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The experimental data from the NIST tabulations are reproduced in Figure 12 with the same precision as the original data can be obtained, i.e., accurate to 5 or 6 figures, as evidenced by the mean-squared regression (R2) in the trendline polynomial coefficients as given. In addition, shown in Figure 12 are redefined equations to give the virial coefficients as shown on the plots. The coefficient a1 inEntthroepyli2q0u20i,d2-2s,t4a3t7e expansion is taken to be equal to the value of wT in the mesophase to descr1ib6 eoft2h6e third-order discontinuity between the mesophase and the liquid state. There is a symmetry between the rigidity of gas and liquid on either side of the mesophase. This observation is empirical though it has a molecular origin in the fluctuations of the available volume and its relationship to the chemical has a molecular origin in the fluctuations of the available volume and its relationship to the chemical potential of both gas and liquid states [52]. potential of both gas and liquid states [52]. (a) (b) (c) Figure 12. Pressure as a function of density for CO2 at a supercritical temperature (350 K or T/Tc = 1.15) Figure 12. Pressure as a function of density for CO2 at a supercritical temperature (350 K or T/Tc = 1.15) as derived from NIST Thermophysical Properties compilation: (a) gas state, (b) supercritical as derived from NIST Thermophysical Properties compilation: (a) gas state, (b) supercritical meso-phase meso-phase and (c) liquid. and (c) liquid. TThheerirgigididitiytyisisooththeermrmddaatatafforrCO22((Fiigurree13))showaclearsymmetryoneiittherssiideeooffththee mmeseosopphhasaeseaalolonnggaanniissootthheerrm[[53]],, which further suggests that the messophasebbooundssnnaarrroowwwitihth inincrcereaasisninggTTaannddmeerrgeeatt or close to the Boyle ttemperattureTB. This is tthetteempeerraatturreeaabboovveewhhicichh B ththeeseseccoonnddvviririaiallccooeefffificciieenttiissposiitiiveand below which it is negativebuttttheanallyttiiccffoorrmaassititppaassseess through zero remains unknown. The same behaviour is seen in the rigidity plots for other liquids, for example water [54]. Equation-of-state experimental data, albeit accurate and painstakingly obtained, may not be the most reliable to decide the issue of critical flatness. It is not easy to distinguish a low curvature region from one that is in fact a straight line in p(ρ)T. The literature critical-point universality theory predicts that the temperature or pressure scales as ∆ρd along the critical isotherm, which could therefore appear to be very flat anyway within the hypothesis. Many p-V-T experimental results for real molecular fluids have required exponents d = 3 to 4, or even higher [54] in order to parameterize an apparent flat top within the experimental uncertainty. The presentation of near-critical experimental results, however, has been adversely affected by hypotheses, which are here seen to be incorrect in the light of experimental data, and hence misrepresent the critical divide at Tc and the supercritical mesophase.PDF Image | Supercritical Fluid Gaseous and Liquid States
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