Worked Example: The HVAC Sensible & Latent Balance
Splitting a cooling load into sensible and latent components, and why over-dehumidifying wastes energy.
10 min read
The psychrometric mass balance lesson tracked water vapour through a cooling coil and found 8 g/s of condensate draining away. This lesson finishes the job: turning that mass balance into the energy balance that actually sizes the cooling coil, splitting the load into the sensible and latent components the HVAC sensible & latent lesson introduced.
Two heat streams, one coil
A cooling coil does two jobs on the same air stream simultaneously, and a proper energy balance keeps them separate:
- Sensible heat removed โ cooling the air's temperature down, at constant moisture content
- Latent heat removed โ condensing water vapour out of the air, at (roughly) constant temperature
Using the same air handling unit as before โ 2 kg/s of dry air, entering at 24 ยฐC and 12 g/kg humidity ratio, leaving the coil at 10 ยฐC and 8 g/kg:
Sensible load. Moist air has a specific heat of about 1.02 kJ/kgยทK:
Q_sensible = แน ร cp ร ฮT = 2 ร 1.02 ร (24 โ 10) = 28.6 kW
Latent load. From the mass balance, 8 g/s (0.008 kg/s) of water vapour condenses. Water's latent heat of condensation near coil surface temperatures (around 10 ยฐC) is about 2,500 kJ/kg โ a little higher than the 2,257 kJ/kg you saw for steam condensing at 100 ยฐC in the steam properties lesson, because latent heat isn't quite constant โ it rises somewhat as temperature falls:
Q_latent = แน_condensate ร h_fg = 0.008 ร 2,500 = 20.0 kW
Total coil load:
Q_total = Q_sensible + Q_latent = 28.6 + 20.0 = 48.6 kW
That 20 kW latent figure is a genuinely useful sanity check against the sensible-latent lesson's occupancy figure โ "100 people = ~10 kW latent" โ this AHU's latent load is the right order of magnitude for a building with a couple of hundred occupants, exactly where you'd expect it to land.
Where the "expensive" part of dehumidification shows up
The sensible-latent lesson describes the standard dehumidification approach as cool, then reheat: cool the air well below the target temperature to force condensation, then add heat back to bring it to a comfortable supply temperature. Suppose this air needs reheating from the coil's 10 ยฐC up to an 18 ยฐC supply temperature:
Q_reheat = แน ร cp ร ฮT = 2 ร 1.02 ร (18 โ 10) = 16.3 kW
That 16.3 kW of reheat is genuinely additional energy โ on top of the 48.6 kW already spent cooling and dehumidifying the same air. It's worth a third of the entire coil load (16.3 รท 48.6 โ 34%), spent purely to correct for having over-cooled the air in the first place. This is exactly the inefficiency the sensible-latent lesson warns about, now with a number attached: every degree of unnecessary reheat is unnecessary cooling paid for twice.
The balance explains the fix
The sensible-latent lesson's advice โ relax the humidity setpoint, or use desiccant/enthalpy-wheel dehumidification instead of cool-and-reheat โ isn't a vague efficiency tip once you can see the numbers behind it. A wider humidity band means less condensate needs removing (a smaller 20 kW latent load), which means less over-cooling, which means less of that 16.3 kW reheat is needed at all. The energy balance doesn't just describe the waste โ it tells you exactly which lever (moisture removed, or degrees of reheat) to pull, and by how much, to shrink it.
This closes the loop on the three worked "real system" balances in this course โ a boiler, a steam system, and now an HVAC coil. The next module turns these numeric balances into pictures, and introduces one more idea โ that not every kilowatt is equally valuable โ before you put the whole method together on a combined balance of your own.