Psychrometrics
Specific enthalpy of moist air
- where
- partial pressure of water vapour (kPa)
- relative humidity (%)
- dry-bulb temperature (°C)
- moisture content (g/kg dry air)
- atmospheric pressure (kPa)
- specific enthalpy (kJ/kg dry air)
Explain this equation
Works out the total heat content of moist air per kilogram of dry air. Multiply the enthalpy change across a coil by the dry-air mass flow to get its total cooling or heating duty.
p_w and W find the moisture content from the RH reading. 1.006 t is the sensible heat in the dry air. W/1000 is kilograms of water per kilogram of air; 2501 is the heat needed to evaporate it at 0 °C and 1.86 t warms the vapour to the air temperature.
Enthalpy is measured from dry air at 0 °C, so only differences matter in practice.
Sense check: 20 °C, 50 % is about 38.5 kJ/kg; 28 °C, 50 % is about 58 kJ/kg. A coil cooling 1.2 kg/s across that 20 kJ/kg range does about 24 kW.
Watch out: use mass flow of dry air, not volume flow, with enthalpy differences.
Total heat content of moist air per kilogram of dry air, from temperature and RH. The difference in enthalpy across a coil times the air mass flow gives its total (sensible plus latent) duty.
Enter your values to see the result.
Good to know
1.006 t is the sensible heat of the dry air; W(2501 + 1.86 t) is the latent heat in the water vapour plus its sensible heat. Enthalpy is measured from dry air at 0 °C. Typical values: about 38.5 kJ/kg at 20 °C, 50 %; about 58 kJ/kg at 28 °C, 50 %.
Common mistake
Multiplying the enthalpy difference by volume flow instead of the mass flow of dry air (≈ 1.2 × m³/s at room conditions).
Limits
Ideal-gas mixture, Magnus saturation pressure, valid for normal HVAC conditions (about −40 to 60 °C).
Sources
- ASHRAE Handbook — Fundamentals (2017), chapter 1 Psychrometrics: Hyland–Wexler saturation pressure (eq. 6), humidity ratio W = 0.621945 pw/(p − pw), enthalpy h = 1.006t + W(2501 + 1.86t), specific volume v = 0.287042(t + 273.15)(1 + 1.607858W)/p, adiabatic mixing
- CIBSE Guide C: Reference data (2007), chapter 1 (properties of humid air) and chapter 4 (flow of fluids in pipes and ducts)
- O. A. Alduchov, R. E. Eskridge, Improved Magnus form approximation of saturation vapor pressure, Journal of Applied Meteorology 35(4), 1996, pp. 601–609 (es = 610.94 exp(17.625t/(t + 243.04)) Pa)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.