The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use
In 1995, the International Association for the Properties of Water and Steam (IAPWS) adopted a new formulation called "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use", which we abbreviate to IAPWS-95 formulation or IAPWS-95 for short. This IAPWS-95 formulation replaces the previous formulation adopted in 1984. This work provides information on the selected experimental data of the thermodynamic properties of water used to develop the new formulation, but information is also given on newer data. The article presents all details of the IAPWS-95 formulation, which is in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data for the following properties: (a) thermal properties of the single-phase region (pρT) and of the vapor-liquid phase boundary (pσρ'ρ″T), including the phase-equilibrium condition (Maxwell criterion), and (b) the caloric properties specific isochoric heat capacity, specific isobaric heat capacity, speed of sound, differences in the specific enthalpy and in the specific internal energy, Joule-Thomson coefficient, and isothermal throttling coefficient. By applying modern strategies for optimizing the functional form of the equation of state and for the simultaneous nonlinear fitting to the data of all mentioned properties, the resulting IAPWS-95 formulation covers a validity range for temperatures from the melting line (lowest temperature 251.2 K at 209.9 MPa) to 1273 K and pressures up to 1000 MPa. In this entire range of validity, IAPWS-95 represents even the most accurate data to within their experimental uncertainty. In the most important part of the liquid region, the estimated uncertainty of IAPWS-95 ranges from ±0.001% to ±0.02% in density, ±0.03% to ±0.2% in speed of sound, and ±0.1% in isobaric heat capacity. In the liquid region at ambient pressure, IAPWS-95 is extremely accurate in density (uncertainty ⩽±0.0001%) and in speed of sound (±0.005%). In a large part of the gas region the estimated uncertainty in density ranges from ±0.03% to ±0.05%, in speed of sound it amounts to ±0.15% and in isobaric heat capacity it is ±0.2%. In the critical region, IAPWS-95 represents not only the thermal properties very well but also the caloric properties in a reasonable way. Special interest has been focused on the extrapolation behavior of the new formulation. At least for the basic properties such as pressure and enthalpy, IAPWS-95 can be extrapolated up to extremely high pressures and temperatures. In addition to the IAPWS-95 formulation, independent equations for vapor pressure, the densities, and the most important caloric properties along the vapor-liquid phase boundary, and for the pressure on the melting and sublimation curve, are given. Moreover, a so-called gas equation for densities up to 55 kg m-3 is also included. Tables of the thermodynamic properties calculated from the IAPWS-95 formulation are listed in the Appendix.