In order to represent the thermodynamic properties of water (H2O) over an extremely large range of temperature and pressure that is not covered by existing equations of state, a new fundamental equation has been developed. The Helmholtz function was fitted to the following kinds of experimental data: (a) pρT data, (b) thermal properties of the saturation curve (ps,ρ′,ρ″), (c) speed of sound w, (d) isobaric heat capacity cp, (e) isochoric heat capacity cv, (f) differences of the internal energy u, (g) differences of the enthalpy h, (h) Joule–Thomson coefficient μ, and (i) the isothermal throttling coefficient δT. A new statistical selection method was used to determine the final form of the equation from a ‘‘bank’’ of 630 terms which also contained functional forms that have not been previously used. This 58-coefficient equation covers the entire fluid region from the melting line to 1273 K at pressures up to 25 000 MPa, and represents the data within their experimental accuracy also in the ‘‘difficult’’ regions below 0 °C, on the entire saturation curve, in the critical region and at very high pressures. The equation was constrained at the critical point as defined by the parameters internationally recommended by the International Association for the Properties of Steam (IAPS). Besides the 58-coefficient equation for the entire pressure range, a 38-coefficient equation is presented for providing a ‘‘fast’’ equation for practical and scientific calculations in the pressure range below 1000 MPa. This equation has, with the exception of the critical region, nearly the same accuracy as the 58-coefficient equation. The quality of the new equations will be illustrated by comparing the values calculated from them with selected experimental data and with the IAPS-84 formulation and the Scaling-Law equation.

Saul, A., & Wagner, W. (1989). A Fundamental Equation for Water Covering the Range from the Melting Line to 1273 K at Pressures up to 25 000 MPa. Journal of Physical and Chemical Reference Data, 18(4), 1537–1564.