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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:

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

In the Temperature-Pressure plane
In the Density-Temperature plane

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

In the Temperature-Pressure plane
In the Density-Temperature plane

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:

Pressure (Density, Temperature)

linear in Pressure
logarithmic in Pressure

Massic enthalpy (Density, Temperature)

linear in Massic enthalpy
logarithmic in Massic enthalpy

Massic internal energy (Density, Temperature)

linear in Massic internal energy
logarithmic in Massic internal energy

Massic Gibbs free energy (Density, Temperature)

linear in Massic Gibbs free energy
logarithmic in Massic Gibbs free energy

Massic entropy (Density, Temperature)

linear in Massic entropy
logarithmic in Massic entropy

Massic isobaric heat capacity (Density, Temperature)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity

Massic isochoric heat capacity (Density, Temperature)

linear in Massic isochoric heat capacity
logarithmic in Massic isochoric heat capacity

Speed of sound (Density, Temperature)

linear in Speed of sound
logarithmic in Speed of sound

Relative pressure coefficient (Density, Temperature)

linear in Relative pressure coefficient
logarithmic in Relative pressure coefficient

Isothermal stress coefficient (Density, Temperature)

linear in Isothermal stress coefficient
logarithmic in Isothermal stress coefficient

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:

Pressure (Density, Temperature)

linear in Pressure
logarithmic in Pressure

Massic enthalpy (Density, Temperature)

linear in Massic enthalpy
logarithmic in Massic enthalpy

Massic internal energy (Density, Temperature)

linear in Massic internal energy
logarithmic in Massic internal energy

Massic Gibbs free energy (Density, Temperature)

linear in Massic Gibbs free energy
logarithmic in Massic Gibbs free energy

Massic entropy (Density, Temperature)

linear in Massic entropy
logarithmic in Massic entropy

Massic isobaric heat capacity (Density, Temperature)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity

Massic isochoric heat capacity (Density, Temperature)

linear in Massic isochoric heat capacity
logarithmic in Massic isochoric heat capacity

Speed of sound (Density, Temperature)

linear in Speed of sound
logarithmic in Speed of sound

Relative pressure coefficient (Density, Temperature)

linear in Relative pressure coefficient
logarithmic in Relative pressure coefficient

Isothermal stress coefficient (Density, Temperature)

linear in Isothermal stress coefficient
logarithmic in Isothermal stress coefficient

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:

Pressure (Density, Temperature)

linear in Pressure
logarithmic in Pressure

Massic enthalpy (Density, Temperature)

linear in Massic enthalpy
logarithmic in Massic enthalpy

Massic internal energy (Density, Temperature)

linear in Massic internal energy
logarithmic in Massic internal energy

Massic Gibbs free energy (Density, Temperature)

linear in Massic Gibbs free energy
logarithmic in Massic Gibbs free energy

Massic entropy (Density, Temperature)

linear in Massic entropy
logarithmic in Massic entropy

Massic isobaric heat capacity (Density, Temperature)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity

Massic isochoric heat capacity (Density, Temperature)

linear in Massic isochoric heat capacity
logarithmic in Massic isochoric heat capacity

Speed of sound (Density, Temperature)

linear in Speed of sound
logarithmic in Speed of sound

Relative pressure coefficient (Density, Temperature)

linear in Relative pressure coefficient
logarithmic in Relative pressure coefficient

Isothermal stress coefficient (Density, Temperature)

linear in Isothermal stress coefficient
logarithmic in Isothermal stress coefficient

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

Density (Temperature, Pressure)

linear in Density
logarithmic in Density
logarithmic in Pressure, linear in Density
logarithmic in Pressure, logarithmic in Density

Massic enthalpy (Temperature, Pressure)

linear in Massic enthalpy
logarithmic in Massic enthalpy
logarithmic in Pressure, linear in Massic enthalpy
logarithmic in Pressure, logarithmic in Massic enthalpy

