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Entropy 2020, 22, 437 13 of 26 13 of 27 Figure 10. Percolation transition points along near-critical isotherms plotted directly from original Figure 10. Percolation transition points along near-critical isotherms plotted directly from original measurements as reported by Gilgen et al. [50] and shown in Figure 4 in the p-T projection. The measurements as reported by Gilgen et al. [50] and shown in Figure 4 in the p-T projection. The extrapolated dashed lines of available volume (PA-blue) and bonded cluster (PB-green) correspond extrapolated dashed lines of available volume (PA-blue) and bonded cluster (PB-green) correspond to to the experimentally observed spinodal lines from the literature. The red line and points are the the experimentally observed spinodal lines from the literature. The red line and points are the coexistence data of Gilgen et al. [51]. coexistence data of Gilgen et al. [51]. 3. Thermophysical Property Compilations Nobody has ever reported a direct observation of a critical density [5]; this is well illustrated by th3e.1.exMteunltsiipvaerahmiegther-pErqeucaistions-oefx-pSteartiemental measurements of the argon liquid-vapour coexistence densities by Gilgen et al. [51]. The highest temperature for which they report both coexisting vapour There is now an abundance of highly accurate p-V-T experimental measurements for a diversity and liquid densities is 150.61 K. They use a cubic scaling equation and a law of rectilinear diameters to of atomic and molecular fluids. The most prolific contributors to the NIST databank [4] are the obtain their critical point temperature (150.69 K), and critical density of 535.6 kg/m3. The mean of the research group of Prof. W. Wagner. Over many decades, they have performed a great service two extreme recorded liquid and vapour densities is 536 kg/m3. The lowest co-existing liquid mass in high-precision measurement and presentation of invaluable thermodynamic data for many density they report is 602 kg/m3. The highest vapour mass density they can observe near Tc is 470 academically and industrially important fluids, as evidenced by NIST physical property databank kg/m3. The line of critical states connects these two points (Figure 9). citations. Experimental researchers since 1965 have never questioned the authenticity of van der Waals hypothesis as “accepted science”, propagated since the mid-1960s via the concept of universality. The 3. Thermophysical Property Compilations Wagner group equations-of-state are not able to reproduce with normal precision the near-critical properties in most of their reports. This admission is now entirely understandable. It is consistent with 3.1. Multiparameter Equations-of-State the non-existence of a singularity, and yet emphasizes what meticulous service the Wagner group have There is now an abundance of highly accurate p-V-T experimental measurements for a diversity provided to the engineering and physical science community in awkward circumstances [4]. of atomic and molecular fluids. The most prolific contributors to the NIST databank [4] are the From the modern literature of thermodynamic p-V-T data on atomic and molecular fluids, research group of Prof. W. Wagner. Over many decades, they have performed a great service in one could choose any one of the 200 fluids listed in the NIST thermo-physical data bank or any high-precision measurement and presentation of invaluable thermodynamic data for many one of the hundreds of experimental papers in the literature. Numerical equations-of-state from the academically and industrially important fluids, as evidenced by NIST physical property databank literature, however, should also be viewed with circumspection, especially in the vicinity of the critical citations. Experimental researchers since 1965 have never questioned the authenticity of van der Waals temperature. The numerical representations of raw experimentally measured data points [4] used in hypothesis as “accepted science”, propagated since the mid-1960s via the concept of universality. The parameterizations are predetermined by an a priori assumption at the outset of the existence of a van Wagner group equations-of-state are not able to reproduce with normal precision the near-critical der Waals singularity at a critical density, and continuity of the supercritical equation-of-state in all its properties in most of their reports. This admission is now entirely understandable. It is consistent with derivatives. The so-called universal exponents for the description of the thermodynamic properties in the non-existence of a singularity, and yet emphasizes what meticulous service the Wagner group the immediate vicinity of Tc have also been incorrectly employed. Thus, even though no one has ever have provided to the engineering and physical science community in awkward circumstances [4]. measured a vanishing density difference up to Tc directly, all the NIST thermodynamic state functions have mistakenly presumed a continuity of gas and liquid to be the underlying science from the outset. One reason for the inadequacy of complex multiparameter equations-of-state with increased experimental precision is that the continuous functional forms are fundamentally incorrect in the vicinity of Tc and in the supercritical mid-range between gas and liquid phases. The mesophase, confined within percolation loci that bound the gas and liquid phases by higher-order discontinuities, can readily be identified. A simple numerical differentiation of NIST equations-of-state, for example,PDF Image | Supercritical Fluid Gaseous and Liquid States
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