Engineering & Science
Watson Correlation: Latent Heat of Vaporization vs Temperature
Scale enthalpy of vaporization ΔH_vap(T_2) = ΔH_vap(T_1) * ((T_c - T_2) / (T_c - T_1))^0.38 (kJ/mol) from normal boiling point up to high-pressure boiler conditions near the critical point.
Why latent heat of vaporization vanishes smoothly to zero at T_c!
Process engineers designing high-pressure steam boilers or distillation reboilers cannot reuse 1 atm latent heats: as saturation temperature T approaches critical temperature T_c, saturated liquid and saturated vapor densities converge until the phase boundary—and latent heat ΔH_vap—vanishes identically to zero at T = T_c! K. M. Watson (Industrial & Engineering Chemistry, 1943) discovered that virtually all pure polar and non-polar fluids obey a universal 0.38 power-law decay: ΔH_vap(T_2) = ΔH_vap(T_1) * ((T_c - T_2) / (T_c - T_1))^0.38!
Track water from its normal boiling point T_1 = 373.15 K (ΔH_vap,1 = 40.66 kJ/mol, T_c = 647.1 K): at a 40-bar utility boiler operating at T_2 = 523.15 K (250 °C), ΔH_vap drops 26% to 30.08 kJ/mol; near subcritical drum conditions T_2 = 600.0 K, ΔH_vap falls nearly in half to 20.83 kJ/mol!
| Steam Saturation Temperature T2 (Tc = 647.1 K) | Reduced Distance (Tc - T2) | Watson ΔH_vap(T2) (kJ/mol) | Fraction of 1-atm ΔH1 |
|---|---|---|---|
| 1-atm Normal Boiling Point (373.15 K) | 273.95 K | 40.66 kJ/mol | 100.0% (Reference) |
| High-Pressure Boiler Drum (523.15 K) | 123.95 K | 30.08 kJ/mol | 74.0% |
| Near-Critical Steam Generator (600.0 K) | 47.10 K | 20.83 kJ/mol | 51.2% |
Watson Scaled Enthalpy of Vaporization ΔH_vap(T_2) (kJ/mol)
Evaluates ΔH_1 * ((T_c - T_2) / (T_c - T_1))^0.38 and returns 0 cleanly right at T_2 = T_c while guarding supercritical T_2 > T_c.
=IF(OR(B2 <= 0, B3 <= 0, B5 <= B3, B4 <= 0, B4 > B5), "Supercritical or Invalid T", IF(B4 = B5, 0, ROUND(B2 * (((B5 - B4) / (B5 - B3)) ^ 0.38), 2)))Specific Latent Heat per Mass Δh_vap(T_2) (kJ/kg)
Converts molar ΔH_vap(T_2) (kJ/mol) into engineering steam-table mass units (kJ/kg) via 1000 * ΔH_vap / MW.
=IF(OR(B2 <= 0, B3 <= 0, B5 <= B3, B4 <= 0, B4 > B5, B6 <= 0), "Supercritical or Invalid T", IF(B4 = B5, 0, ROUND(1000 * B2 * (((B5 - B4) / (B5 - B3)) ^ 0.38) / B6, 1)))Try the example
Use the original values or change them to test your understanding.