Joule – Thomson Inversion Curves for Van Der Waals Gas from a Mathematical Point of View

A continuation of our ongoing investigation into Joule - Thomson inversion curves for van der Waals gas, is performed from a mathematical viewpoint. The methodology basis of our analysis is the quadratic polynomial theory. In this context, focusing on the parametric equation of inversion curves in a P - V frame of reference we obtain a qualitative illustration of variables T, V by means of two inequality relations. However, we should elucidate that these inequalities are valid only for the intersection points between the family of Joule - Thomson inversion curves and the isothermal spinodal lines, provided that they are both sketched in a common P - V coordinate system. The mathematical treatment of the parametric equation of these curves has been carried out in a rigorous manner and no further restriction is introduced for the variables T, V. Thus, the proposed inequalities have a wider range of validity when compared with those that had been previously presented by the author and therefore their possible applications to P - V - T surfaces of van der Waals gas, are also wider.