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Thermodynamic Properties of Ordinary Water Substance for Industrial Use

in region 3 of IAPWS-IF97:

Backward Equations: T(p, s) and v(p, s)

Developed by Russian National Committee (RNC) of

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

This calculation page is based on the

"Revised Supplementary Release on Backward Equations for the Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam" [1] provided by IAPWS.

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

Authors (and responsible persons):

Moscow Power Engineering Institute (MPEI). Last update: 2013/01/13

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

Input parameters

Formulation reference values

Dimensionless input parameters

Main backward equations

The temperature in subregion 3a is represented by the equation

Eq. (6) in [1]

Coefficients from Table 10 [1] (can be downloaded here in text format):

Extracting data to vectors:

The temperature in subregion 3a

The temperature in subregion 3b is represented by the equation

Eq. (7) in [1]

Coefficients from Table 11 [1] (can be downloaded here in text format):

The temperature in subregion 3b

The specific volume in subregion 3a is represented by the equation

Eq. (8) in [1]

Coefficients from Table 13 [1] (can be downloaded here in text format):

The specific volume in subregion 3a

The specific volume in subregion 3b is represented by the equation

Eq. (9) in [1]

Coefficients from Table 14 [1] (can be downloaded here in text format):

The specific volume in subregion 3b

Determining the subregion

Subregion of region 3 for given entropy and pressure is

Boundary equation p_{sat}(s) for the saturation line of region 3

The boundary equation of saturation pressure in region 3

Eq. (11) in [1]

Coefficients from Table 19 [1] (can be downloaded here in text format):

The saturation pressure in region 3

Determination of region

Calculated properties in region 3

Temperature

Specific volume

References

1. Revised Supplementary Release on Backward Equations for the Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. Kyoto, Japan, September 2004, available at http://www.iapws.org