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# Phase diagrams of ordinary water

On this page are presented some phase diagrams for water. Every data point plotted on the graphs shown below was computed using one or a combination of several models published by the International Association for the Properties of Water and Steam (IAPWS). These publications (Realeases in the IAPWS lingo) are identified by the letter R and a number. Very briefly:

• R6 is the "master equation" that has been carefully fitted over a wide range of experimental results and represents the state of the art for the evaluation of the thermodynamic properties of water. It is expressed in terms of Helmholtz energy as a function of density and temperature, from which all the other properties can be obtained by some combinations of derivatives.
• R7 is an approximation of R6 that allow direct and fast calculations of properties, e.g. as functions of temperature and pressure, where R6 would require a computational expensive inversion. Below are presented diagrams built with R7 as well as the same obtained by inverting R6 (under the sobriquet "R6 inverse"), and the differences between the two ("R7 vs. R6 inverse")
• R14 describes the boundaries between fluid water and various phases of ice (a.k.a. melting and sublimation curves). The saturation curve can be directly calculated in the P-T plane using R7.
• R10 describes ice Ih.
• R12 provides the viscosity of liquid and gaseous water.
The implementation of the IAPWS models used to compute the data is isto/iapws. When needed, the inversions were performed using the isto/root_finding library. The plots were rendered using Gnuplot.

Contact: rf.srnc@gnort-el.leunamme

Contents:

## Phases boundaries

Phases boundaries calculated using

• Wagner, W., Cooper, J. R., Dittmann, A., Kijima, J., Kretzschmar, H., Kruse, A., Mareš, R., Oguchi, K., Sato, H., Stöcker, I., Sǐfner, O., Takaishi, Y., Tanishita, I., Trübenbach, J., and Willkommen, T. (January 1, 2000). "The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam ." ASME. J. Eng. Gas Turbines Power. January 2000; 122(1): 150–184. https://doi.org/10.1115/1.483186
• Wolfgang Wagner, Thomas Riethmann, Rainer Feistel, Allan H. Harvey, "New Equations for the Sublimation Pressure and Melting Pressure of H2O Ice Ih", Journal of Physical and Chemical Reference Data 40, 043103 (2011) https://doi.org/10.1063

## Spinodal lines

Here we use IAPWS 95 (a.k.a. R6) to find the spinodal lines, i.e. locus of points where the compressibility is zero. "Spinodal line (liq)" uses R6 on the liquid side (densities > critical density). "Spinodal line (gas), candidate 1" and "Spinodal line (gas), candidate 1" use R6 on the vapor side (densities < critical density). It so happens that there are two solutions on this side, although the second one has probably no thermophysical sense. "Spinodal line (gas), R6 gas" uses the gas equation of state found in the paper of W. Wagner and A. Pruß (eq. 3.2) (but not on the official IAPWS guideline). Unfortunately, its validity range does not extend beyond a density of 55 kg/m3

## R6: The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use

Provides direct calculations of the properties of ordinary water (i.e. water and stean) in terms of (density, temperature).

Range : 273.16 K ≤ T < 2273.16 K and 0 kg/m3 ≤ ρ ≤ 1000 kg/m3

Implements the following:

• W. Wagner and A. Pruß , "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use", Journal of Physical and Chemical Reference Data 31, 387-535 (2002) https://doi.org/10.1063/1.1461829

## R6_gas: Equation for the gas phase

Provides direct calculations of the properties of ordinary water (i.e. water and stean) in terms of (density, temperature).

Range : 273 K ≤ T < 2273 K and 0 kg/m3 ≤ ρ ≤ 55 kg/m3

Implements eq. 3.2 in:

• W. Wagner and A. Pruß , "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use", Journal of Physical and Chemical Reference Data 31, 387-535 (2002) https://doi.org/10.1063/1.1461829

## R6 vs. R6_gas: Compare R6 gas equation to the generic fluid equation

Range : 273 K ≤ T < 2273 K and 0 kg/m3 ≤ ρ ≤ 55 kg/m3

Implementsn:

• W. Wagner and A. Pruß , "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use", Journal of Physical and Chemical Reference Data 31, 387-535 (2002) https://doi.org/10.1063/1.1461829

## R6 inverse

Provides indirect calculations of the properties of ordinary water in terms of (pressure, temperature) by inverting the P(ρ, T) relation of R6.

Range: 173.15 K ≤ T ≤ 1273.15 K and 0 MPa ≤ P ≤ 1000 MPa

## R6 inverse, extended to 5000 K, 100 GPa

This is R6 inverse over an extended (P, T) range.

The phase boundary for P > 20 GPa is totally arbitrary, as no model is available in this range (AFAIK).

Range: 173.15 K ≤ T ≤ 5073.15 K and 0 MPa ≤ P ≤ 100 GPa

## R7: The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

Provides direct calculations of the properties of ordinary water (i.e. water and stean) in terms of (pressure, temperature).

