The figure above shows the five regions into which the entire range of validity of IAPWS-IF97 is divided. Regions 1 and 2 are both individually covered by a fundamental equation for the specific Gibbs free energy g(p,T), region 3 by a fundamental equation for the specific Helmholtz free energy f(ρ,T), and the saturation curve, corresponding to region 4, by a saturation-pressure equation p_s(T). The high-temperature region 5 is also covered by a g(p,T) equation. These five equations, shown in rectangular boxes in the figure, form the so-called basic equations.

In addition to these basic equations, so-called backward equations are provided for regions 1 to 4. These backward equations were developed in the following combinations of variables: For regions 1 and 2 as equations of the form T(p,h), T(p,s), and p(h,s), for region 3 as equations of the form T(p,h), v(p,h), T(p,s), v(p,s), p(h,s) and v(p,T). The backward equation for the entire region 4 is a saturation-temperature equation T_s(p), which is mathematically completely consistent with the saturation-pressure equation p_s(T). For the technically most important part of region 4 (s ≥ s(623.15 K)), there is a saturation-temperature equation of the form T_s(h,s). In the figure above, in addition to the (framed) basic equations, all of these types of backward equations (marked in grey) are assigned to the corresponding region of IAPWS-IF97.

With these backward equations, properties that depend on the input quantities (p,h), (p,s) and (h,s), in region 3 also on the input quantities (p,T), are calculable without iterations and thus very quickly.

A comprehensive description of the IAPWS-IF97 is given in the book

Kretzschmar, H.-J., Wagner, W., International Steam Tables - Properties of Water and Steam based on the Industrial Formulation IAPWS-IF97. Springer-Verlag (Berlin), 2019.

This book also contains the IAPWS equations for the most important transport properties and some other properties, three overview diagrams (Mollier h-s diagram, T-s diagram, log(p)-h diagram) and pressure-temperature diagrams with isolines of more than 25 properties. For more details (contents, sample pages, etc.) see here.

2. Software for IAPWS-IF97

On the basis of IAPWS-IF97, including all of the backward equations as well as the IAPWS equations for the transport properties and further properties, there is a software package called IAPWS-IF97BO for the calculation of a large number of properties. The software was specially developed with a view to optimal programming in order to achieve short computing times.

When applying the software, it is not necessary to know which region of IAPWS-IF97 the property to be calculated belongs to. Based on the given input quantities, the software automatically determines which equation of IAPWS-IF97 has to be applied.

With our software package IAPWS-IF97BO, 21 thermodynamic properties, five partial derivatives, five transport properties and three further properties of water and steam can be calculated.

2.1 Thermodynamic properties

Based on the corresponding equations of IAPWS-IF97 the following thermodynamic properties can be calculated:

 Table 1  Calculable thermodynamic properties.

All these properties can be calculated in the entire range of validity of IAPWS-IF97, see Sec. 1. Concerning region 4 (two-phase region), the properties ν, ρ, h, s, u, f, g and x can also be calculated within the two-phase region. The other properties can only be calculated on the phase boundaries (saturated-liquid line and saturated-vapour line) because they are not defined within the two-phase region.

2.2 Transport properties and further properties

The following transport properties and further properties can be calculated with the software:

 Table 2  Calculable five transport properties
 and three further properties.

The internationally agreed equations for calculating these properties, which do not belong to IAPWS-IF97, are described in the book “International Steam Tables” mentioned at the end of Sec. 1 and in the corresponding IAPWS releases IAPWS R12-08 for the viscosity, IAPWS R15-11 for the thermal conductivity, IAPWS R8-97 for the static dielectric constant, IAPWS R9-97 for the refractive index and IAPWS R1-76(2014) for the surface tension, see http://www.iapws.org/. It should be noted that these equations are functions of temperature and density (not pressure). This fact has consequences for the necessity of iterations. The surface tension is a function of temperature only.

Except for the dielectric constant ε, all the other properties can be calculated in the entire range of validity of IAPWS-IF97, see at the beginning of Sec. 1. The range of validity of the equation for ε is limited to 873.15 K, but the equation can be reasonably extrapolated up to 1073.15 K. The surface tension σ(T) refers only to the two-phase region, region 4.

2.3 Combinations of input variables for calculating the several properties

2.3.1 Regions 1-5

For regions 1-3 and 5 (single-phase regions) and region 4 (two-phase region), all properties listed in Tables 1 and 2 can be calculated as a function of the pairs of input variables shown in Table 3. For region 5, properties for input variables other than (p,T) are calculated via iterations only; there are no backward equations. Properties in region 4 cannot be calculated for the combination (p,T) as input variables, because p and T are not independent of each other in this region.

 Table 3  Possible combinations of
 input variables for calculations in
 regions 1 to 5; for region 4, (p,T)
 cannot be used, see text above.

The most important properties can be calculated directly from the functions in the software for the pairs of input variables listed in Table 3. The calculation of further properties as functions of all the pairs of input variables is possible by corresponding combinations of functions contained in the software.

2.3.2 Calculations of properties in region 4 (two-phase region)

For region 4 (two-phase region (0 < x < 1), saturation pressure p_s, saturation temperature T_s, saturated-liquid line [('), x = 0, bubble line], saturated-vapour line [("), x = 1, dew line]), the properties in the left column of Table 4 can be calculated from the functions given in the software for all listed input variables.

 Table 4  Calculable properties for the entire region 4 (saturated-liquid line,
 saturated-vapour line and within the two-phase region) from the
 corresponding functions listed in the software.

Those properties listed in Tables 1 and 2 that are not given in the left column of Table 4 cannot be calculated within the two - phase region (0 < x < 1) but only on the saturated-liquid line (x = 0) and saturated-vapour line (x = 1); these properties are not defined within the two - phase region

2.4 IAPWS-IF97 DLL and Excel Add-In for the calculation of thermophysical properties

For the integration of the IAPWS-IF97 into Windows-based standard programs, the software package IAPWS-IF97BO contains the dynamic link library (DLL) IF97BO.dll, optimized and built with the Intel Parallel Studio XE 2015 Composer Edition for Fortran (version 15.07.287). The DLL provides numerous functions that allow the calculation of all properties listed in Tables 1 and 2 for all combinations of input variables given in Tables 3 and 4.

The software allows whether the desired properties should be calculated using the backward equations contained in IAPWS-IF97, or only the basic equations with iterations should be used, if iterations are necessary for the calculation of the corresponding property. In this case, the backward equations are used to calculate the initial values, so that these iterations are significantly faster than without these initial values. The functions are called up using simple function names, which contain abbreviations for the desired property and the required input variables. For example, to calculate the specific enthalpy h for given values of pressure p and temperature T, the function HBPT is available for using the backward equations and the function HOPT is available for the calculation without the use of the backward equations.

In addition, the IAPWS-IF97BO software package, available in 32-Bit or 64-Bit, contains a Microsoft Excel Add-in that allows a simple integration of the DLL into Microsoft Excel. Since installing the IAPWS-IF97BO Excel Add-In adds all functions exported with the DLL to the standard Microsoft Excel function set, the desired thermodynamic and transport properties can be called either by direct input of the formula listed in the manual into an Excel spreadsheet or very conveniently with the help of the function wizard of Microsoft Excel.