Thermodynamics of pure liquid water: Sound speed measurements to 700 MPa down to the freezing point, and an equation of state to 2300 MPa from 240 to 500 K

Abstract

Accurate thermodynamic properties for aqueous solutions under an increasing range of pressures, temperatures, and compositions are needed to address a variety of technical and scientific challenges. This study provides measurements for improving the high-pressure and low-temperature representation of liquid water. Sound speeds of pure liquid water are reported between 0.1 and 700 MPa, from 353 K down to the melting curves of the ice phases. The new sound speed measurements have a relative standard uncertainty of 100–170 ppm (from 0.1 to 700 MPa), with standard uncertainties of 20 mK for the temperature measurements and 0.02–0.14 MPa (from 0.1 to 700 MPa) for the pressure measurements. Using additional published measurements, a new equation of state is derived extending from 240 to 500 K and from 0.1 to 2300 MPa, covering much of the subcritical domain of water up to the ice VI–ice VII transition. Analyses of measurements and construction of the equation of state are accomplished with a flexible computational thermodynamic framework based on local basis functions in the form of tensor B-splines. Relative to IAPWS-95 (the most comprehensive representation available), improvements in the accuracies of density, sound speed, and specific heat are expected above 100 MPa, particularly near the solid-fluid phase boundaries.

Holistic Approach for Studying Planetary Hydrospheres: Gibbs Representation of Ices Thermodynamics, Elasticity, and the Water Phase Diagram to 2,300 MPa

“…The SeaFreeze representations are thermodynamically consistent within and between phases. Gibbs energies and entropies of all phases are referenced to IAPWS‐95 values for water at its vapor‐fluid‐ice Ih triple point (Bollengier et al, ). This tool gives equilibrium thermodynamic properties (including phase boundaries, density, heat capacities, bulk modulus, thermal expansivity, chemical potentials) as well as shear moduli and seismic wave velocities for each phase extending into metastable regimes.…”

“…In the IAPWS‐95 representation of water (Wagner & Pruß, ), the internal energy and entropy are set to zero at its liquid‐vapor‐solid triple point. This convention was also adapted for the Gibbs energy representation of water by Bollengier et al () that provides more accurate thermodynamic properties at high pressures and in the supercooled regime. Here the reference energy G o of each ice phase was set to be internally consistent with Bollengier et al () values by matching the Gibbs energy of the ice phase with water at each lower pressure triple point on the melt line (e.g., ice Ih‐III‐liquid triple point for ice III).…”

“…This convention was also adapted for the Gibbs energy representation of water by Bollengier et al () that provides more accurate thermodynamic properties at high pressures and in the supercooled regime. Here the reference energy G o of each ice phase was set to be internally consistent with Bollengier et al () values by matching the Gibbs energy of the ice phase with water at each lower pressure triple point on the melt line (e.g., ice Ih‐III‐liquid triple point for ice III). For ice II, the reference energy G o is set to be consistent with the computed Gibbs energy of ice III at the ice Ih‐II‐III triple point.…”

“…In the IAPWS-95 representation of water (Wagner & Pruß, 2002), the internal energy and entropy are set to zero at its liquid-vapor-solid triple point. This convention was also adapted for the Gibbs energy representation of water by Bollengier et al (2019) that provides more accurate thermodynamic properties at high pressures and in the supercooled regime.…”

“…Here the reference energy G o of each ice phase was set to be internally consistent with Bollengier et al (2019) values by matching the Gibbs energy of the ice phase with water at each lower pressure triple point on the melt line (e.g., ice Ih-III-liquid triple point for ice III). For ice II, the reference energy G o is set to be consistent with the computed Gibbs energy of ice III at the ice Ih-II-III triple point.…”