Van der Waals supercritical fluid: Exact formulas for special lines

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 gamma of a van der Waals fluid were analyzed. In the critical point, the van der Waals fluid has gamma = 8/3, corresponding to a soft sphere particle system with exponent n = 14. (C) 2011 American Institute of Physics. [doi:10.1063/1.3627231]