IF97 Steam Tables

This page documents the basic equations implemented in Iapws_if97.

Saturation equations

For the saturation line (Region 4) the following equations are used:

Pressure as function of temperature:

$ \ln(p) = 4 \cdot \ln\left(\frac{2 C}{-B + \sqrt{B^2-4 A C}}\right) $

where

$ A = \theta^2 + 1167.0521452767\,\theta - 724213.16703206
B = -17.073846940092\,\theta^2 + 12020.82470247\,\theta - 3232555.0322333
C = 14.91510861353\,\theta^2 - 4823.2657361591\,\theta + 405113.40542057
\theta = T - \frac{0.23855557567849}{T-650.17534844798} $

Temperature as function of pressure is obtained by solving the inverse relation.

Region 1 and 2

The specific Gibbs free energy is expressed with dimensionless variables $\pi$ and $\tau$. For region 1

$ \gamma(\pi,\tau)=\sum n_i (7.1-\pi)^{I_i} (\tau-1.222)^{J_i} $

while region 2 uses an ideal and residual part

$ \gamma(\pi,\tau)=\ln\pi + \sum n_i^0\tau^{J_i^0} + \sum n_i^r\pi^{I_i^r}(\tau-0.5)^{J_i^r} $

Thermodynamic properties follow from derivatives of $\gamma$:

$ v = \frac{R T}{p}\,\pi\, \gamma_{\pi} \quad\quad h = R T\tau\, \gamma_{\tau}
s = R(\tau\gamma_{\tau}-\gamma) $

where $R=0.461526\,\mathrm{kJ\,kg^{-1}\,K^{-1}}$.

Published units and phase boundary

PhaseWaterIAPWS stores molar volume in m3/mol. Its public density methods return kg/m3, mol/m3, or lb/ft3 as requested. Region 1 is published as an aqueous phase and Region 2 as a gas phase, using the same saturation boundary as the property equations; density is not used as a substitute phase classifier.

Numerical verification and limits

The model-specification gate reproduces all six Region 1 and Region 2 verification states in Tables 5 and 15 of the revised IAPWS-IF97 release. It checks specific-volume-derived density and compressibility factor, internal energy, enthalpy, entropy, Gibbs energy, heat capacity and sound speed through both SystemWaterIF97 and the exact PhaseWaterIAPWS path. It also traverses the six states on one reused system to detect stale state and verifies H = U + PV and G = H - TS on a consistent molar basis.

This compact implementation and its executable qualification cover only the declared Region 1/2 points. They do not qualify Region 3 or 5, two-phase interpolation, Cv, fugacity, flashes, transport properties, mixtures or arbitrary states across the full IF97 validity envelope.