Formula
On the saturation line the pressure and temperature are linked by the IAPWS-IF97 region 4 equation; the liquid and vapour properties come from the region 1 and region 2 equations at that state:
\(T_{sat} = T_{sat}(p) \quad\text{or}\quad p_{sat} = p_{sat}(T) \qquad h_{fg} = h_g - h_f\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(\text{mode}\) | look up by pressure or by temperature | – |
| \(p\) | absolute pressure entered | Pa |
| \(T\) | temperature entered | K |
| \(p_{sat}\) | saturation pressure | Pa |
| \(T_{sat}\) | saturation (boiling) temperature | K |
| \(h_f\) | saturated liquid enthalpy | J/kg |
| \(h_g\) | saturated vapour enthalpy | J/kg |
| \(h_{fg}\) | latent heat of vaporisation | J/kg |
| \(s_f\) | saturated liquid entropy | J/(kg·K) |
| \(s_g\) | saturated vapour entropy | J/(kg·K) |
| \(v_f\) | saturated liquid specific volume | m³/kg |
| \(v_g\) | saturated vapour specific volume | m³/kg |
Method and standards
IAPWS R7-97(2012), the Industrial Formulation 1997: region 4 saturation equation for \(p_{sat}(T)\) and its inverse \(T_{sat}(p)\); region 1 for the liquid and region 2 for the vapour up to 350 °C, and region 3 (by iteration on density) from 350 °C to the critical point. Enthalpy and entropy are referenced to the triple-point liquid, as in every IF97 steam table.
Assumptions and limits
- Pure water; dissolved solids raise the boiling point slightly.
- Valid from the triple point (0.01 °C, 611.657 Pa) to the critical point (373.946 °C, 220.64 bar).
- Pressure is absolute.
References
- IAPWS R7-97(2012) IF97
Questions and answers
At what temperature does water boil at 10 bar?
At 10 bar absolute the saturation temperature is 179.89 °C (453.04 K). At 10 bar gauge (11.01 bar absolute) it is about 184 °C, so check whether a reading is gauge or absolute.
Why does the latent heat fall as pressure rises?
The liquid and vapour become more alike as the critical point (220.64 bar, 373.95 °C) is approached. At 1 atm h_fg is 2 257 kJ/kg; at 100 bar it is 1 318 kJ/kg; at the critical point it is zero.
Which pressure should I enter for a boiler drum?
The absolute drum pressure. Choose a gauge unit (bar g, kg/cm² g, psig) to type a gauge reading; the calculator adds one standard atmosphere.