Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State
- 1 Department of Physics, University of Algarve, Faro, Portugal
Abstract
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> < <i>T</i><i><sub>B</i></sub>)<sub> </sub>within the gas phase. The Boyle-work line (<i>p</i>/<i>ρ</i><i><sub>BW</i></sub>)<i><sub>T</i></sub> is related exactly at lower densities as <i>T</i><i> </i><i>→</i> <i>T</i><i><sub>B</i></sub>, and accurately for liquid densities, by <i>ρ</i><i><sub>BW</i></sub>(<i>T</i>) = −(<i>b</i><sub>2</sub>/<i>b</i><sub>3</sub>)<i><sub>T</i></sub>. The RS line, <i>ω</i>(<i>T</i>) = <i>RT</i>, defines a new liquid-density ground-state physical constant (<i>ρ</i><i><sub>RS</i></sub>(0) = (2/3)<i>ρ</i><i><sub>BW</i></sub>(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below <i>T</i><i><sub>B</i></sub> are obtainable from <i>b</i><sub>2</sub>(<i>T</i>). A BW-line ground-state crystal density <i>ρ</i><i><sub>BW</i></sub>(0) can be defined by the pair potential minimum. The Ar<sub>2</sub> pair potential, ∅ ij ( r ij ) determines <i>b</i><sub>2</sub>(<i>T</i>) analytically for all <i>T</i>. This report, therefore, advances the salient objective of liquid-state theory: an argon <i>p</i>(<i>ρ</i>,<i>T</i>) Equation-of-state is obtained from ∅ ij ( r ij ) for all fluid states, without any adjustable parameters.
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