Van der Waals supercritical fluid: Exact formulas for special lines Available to Purchase

In the framework of the van der Waals model, analytical expressions for the locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, density fluctuation, and sound velocity in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into single Widom line only at T < 1.07T_c, P < 1.25P_c and become smeared at T < 2T_c, P < 5P_c, where T_c and P_c are the critical temperature and pressure. The behavior of the Batschinski lines and the pseudo-Gruneisen parameter γ of a van der Waals fluid were analyzed. In the critical point, the van der Waals fluid has γ = 8/3, corresponding to a soft sphere particle system with exponent n = 14.