Massic internal energy (Temperature, Pressure)

linear in Massic internal energy
logarithmic in Massic internal energy
logarithmic in Pressure, linear in Massic internal energy
logarithmic in Pressure, logarithmic in Massic internal energy

Massic Gibbs free energy (Temperature, Pressure)

linear in Massic Gibbs free energy
logarithmic in Massic Gibbs free energy
logarithmic in Pressure, linear in Massic Gibbs free energy
logarithmic in Pressure, logarithmic in Massic Gibbs free energy

Massic entropy (Temperature, Pressure)

linear in Massic entropy
logarithmic in Massic entropy
logarithmic in Pressure, linear in Massic entropy
logarithmic in Pressure, logarithmic in Massic entropy

Massic isobaric heat capacity (Temperature, Pressure)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity
logarithmic in Pressure, linear in Massic isobaric heat capacity
logarithmic in Pressure, logarithmic in Massic isobaric heat capacity

Massic isochoric heat capacity (Temperature, Pressure)

linear in Massic isochoric heat capacity
logarithmic in Massic isochoric heat capacity
logarithmic in Pressure, linear in Massic isochoric heat capacity
logarithmic in Pressure, logarithmic in Massic isochoric heat capacity

Speed of sound (Temperature, Pressure)

linear in Speed of sound
logarithmic in Speed of sound
logarithmic in Pressure, linear in Speed of sound
logarithmic in Pressure, logarithmic in Speed of sound

Relative pressure coefficient (Temperature, Pressure)

linear in Relative pressure coefficient
logarithmic in Relative pressure coefficient
logarithmic in Pressure, linear in Relative pressure coefficient
logarithmic in Pressure, logarithmic in Relative pressure coefficient

Isothermal stress coefficient (Temperature, Pressure)

linear in Isothermal stress coefficient
logarithmic in Isothermal stress coefficient
logarithmic in Pressure, linear in Isothermal stress coefficient
logarithmic in Pressure, logarithmic in Isothermal stress coefficient

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

Density (Temperature, Pressure)

linear in Density
logarithmic in Density
logarithmic in Pressure, linear in Density
logarithmic in Pressure, logarithmic in Density

Massic enthalpy (Temperature, Pressure)

linear in Massic enthalpy
logarithmic in Massic enthalpy
logarithmic in Pressure, linear in Massic enthalpy
logarithmic in Pressure, logarithmic in Massic enthalpy

Massic internal energy (Temperature, Pressure)

linear in Massic internal energy
logarithmic in Massic internal energy
logarithmic in Pressure, linear in Massic internal energy
logarithmic in Pressure, logarithmic in Massic internal energy

Massic Gibbs free energy (Temperature, Pressure)

linear in Massic Gibbs free energy
logarithmic in Massic Gibbs free energy
logarithmic in Pressure, linear in Massic Gibbs free energy
logarithmic in Pressure, logarithmic in Massic Gibbs free energy

Massic entropy (Temperature, Pressure)

linear in Massic entropy
logarithmic in Massic entropy
logarithmic in Pressure, linear in Massic entropy
logarithmic in Pressure, logarithmic in Massic entropy

Massic isobaric heat capacity (Temperature, Pressure)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity
logarithmic in Pressure, linear in Massic isobaric heat capacity
logarithmic in Pressure, logarithmic in Massic isobaric heat capacity

Massic isochoric heat capacity (Temperature, Pressure)

linear in Massic isochoric heat capacity
logarithmic in Massic isochoric heat capacity
logarithmic in Pressure, linear in Massic isochoric heat capacity
logarithmic in Pressure, logarithmic in Massic isochoric heat capacity

Speed of sound (Temperature, Pressure)

linear in Speed of sound
logarithmic in Speed of sound
logarithmic in Pressure, linear in Speed of sound
logarithmic in Pressure, logarithmic in Speed of sound

