Author(s)

Ahmad Eltahlawy¹, Igor Khmelinskii¹, Leslie V. Woodcock^2*

¹Department of Chemistry and Pharmacy, University of Algarve, Faro, Portugal.
²Department of Physics, University of Algarve, Faro, Portugal.

We investigate a representation of thermodynamic equations-of-state for water and steam using only physical constants and zero ad hoc parameters. Following the reported phase equilibria 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 pure fluids are seen to exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)_T along isotherms from the critical point (T_c) to Boyle temperature (T_B), on either side of the supercritical mesophase for T > T_c. We report an analysis of H₂O based upon a knowledge of the lower virial coefficients b₂ and b₃, that describe the gas region (steam) for all T. We show that the same coefficients also describe the supercritical liquid-side range “water” in an expansion about a rigidity-symmetry (R-S) line defined by ω(ρ_RS)_T = RT (R is ideal gas constant). We report further investigation into the Boyle-work line, w = p/ρ(ρ_BW)_T = RT. A revised Boyle temperature for H₂O is reported: T_B = 1567 ± 20 K. The BW-line is linear in the gas and supercritical liquid regions between T_B and T_C. It interpolates to a ground state solid-range constant ρ_BW(0) at an ice density 82.56 mol/l. Cluster expansions in powers of density truncated at b_n < b₄, equate steam virial coefficients with both BW and RS lines. We find both lines are continuous in all derivatives, and linear within the stable fluid phases. Simple relationships arise from the observation that the higher virial coefficients (b_n, n ≥ 4) cancel due to cluster equilibria, or are negligible (0 < T < T_B) in the steam regions. All thermodynamic state functions f(p,T) for H₂O below T_B, are obtainable from the critical ratio of virial coefficients −(b₂/b₃)_Tc determined from the linear Boyle line given only one H₂O ρ_BW(0) ground-state density physical constant.

Liquid-State Theory, Cluster Physics, Fluid Thermodynamics, Boyle Line, Rigidity-Symmetry Line, Water Equation-of-State

Eltahlawy, A. , Khmelinskii, I. and Woodcock, L. (2025) Water-Steam Thermodynamic Equations-of-State from Boyle and Rigidity-Symmetry Lines. Journal of Modern Physics, 16, 518-535. doi: 10.4236/jmp.2025.164027.