Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

Abstract

The law of corresponding states (LCS), based on a generalized van der Waals equation of state (gvdWEoS) has been formulated by rescaling its thermodynamic variables with liquid- vapour critical—point parameters, the spinodal, the thermodynamic limit of superheat (TLS) and the supercritical (SC) point. This gvdWEoS differs from the known van der Waals equation of state (vdWEoS) by the modified attractive term. The scaling properties have been derived on the basis of the gvdWEoS. The expressions for the isothermal compressibility, a derivate of Gibbs free energy, have been derived. In all the cases of rescaling, the gvdWEoS has the similar functional form and the expression for isothermal compressibility has a similar functional form. This shows that the parameters of any spinodal-point on the phase diagram, including the TLS as a particular case, and the SC point, characteristic point on the quasispinodal, provide the alternate scales of parameterizing the thermodynamic properties of substances other than the liquid-vapour critical point. Moreover, an isothermal compressibility regularity is formulated on the basis of the gvdWEoS and it is found to satisfactorily trace the literature data for saturated liquid alkali metals.