the equation determining a as a function 

 of V- and T; it actually gives for « values enclosed between 1 

 (^= — go) and infinity (.ï=-fx»)'). It is a fairly complicated 



1 



relation, as A^ itself contains «; but as — only changes between nar- 



a 



row limits, these limits themselves are not modified thereby and the 



law of change of X is moreover mainly determined by that of v 



and T. 



The manner in which « changes with v and T is most easily 



understood by putting ^ = 1 and s — 0, that is /; independent of 



V and Gj: independent of «. Expression (12) then reduces to , 



log[ 1 + (12') 



a e^ \ v—b^ 



where 



E H 

 q= \- I (12") 



is now only a function of the temperature. In this case it will be 

 seen, that at a constant value of e'U i. e. at constant temperature, 

 1 



— diminishes continually from 1 to 0, when v decreases from oo to 

 a 



b, so that along an isothermal a steadily increases from 1 (z; = oo ) 

 to 00 {v = b). When the temperature falls towards 7^ = at constant 

 volume the degree of association increases regularly up to a = oo , 

 at least if E and H depend on the temperature in such a manner 

 that at 7'=0 q = cc ; similarly with rising temperature « falls 

 towards unity, if q approaches — oo ; it will appear in ^ 10 that 

 this must be so. 



According to the law of dependence assumed between b and v 

 the course of ƒ (v) (equation 8') remains in the main unchanged, so 

 that the change of a with v and 7' also remains very much the 



1) The following table shows the manner in which - changes with X: 



a 



A=...— 5 -4 -3-2-1012 34567. 



1 



-=... 1 0,99 0,98 0,93 0,85 0,69 0,48 0,28 0,16 0,08 0,03 0,01 0... 



