%0 Journal Article
%T Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State
%A Leslie V. Woodcock
%J Journal of Modern Physics
%P 613-633
%@ 2153-120X
%D 2024
%I Scientific Research Publishing
%R 10.4236/jmp.2024.155029
%X We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density <i>ρ</i>(<i>p</i>,<i>T</i>), and Gibbs energy <i>G</i>(<i>p</i>,<i>T</i>), of fluids, e.g. CO<sub>2</sub>, H<sub>2</sub>O and argon exhibit a symmetry characterised by the rigidity, <i>ω</i> = (d<i>p</i>/d<i>ρ</i>)<i><sub>T</i></sub>, between gaseous and liquid states along any isotherm from critical (<i>T</i><i><sub>c</i></sub>) to Boyle (<i>T</i><i><sub>B</i></sub>) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (<i>ω</i><i> </i>= <i>ρ</i><i><sub>rs</i></sub>(<i>T</i>) = <i>RT</i>) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (<i>w</i> = (<i>p</i>/<i>ρ</i>)<i><sub>T</i></sub> = <i>RT</i>), and to percolation lines of gas (PB) and liquid (PA) phases by: <i>ρ</i><i><sub>BW</i></sub>(<i>T</i>) = 2<i>ρ</i><i><sub>PA</i></sub>(<i>T</i>) = 3<i>ρ</i><i><sub>PB</i></sub>(<i>T</i>) = 3<i>ρ</i><i><sub>RS</i></sub>(<i>T</i>)/2 for <i>T</i> < <i>T</i><i><sub>B</i></sub>. These simple relationships arise, because the higher virial coefficients (<i>b</i><i><sub>n</i></sub>, <i>n</i> ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 < <i>T</i> <
%K Liquid-State Theory
%K Cluster Physics
%K Percolation Lines
%K Fluid Thermodynamics
%K Boyle Line
%K Rigidity-Symmetry Line
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=132536