ANALYSIS OF THE CRITICAL LINE NETWORK FOR THE VANDERWAALS-EQUATION ATTHE VAN-LAAR POINT

The density-density plot of the critical lines of the van der Waals eq uation at the van Laar point is analyzed through its algebraic propert ies. It is shown that this curve is an irreducible expression of the f ifth degree of genus one. In addition, we show the topology of the sec ond branch, i.e., the T = 0 solution, which will interact with the fir st branch as soon as the energy parameters are slightly different from the van Laar values. Finally, we analyze the behavior of the van der Waals equation near the point at which liquid-liquid separation takes place.