Analysis of p, T, ρ-data for all fluid states via comparison with a transcribed Van der Waals equation

Abstract

The old concepts of the Van der Waals equation (vdW EOS) and of the virial equation, truncated to the second virial coefficient, can be rewritten with a function defined as cc=(p−R·T/M)/ρ2. This function arises from introducing the ideal gas law into the thermodynamic equation of state, which describes the volume dependence of the internal energy. Thus both concepts can be superimposed and then complement one another. This allows an almost complete and correct description of the p/T/ρ-behavior of real fluids in the gaseous, liquid, critical and supercritical state up to the Joule inversion curve. The function cc, used as structure parameter with constant values, reveals a hidden feature of the vdW EOS, which describes a linear function between density and temperature for iso-cc-lines. This is empirically correct for 16 examined regular pure fluids. Non-regular fluids like He, H2, water and acetonitrile, which show more or less slightly curved iso-cc-lines, can be linearized using a simple factor, applied to the density, and then be described in a similar manner like regular fluids.