Formula
The state is located in the IAPWS-IF97 regions and the properties follow from the Gibbs or Helmholtz free energy of that region:
\(\text{region 1, 2, 5:}\; g(p, T) \quad\Rightarrow\quad v = \left(\frac{\partial g}{\partial p}\right)_T,\; h = g - T\left(\frac{\partial g}{\partial T}\right)_p,\; s = -\left(\frac{\partial g}{\partial T}\right)_p,\; c_p = -T\left(\frac{\partial^2 g}{\partial T^2}\right)_p\)
\(\text{region 3:}\; f(\rho, T) \;\text{with}\; p(\rho, T) = p \;\text{solved for}\; \rho \qquad \Delta T_{sh} = T - T_{sat}(p) \qquad \nu = \mu / \rho \qquad Pr = c_p \mu / k\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(p\) | absolute pressure | Pa |
| \(T\) | temperature | K |
| \(\text{phase}\) | compressed liquid, superheated steam or supercritical fluid | – |
| \(T_{sat}\) | saturation temperature at \(p\) | K |
| \(\Delta T_{sh}\) | degree of superheat (vapour only) | K |
| \(h\) | specific enthalpy | J/kg |
| \(s\) | specific entropy | J/(kg·K) |
| \(v\) | specific volume | m³/kg |
| \(\rho\) | density | kg/m³ |
| \(c_p\) | isobaric specific heat capacity | J/(kg·K) |
| \(\mu\) | dynamic viscosity | Pa·s |
| \(\nu\) | kinematic viscosity | m²/s |
| \(k\) | thermal conductivity | W/(m·K) |
| \(Pr\) | Prandtl number | – |
| \(w\) | speed of sound | m/s |
Method and standards
FireCAD's own implementation of the IAPWS Industrial Formulation 1997 (Revised Release 2007): regions 1, 2 and 5 from their Gibbs equations, region 3 from the Helmholtz equation with the density found by iteration, the saturation line from the region 4 equation. Transport properties from the IAPWS 2008 (viscosity) and 2011 (thermal conductivity) formulations at the IF97 density. Verified against the check values printed in the releases.
Assumptions and limits
- 0 to 800 °C up to 1 000 bar, and 800 to 2 000 °C up to 500 bar (IF97 range). Above 800 °C the transport properties are extrapolations.
- The critical enhancement of viscosity and conductivity is omitted; it matters only within about 1 % of the critical point.
- Pressures are absolute. Enter gauge readings with a gauge unit (bar g, kg/cm² g, psig) and the page adds one standard atmosphere.
References
- IAPWS R7-97(2012) IF97
- IAPWS R12-08 viscosity
- IAPWS R15-11 thermal conductivity
Questions and answers
What is the degree of superheat?
The temperature above the saturation temperature at the same pressure, T − T_sat(p). Steam at 10 bar(a) and 250 °C is 70 K superheated because water boils at 179.9 °C at 10 bar.
What does "compressed liquid" mean?
Water below its boiling temperature at the given pressure. Its properties are close to those of saturated water at the same temperature, which is why older tables give only the saturated values.
Why is there no result exactly at saturation?
On the saturation line the properties depend on the steam quality, not on pressure and temperature alone. Use the flash steam or saturated water calculators for wet steam.