{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T22:56:39Z","timestamp":1784760999430,"version":"3.55.0"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T00:00:00Z","timestamp":1515024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface \u03c1(p,T) which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (Tc) and pressure (pc) and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at Tc on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (TB), critical temperature (Tc), critical pressure (pc) and coexisting densities of gas (\u03c1cG) and liquid (\u03c1cL) along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below TB, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp\/d\u03c1)T to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO2, argon, water and SF6, with focus on the supercritical mesophase and critical region.<\/jats:p>","DOI":"10.3390\/e20010022","type":"journal-article","created":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T11:52:47Z","timestamp":1515066767000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Thermodynamic Fluid Equations-of-State"],"prefix":"10.3390","volume":"20","author":[{"given":"Leslie","family":"Woodcock","sequence":"first","affiliation":[{"name":"Department of Physics, University of Algarve, 8005-139 Faro, Portugal"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,4]]},"reference":[{"key":"ref_1","unstructured":"Van der Waals, J.D. 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