Relative pressure coefficient (Temperature, Pressure)

linear in Relative pressure coefficient
logarithmic in Relative pressure coefficient
logarithmic in Pressure, linear in Relative pressure coefficient
logarithmic in Pressure, logarithmic in Relative pressure coefficient

Isothermal stress coefficient (Temperature, Pressure)

linear in Isothermal stress coefficient
logarithmic in Isothermal stress coefficient
logarithmic in Pressure, linear in Isothermal stress coefficient
logarithmic in Pressure, logarithmic in Isothermal stress coefficient

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:

Density (Temperature, Pressure)

linear in Density
logarithmic in Density
logarithmic in Pressure, linear in Density
logarithmic in Pressure, logarithmic in Density

Massic enthalpy (Temperature, Pressure)

linear in Massic enthalpy
logarithmic in Massic enthalpy
logarithmic in Pressure, linear in Massic enthalpy
logarithmic in Pressure, logarithmic in Massic enthalpy

Massic internal energy (Temperature, Pressure)

linear in Massic internal energy
logarithmic in Massic internal energy
logarithmic in Pressure, linear in Massic internal energy
logarithmic in Pressure, logarithmic in Massic internal energy

Massic entropy (Temperature, Pressure)

linear in Massic entropy
logarithmic in Massic entropy
logarithmic in Pressure, linear in Massic entropy
logarithmic in Pressure, logarithmic in Massic entropy

Massic isobaric heat capacity (Temperature, Pressure)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity
logarithmic in Pressure, linear in Massic isobaric heat capacity
logarithmic in Pressure, logarithmic in Massic isobaric heat capacity

Massic isochoric heat capacity (Temperature, Pressure)

linear in Massic isochoric heat capacity
logarithmic in Massic isochoric heat capacity
logarithmic in Pressure, linear in Massic isochoric heat capacity
logarithmic in Pressure, logarithmic in Massic isochoric heat capacity

Speed of sound (Temperature, Pressure)

linear in Speed of sound
logarithmic in Speed of sound
logarithmic in Pressure, linear in Speed of sound
logarithmic in Pressure, logarithmic in Speed of sound

Isobaric cubic expansion coefficient (Temperature, Pressure)

linear in Isobaric cubic expansion coefficient
logarithmic in Isobaric cubic expansion coefficient
logarithmic in Pressure, linear in Isobaric cubic expansion coefficient
logarithmic in Pressure, logarithmic in Isobaric cubic expansion coefficient

Isothermal compressibility (Temperature, Pressure)

linear in Isothermal compressibility
logarithmic in Isothermal compressibility
logarithmic in Pressure, linear in Isothermal compressibility
logarithmic in Pressure, logarithmic in Isothermal compressibility

Relative pressure coefficient (Temperature, Pressure)

linear in Relative pressure coefficient
logarithmic in Relative pressure coefficient
logarithmic in Pressure, linear in Relative pressure coefficient
logarithmic in Pressure, logarithmic in Relative pressure coefficient

Isothermal stress coefficient (Temperature, Pressure)

linear in Isothermal stress coefficient
logarithmic in Isothermal stress coefficient
logarithmic in Pressure, linear in Isothermal stress coefficient
logarithmic in Pressure, logarithmic in Isothermal stress coefficient

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:

Density (Temperature, Pressure)

linear in Density
logarithmic in Density
logarithmic in Pressure, linear in Density
logarithmic in Pressure, logarithmic in Density

Massic enthalpy (Temperature, Pressure)

linear in Massic enthalpy
logarithmic in Pressure, linear in Massic enthalpy

Massic internal energy (Temperature, Pressure)

linear in Massic internal energy
logarithmic in Pressure, linear in Massic internal energy

Massic entropy (Temperature, Pressure)

linear in Massic entropy
logarithmic in Pressure, linear in Massic entropy

Massic isobaric heat capacity (Temperature, Pressure)

linear in Massic isobaric heat capacity
logarithmic in Massic isobaric heat capacity
logarithmic in Pressure, linear in Massic isobaric heat capacity
logarithmic in Pressure, logarithmic in Massic isobaric heat capacity

