The Calculation, Explained
Why saturation locks pressure to temperature
When liquid water and its vapour share a space and reach equilibrium, the pressure is fixed by the temperature alone — add heat and liquid boils rather than warming; remove the vapour space (a completely liquid-full vessel) and the rule collapses, which is why a water-solid boiler part is a pressure accident waiting for a relief valve. Every drum, deaerator, condenser and steam trap in the plant lives on this curve. A condenser at 0.10 bar abs condenses at 45.8 °C and not a degree lower; an HRSG drum at 40 bar holds its water at 250 °C whether the control room believes it or not.
The equation
The rigorous formulation is IAPWS IF97, the international steam-table standard. For engineering estimation the Antoine equation reproduces the curve closely across the whole practical range:
with constants A = 8.07131, B = 1730.63, C = 233.426 below 99 °C and A = 8.14019, B = 1810.94, C = 244.485 above it (NIST data for water). Latent heat is estimated with the Watson correlation from its 100 °C value:
Assumptions and applicability
- Accuracy of the Antoine form is roughly ±0.5% on pressure across 1–374 °C — ample for operations and troubleshooting. For custody, warranty or design numbers use IAPWS IF97 steam tables.
- All pressures are absolute. A gauge reading of "10 bar" in the plant is about 11 bar abs, saturating near 184 °C, not 180 °C — the commonest saturation error in the field.
- The relation holds only where liquid and vapour coexist. Superheated steam and subcooled water are off the curve entirely; their temperatures are free variables.
- The curve ends at the critical point, 374 °C / 221 bar. Supercritical plant has no saturation at all.
Worked example (the defaults above)
Water at 180 °C saturates at 9.97 bar abs (steam tables: 10.02 bar) — and the Watson correlation puts latent heat at ≈ 1,980 kJ/kg, about 2% under the tabulated 2,015 kJ/kg, a fair picture of estimation accuracy. Run backwards, a drum holding 10 bar abs sits at 180 °C: that is the temperature its level gauges, drain pots and the metal itself are living at, whatever the load is doing.
References
IAPWS IF97 — Industrial Formulation for the Thermodynamic Properties of Water and Steam; Antoine constants per NIST Chemistry WebBook (water).
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