Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

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 ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO₂, H₂O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)_T, between gaseous and liquid states along any isotherm from critical (T_c) to Boyle (T_B) 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 (ω = ρ_rs(T) = RT) 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) (w = (p/ρ)_T = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρ_BW(T) = 2ρ_PA(T) = 3ρ_PB(T) = 3ρ_RS(T)/2 for T < T_B. These simple relationships arise, because the higher virial coefficients (b_n, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 < T <