(3Ö) 



pronounced inflection point up to the last ^). For values of g) ]> 1, 

 the curve C^C^ lies partially on the left of the curve x=y^, and 

 the point of contact at I) passes into two points of intersection. 



By an approximate solution of (2b) and substitution in (1^) and 

 (3) of the values found, the foUovv^ing points of the two plaitpoint 

 curves are calculated. (The other values of a> or ^' are either imaginary 

 or do not satisfy). 



<f = l 



Curve C„C. 



i 



X r= 0,5 0,6 0,7 0,8 0,9 



u = 1 0,49 0,43 0,39 0,36 0,33 



T = 1 1,78 1,98 2,13 2,20 2,37 



x=oo 6,^4 5,75 5,05 4,51 4 



Curve C,A 



« = 0,33 0.4 0.51) 0,6 0,7 



x=0 0,021 0.041 0,042 0,023 



T==0,59 0,63 0,62 0,51 0,33 



^r=l 1,15 1,08 —3,09 - 



0,8 0,9 1 

 0,010 0,0017 

 0,16 0,042 

 8,64 -16,9 - 27 



It is seen that the pressure begins to be negative for points in the 

 neighbourhood of A. This is not remarkable; also for a simple 

 substance the points of inflection in the ideal isotherms reach to 

 within the region of the negative pressures. Though the pressures 

 in some points on the spinodal curve are negative, this is no reason 

 why those on the connodal curves should be so. 



The limits of the region of negative pressures on the spinodal 

 curves may be easily fixed (see the dotted curves in fig. 1) by solution 

 of the equation (see (3a)) 



2x (1 — cc) = (<p + xf (1 - a>) (2co — 1). 



If we put here (1 — a>) (2a) — 1) := 0, we find : 



_ (I — g^d) ± 1/1 — 2(p(^+ 1)6 



2^6 

 In this way we calculate for (p =^1: 



X = 



to= 1 



That jr approaches 

 immediately from (3) 



0,9 

 0,04= 

 0,84 

 to - 



0,8 



0,07 



0,75^ 



27 



0,7 



0,07 



0,75= 



0,6 

 0,04= 



0,84 



0,5 







1. 



For as 



for 



T 



prove 

 value of (p 



1— cu 



27 1 / \ 



presently, jr = y — ( — 2yM =: 



X = 0, a> = 1, T = follows 

 approaches to 0, as we shall 



-27, independent of the 



1) For this plaitpoint curve (^ = the following points are easily calculated: 

 ^' = 0,9 0,8 0,7 0,6 0,5 0,4 

 x = 0,507 0,528 0,567 0,623 0,712 0,853 

 The equation (2Ö), viz., passes then into the following quadratic equation in xu 

 a;2«2 (9 _ io<i, + 3«2) _ 3^^. (2 — «) + 1 = 0. 

 The other value for x is always > 1. 

 ') The maximum lies at « = 0,54; x is then about = 0,043. 



