Water-Steam Thermodynamic Equations-of-State from Boyle and Rigidity-Symmetry Lines

Abstract

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 = (d p /d ρ ) 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 H 2 O based upon a knowledge of the lower virial coefficients b 2 and b 3 , 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 H 2 O 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 < b 4 , 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 H 2 O below T B , are obtainable from the critical ratio of virial coefficients −(b 2 / b 3 ) Tc determined from the linear Boyle line given only one H 2 O ρ BW (0) ground-state density physical constant.