406 



For the ratios in question are about the same for all these sub- 

 stances — provided only that thej be in corresponding states (e.g. 

 111 = ^/2) — which will approximately be the case when the critical 

 temperatures are not too divergent. Only in the fore- factor °2/,,^o 

 care has of course been taken by means of the factor 7 that the 

 corrections in question are duly observed^). 

 As according to (1) 



« a At' Au 



i.. = AP+— Ai. = AP + = AP-f 7P.i(7'i. + ^ij — 



(see above), it immediately follows from (10'') that 

 1 

 24 



^=1^, (l-T)j(l-l/r^)-V,A,(l-T)(l+^, . (11) 



from which Avi^ can be calculated {v = 1). 



When the critical pressures of the two components are equal, 

 then T is =r 1 and w and Av both become = 0. As we already 

 pointed out in our tirst paper, then (i.e. with very small difference 

 of pjt^ and pje^) 1 — T is greater than (1 — t)*, so that the part with 

 At» will predominate in tv. But if the critical pressures differ some- 

 what more, the first part will continue to predominate. As will 

 appear from the calculation in the following paragraph, the part 

 with Av is at most 7$ of the first part, but often it is much less. 

 Hence the principal term of lo remains AP, and this may be repre- 

 sented by the single formula (a? = V,) : 



10^ - AP.^ = 7. ^1 Tj^ (1-^)'. 



If one wants, therefore, to form an approximate idea of the value 

 of the heat of mixing lu, it will mostly be sufficient to calculate 

 the said value of AP. 



The value of Av will sometimes be positive, sometimes negative. 

 Not always are the conditions for contraction (Av negative) fulfilled 

 — see ^ 3: "As regards the sign of Av" etc. According to the 

 tables on p. 160— 161, 169 and 176 of Kremann's cited book there 

 are about an equal number of mixtures of normal liquids with 

 a positive as with a negative Ai?. Everything, of course, depends on 

 whether 



(l-l/7)-7.^i(l-f)(lH-9^)> of <0, 



^) As RTk = %7 >. °^/bj: in which ?. is about ^^ .ig for ordinary substances, 

 "i/fj^^y^RTk. Now a at T = ^o Tk is about 1,4 a^ and v = 0,73 &^, so that 

 we have "Jv = 2 °i/i, =lRTn, 



