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Thermodynamic Properties of cold and supercooled liquid H_{2}O (ordinary water substance)

Developed by Russian National Committee (RNC) of

International Association for the Properties of Water and Steam (IAPWS).

This calculation page is based on the

"Guideline on Thermodynamic Properties of Supercooled Water" [1]

provided by IAPWS.

Detailed information about used equations, constants, range of validity etc is presented in PDF version of IAPWS Release which can be downloaded from IAPWS web site www.iapws.org

Authors (and responsible persons):

from National Research University "Moscow Power Engineering Institute" (MPEI). Last update: 2015/06/30

Note that displayed last digits depends on numeric implementation of underlying formulations.

Input parameters

Formulation reference values

Dimensionless input parameters

Main equations

The specific Gibbs free energy is represented by the equation

Eq. (1) in [1]

The dimensionless regular background Gibbs energy and few parameters

Coefficients from Table 2 [1] (can be downloaded here in text format):

Extracting data to vectors:

The dimensionless regular background Gibbs energy

Eq. (3) in [1]

Additional parameters

Eq. (5) in [1]

The field L has the form

Eq. (4) in [1]

The interaction parameter

Eq. (6) in [1]

The mole fraction x of the low-density structure

The mole fraction x of the low-density structure depends on pressure and temperature, and is found by minimizing the Gibbs energy as a function of x at constant temperature and pressure

which corresponds to the condition:

Eq. (8) in [1]

Intervals in which x, the solution of Eq. (8) in [1], is located

Eq. from Table 4 in [1]

Initial value for mole fraction of low-density structure

Search for the value of x using built-in procedure. Note that the tolerance may be slight different

Check the results:

Dimensionless Gibbs Free Energy and it's derivativies

The dimensionless Gibbs free energy is represented by the equation

The partial derivatives for field value

Eq. from Table 3 in [1]

The partial derivatives for dimensionless regular background Gibbs energy

The order parameter

Eq. (12) in [1]

The susceptibility

Thermodynamic properties

Specific volume:

Eq. (13) in [1]

Density:

Specific entropy

Eq. (14) in [1]

The isothermal compressibility

Eq. (15) in [1]

The thermal expansion coefficient

Specific isobaric heat capacity

Specific isochoric heat capacity

Eq. (16) in [1]

Speed of sound

Eq. (17) in [1]

References

1. Guideline on Thermodynamic Properties of Supercooled Water. Stockholm, Sweden, July 2015, available at http://www.iapws.org