( 66 ) 



Now let the point from which we starl be (lie point of' the binodal 

 curve lying on the vapour side. Then, if' we appl.\ Maxwell's rule 

 in the two curves, it follows from the circumstance that /oisalways 

 larger for the curve at constant x, in t lie first place that Maxwell's 

 line for this p-curve lies higher than that for the p-curve when we 

 follow the (/dine, and in the second place that on the vapour side 

 the binodal curve for given ,/■ always lies at larger volumes than 

 the vapour volumes would be when every mixture was to be con- 

 sidered as homogeneous. In the same way on the liquid side at 

 smaller volumes. Just as the binodal line lies outside the line 



— — 0, the binodal line lies outside the phases which would coexist 



if every mixture should behave as a simple substance. Properties 

 which also immediately follow from the ip-surface. 



In fig. lb only (/dines of lower degree intersect the spinodal 

 curve. The (/dine of the highest degree which still has points in 

 common with the spinodal curve, which points are coinciding points 

 is that passing through the plaitpoint. When we follow this g-line 

 maximum and minimum pressure will have coincided, and drawing 

 j> as function of v, we get a line which has an horizontal tangent 

 in the plaitpoint, and at the same time a point of inflection, just 

 as an ordinary isotherm in the critical point. This is a remark 

 which alwavs holds for a plaitpoint, also for a hidden plaitpoint; 



fdp\ (d*p\ 



but then the special point in the p-line where I — I and I -— J is 



equal to 0, lies on the unstable branch. There is a third possibility 

 for the situation of this special point, viz. that it lies on what we 

 might call the liquid branch of the //dine, as will presently appear. 

 Let us now consider the case of fig. 8, and let us choose there 

 a ff-line which intersects the spinodal curve 4 times, as is the case 

 with one of the (/dines drawn. If starting at large volume we 

 follow this (/dine, we meet, still at large volume, the spinodal line 

 in a point where p has a maximum value; in the second point 

 where the (/dine leaves the unstable region for the first time, there 

 is maximum pressure. In the third point where this (/dine enters 

 the unstable region again, there is again maximum pressure, and in 

 the fourth point when the unstable region is finally left there is 

 again minimum pressure. Now to draw p properly as function of 



v, we must know the value of I — - . Now: 



dp 



(dp\ _ dp_ AAA 