Isothermal compressibility (Temperature, Pressure)

linear in Isothermal compressibility
logarithmic in Isothermal compressibility
logarithmic in Pressure, linear in Isothermal compressibility
logarithmic in Pressure, logarithmic in Isothermal compressibility

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:

Viscosity (Density, Temperature)

linear in Viscosity
logarithmic in Viscosity

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

Viscosity (Temperature, Pressure)

linear in Viscosity
logarithmic in Viscosity
logarithmic in Pressure, linear in Viscosity
logarithmic in Pressure, logarithmic in Viscosity

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)

Density difference, relative to R6 value (Temperature, Pressure)

linear in Density difference, relative to R6 value
logarithmic in Density difference, relative to R6 value
logarithmic in Pressure, linear in Density difference, relative to R6 value
logarithmic in Pressure, logarithmic in Density difference, relative to R6 value

Massic enthalpy difference, relative to R6 value (Temperature, Pressure)

linear in Massic enthalpy difference, relative to R6 value
logarithmic in Massic enthalpy difference, relative to R6 value
logarithmic in Pressure, linear in Massic enthalpy difference, relative to R6 value
logarithmic in Pressure, logarithmic in Massic enthalpy difference, relative to R6 value

Massic internal energy difference, relative to R6 value (Temperature, Pressure)

linear in Massic internal energy difference, relative to R6 value
logarithmic in Massic internal energy difference, relative to R6 value
logarithmic in Pressure, linear in Massic internal energy difference, relative to R6 value
logarithmic in Pressure, logarithmic in Massic internal energy difference, relative to R6 value

Massic entropy difference, relative to R6 value (Temperature, Pressure)

linear in Massic entropy difference, relative to R6 value
logarithmic in Massic entropy difference, relative to R6 value
logarithmic in Pressure, linear in Massic entropy difference, relative to R6 value
logarithmic in Pressure, logarithmic in Massic entropy difference, relative to R6 value

Massic isobaric heat capacity difference, relative to R6 value (Temperature, Pressure)

linear in Massic isobaric heat capacity difference, relative to R6 value
logarithmic in Massic isobaric heat capacity difference, relative to R6 value
logarithmic in Pressure, linear in Massic isobaric heat capacity difference, relative to R6 value
logarithmic in Pressure, logarithmic in Massic isobaric heat capacity difference, relative to R6 value

Massic isochoric heat capacity difference, relative to R6 value (Temperature, Pressure)

linear in Massic isochoric heat capacity difference, relative to R6 value
logarithmic in Massic isochoric heat capacity difference, relative to R6 value
logarithmic in Pressure, linear in Massic isochoric heat capacity difference, relative to R6 value
logarithmic in Pressure, logarithmic in Massic isochoric heat capacity difference, relative to R6 value

Speed of sound difference, relative to R6 value (Temperature, Pressure)

linear in Speed of sound difference, relative to R6 value
logarithmic in Speed of sound difference, relative to R6 value
logarithmic in Pressure, linear in Speed of sound difference, relative to R6 value
logarithmic in Pressure, logarithmic in Speed of sound difference, relative to R6 value

Relative pressure coefficient difference, relative to R6 value (Temperature, Pressure)

linear in Relative pressure coefficient difference, relative to R6 value
logarithmic in Relative pressure coefficient difference, relative to R6 value
logarithmic in Pressure, linear in Relative pressure coefficient difference, relative to R6 value
logarithmic in Pressure, logarithmic in Relative pressure coefficient difference, relative to R6 value

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

linear in Isothermal stress coefficient difference, relative to R6 value
logarithmic in Isothermal stress coefficient difference, relative to R6 value
logarithmic in Pressure, linear in Isothermal stress coefficient difference, relative to R6 value
logarithmic in Pressure, logarithmic in Isothermal stress coefficient difference, relative to R6 value

Updated 2021-12-14