It is an approximation of R6.

Range: (173.15 K ≤ T < 1273.15 K and 0 MPa ≤ P ≤ 100 MPa) and (1073.15 K ≤ T ≤ 2273.15 K and 0 MPa ≤ P ≤ 50 MPa)

Implements the following:

• Wagner, W., Cooper, J. R., Dittmann, A., Kijima, J., Kretzschmar, H., Kruse, A., Mareš, R., Oguchi, K., Sato, H., Stöcker, I., Sǐfner, O., Takaishi, Y., Tanishita, I., Trübenbach, J., and Willkommen, T. (January 1, 2000). "The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam ." ASME. J. Eng. Gas Turbines Power. January 2000; 122(1): 150–184. https://doi.org/10.1115/1.483186
• Kretzschmar, H., Cooper, J. R., Dittmann, A., Friend, D. G., Gallagher, J. S., Knobloch, K., Mareš, R., Miyagawa, K., Stöcker, I., Trübenbach, J., Wagner, W., and Willkommen, T. (June 22, 2004). "Supplementary Backward Equations for Pressure as a Function of Enthalpy and Entropy li(h,s) to the Industrial Formulation IAPWS-IF97 for Water and Steam." ASME. J. Eng. Gas Turbines Power. July 2006; 128(3): 702–713. https://doi.org/10.1115/1.1915392
• Kretzschmar, H., Cooper, J. R., Dittmann, A., Friend, D. G., Gallagher, J. S., Harvey, A. H., Knobloch, K., Mareš, R., Miyagawa, K., Okita, N., Stöcker, I., Wagner, W., and Weber, I. (January 10, 2006). "Supplementary Backward Equations T(li,h)⁠, v(li,h)⁠, and T(li,s)⁠, v(li,s) for the Critical and Supercritical Regions (Region 3) of the Industrial Formulation IAPWS-IF97 for Water and Steam." ASME. J. Eng. Gas Turbines Power. January 2007; 129(1): 294–303. https://doi.org/10.1115/1.2181598
• Kretzschmar, H., Cooper, J. R., Gallagher, J. S., Harvey, A. H., Knobloch, K., Mareš, R., Miyagawa, K., Okita, N., Span, R., Stöcker, I., Wagner, W., and Weber, I. (January 16, 2007). "Supplementary Backward Equations li(h,s) for the Critical and Supercritical Regions (Region 3), and Equations for the Two-Phase Region and Region Boundaries of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam." ASME. J. Eng. Gas Turbines Power. October 2007; 129(4): 1125–1137. https://doi.org/10.1115/1.2719267
• Kretzschmar, H., Harvey, A. H., Knobloch, K., Mareš, R., Miyagawa, K., Okita, N., Span, R., Stöcker, I., Wagner, W., and Weber, I. (April 13, 2009). "Supplementary Backward Equations v(li,T) for the Critical and Supercritical Regions (Region 3) of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam." ASME. J. Eng. Gas Turbines Power. July 2009; 131(4): 043101. https://doi.org/10.1115/1.3028630

## R10: Revised Release on the Equation of State 2006 for H2O Ice Ih

Provides direct calculations of the properties of ordinary water in its solid hexagonal phase I in terms of (pressure, temperature).

Range: 0 K ≤ T < 273.16 K and 0 MPa ≤ P ≤ 210 MPa

Implements the following:

• Rainer Feistel, and Wolfgang Wagner. "A New Equation of State for H2O Ice Ih", Journal of Physical and Chemical Reference Data 35, 1021-1047 (2006) https://doi.org/10.1063/1.2183324

## R12: Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance

Viscosity of liquid and gaseous water in the density-temperature plane.

Range : 273.16 K ≤ T < 2273.16 K and 0 kg/m3 ≤ ρ ≤ 1000 kg/m3

Implements the following:

• M. L. Huber, R. A. Perkins, A. Laesecke, D. G. Friend, J. V. Sengers, M. J. Assael I. N. Metaxa, E. Vogel, R. Mareš, and K. Miyagawa , "New International Formulation for the Viscosity of H2O", Journal of Physical and Chemical Reference Data 38, 101-125 (2009) https://doi.org/10.1063/1.3088050

## R12, viscosity in the temperature-pressure plane

Viscosity in th P-T plane using r6 inverse

Range: 0 K ≤ T < 1273.15 K and 0 MPa ≤ P ≤ 1000 MPa

## R7 vs. R6 inverse

Comparison between the values obtained via R7 and R6 inverse.

Range: (173.15 K ≤ T < 1273.15 K and 0 MPa ≤ P ≤ 100 MPa) and (1073.15 K ≤ T ≤ 2273.15 K and 0 MPa ≤ P ≤ 50 MPa)

### Isothermal stress coefficient difference, relative to R6 value (Temperature, Pressure)

Updated 2021-12-14