Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids

Abstract

We have found the curves on the density-temperature plane, along which the values of free energy and chemical potential correspond to ideal gas quantities. At first, we have applied the van der Waals equation to construct them and to derive their equations. Then we have shown that the same lines for real substances (Ar, N, CH, SF, H, HO) and for the model Lennard-Jones system constructed on the basis of the measurements data and calculations are well matched with the derived equations. The validity and deviations from the obtained similarity laws are discussed.

The Line of Ideal Isothermal Compressibility

“…Moreover, they were valid even for some substances for which the Z-lines are not straight. Notable differences between the results of analytical equations on the basis of the VdW system and the real F- and μ-lines were observed only near the freezing line …”

“…Notable differences between the results of analytical equations on the basis of the VdW system and the real F-and μ-lines were observed only near the freezing line. 30 Here, we should remark that all abovementioned ideal contours can be described by the VdW model. Evidently, it is not the case for any ideal line because the VdW model can incorrectly describe various derivatives with respect to the temperature.…”

“…Further, the ideal contours can be constructed for other values as well, for instance, 30 the free energy F and the chemical potential μ. The resulting lines, denoted as the F-line and the μline correspondingly, are no longer straight even for the VdW system.…”

The Line of the Unit Compressibility Factor (Zeno-Line) for Crystal States

“…There are also the ideal lines 28 for the free energy (F-line) and chemical potential (μ-line). Corresponding n−T dependencies can be also derived 28 from VDW EoS.…”

“…There are also the ideal lines 28 for the free energy (F-line) and chemical potential (μ-line). Corresponding n−T dependencies can be also derived 28 from VDW EoS. They are not linear, but they are also valid for many real substances, like the straight ideal lines, mentioned above.…”