MECH3260 Chap.4 Psychrometry and Air Conditioning
Psychrometry and Air Conditioning
Week 4 applies the mixtures toolkit from Chapter 3 to moist air, the dry-air and water-vapour mixture behind air conditioning, ventilation and drying. It defines specific and relative humidity, dew point and wet-bulb temperature, and the enthalpy of moist air, all of them built on Dalton partial pressures.
It then leaves the tables behind for the psychrometric chart, where any two properties fix a state and the rest are read off, and treats the four standard processes as directions of travel on that chart: adiabatic mixing of two streams, evaporative cooling along a constant wet-bulb line, heating with humidification, and cooling with dehumidification.
The chapter finishes with system sizing, separating sensible from latent loads and using their ratio to fix the slope of the load line.
What this chapter covers
- 01
Specific (absolute) humidity omega = m_v/m_a = 0.622 P_v/(P-P_v), typically 0.01-0.02 kg/kg dry air
- 02
Relative humidity phi = P_v/P_sat(T) -- the humidity measure that governs thermal comfort
- 03
Why the same absolute water content gives a lower phi as temperature rises (P_sat rises steeply with T)
- 04
Dew point: the saturation temperature at the air's actual P_v -- the temperature at which condensation begins
- 05
Wet-bulb temperature: the steady reading of an evaporatively-cooled thermometer, equal to dry-bulb only at phi=100%
- 06
Enthalpy of moist air per kg of dry air, h = cp T + omega hg
Enthalpy and water mass of a moist-air exam hall
- +1Vapour pressure: P_v = phi P_sat = 0.60(2.645) = 1.587 kPa.
- +2Specific humidity: omega = 0.622 P_v/P_a = 0.00993 kg/kg dry air.
- +2Mixture enthalpy: h = cp T + omega hg = 47.35 kJ/kg dry air.
- +2Mass of dry air m_a = 234.9 kg (ideal-gas law on partial pressure and volume).
- +1Mass of water vapour m_v = omega m_a = 2.33 kg.
Key terms
- Specific humidity
- The mass of water vapour carried per unit mass of dry air, obtained from the vapour and total pressures. It is the quantity that stays constant during simple heating or cooling, which makes it the natural bookkeeping variable for water.
- Relative humidity
- The actual vapour pressure divided by the saturation pressure at the same temperature. Because saturation pressure climbs steeply with temperature, this number moves whenever the air is heated or cooled even if no water is added or removed.
- Dew point
- The temperature at which moist air cooled at constant pressure and constant water content first reaches saturation. Below it, water condenses out, which is why it governs condensation on windows, pipes and cooling coils.
- Wet-bulb temperature
- The temperature reached by a wetted thermometer in a moving air stream, where evaporation and convection balance. Lines of constant wet-bulb temperature are the paths that adiabatic saturation and evaporative cooling follow on the chart.
- Saturation line
- The hundred percent relative humidity curve that bounds the psychrometric chart on the left. Air cannot normally sit beyond it, so a process line that would cross it signals that condensate forms and the simple analysis stops applying.
- Sensible load
- A heat load that acts by raising air temperature, arising from lights, occupants, equipment, solar gain and conduction through the building fabric. It is removed by cooling the air.
- Latent load
- A heat load that arrives as moisture, from occupants, cooking or open water. It raises air enthalpy without raising temperature and can only be removed by condensing water on the coil.
- Grand sensible heat factor
- The total sensible load divided by the sum of the total sensible and total latent loads. It fixes the direction of the apparatus load line on the chart, just as the room factor fixes the direction of the room line.
Psychrometry and Air Conditioning FAQ
Why does relative humidity change when no water is added or removed?
Relative humidity compares the actual vapour pressure with the saturation pressure at the current temperature, and saturation pressure rises sharply as air warms. Heat a room at constant water content and the denominator grows, so the ratio falls and the air feels dry. Cool the same air and the ratio climbs until it reaches one, at which point condensation begins. Nothing about the water content changed in either direction.
Is an evaporative cooler a sensible purchase in Sydney?
Not particularly, and the chart shows why in one glance. Evaporative cooling travels along a constant wet-bulb line until it meets the saturation line, and the length of that run is the temperature drop available. In dry inland air the run is long and the drop is large. In humid coastal air the state already sits close to saturation, so only a small drop is possible and the device disappoints.
A question asking whether the technology suits a location wants that distance read off the chart.
Why does a real air-conditioning system reheat air it has just cooled?
Because cooling with dehumidification has to overshoot. Air is cooled to its dew point and then follows the saturation line while water condenses out and drains away, and the air leaving that coil is both colder and damper-feeling than the room wants. A reheat section warms it back to the supply condition at unchanged water content.
The apparent waste is the price of removing the latent load, which cannot be done at the delivery temperature.
What is the most common way to undersize a cooling coil?
Forgetting that outside air loads the system twice. Air leaking in around closed openings is infiltration, and air supplied deliberately to keep the space fresh is ventilation. Both arrive at a different temperature and a different humidity from the room, so both contribute a sensible load and a latent load.
In a humid climate the latent half is the larger of the two, and leaving it out produces a coil that holds temperature but never controls humidity.
Exam move
Keep the four humidity descriptors assigned to separate jobs rather than treating them as interchangeable: specific humidity for mass balances on water, relative humidity for comfort and condensation-risk judgements, dew point for questions about surfaces, and wet-bulb temperature for evaporative processes.
Then get a real psychrometric chart in front of you and practise placing states and drawing paths, because chart questions award method marks for a correctly directed process line even when a read value is slightly off.
Learn the four processes as directions first and formulas second: horizontal for heating, along a wet-bulb line for evaporative cooling, a straight join for adiabatic mixing, and down then along the saturation line for dehumidification. Leave load calculations until last, and when you get there, list the outside-air contribution in both the sensible and the latent column before adding anything up.
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