Psychrometry and air conditioning load

Why it matters

Comfort depends on humidity as much as on temperature, and in most of India the moisture in the air, not the heat, dominates air-conditioning design for half the year. Psychrometry gives the tools to describe moist air and track it through coils, humidifiers, evaporative coolers and mixing boxes. Load estimation then sizes the plant: how much air to supply, how cold, and how much refrigeration capacity is needed. The same ideas apply to clean rooms, data centres, drying ovens and condensation control in enclosures.

Key ideas

Moist air is a mixture of dry air and water vapour, both treated as ideal gases at the low partial pressures involved. Properties are quoted per kg of dry air (kg da), because the dry-air mass stays constant through most processes while the moisture changes.

Humidity measures.

• Specific humidity (humidity ratio) ω: kg of vapour per kg of dry air.
• Relative humidity φ: vapour partial pressure ÷ saturation pressure at the same dry-bulb temperature.
• Degree of saturation μ: ω ÷ ω_sat at the same temperature; it is slightly less than φ.
• Dew-point temperature (DPT): the saturation temperature at the vapour partial pressure; cooling air below it at constant ω condenses moisture.

Temperatures. Dry-bulb (DBT) is the ordinary temperature. Wet-bulb (WBT) is read by a thermometer with a wetted wick in moving air; evaporation cools it, so WBT ≤ DBT, with equality only at saturation. For air–water mixtures WBT is practically equal to the adiabatic saturation temperature. For unsaturated air: DPT < WBT < DBT. Wet-bulb depression (DBT − WBT) indicates how dry the air is.

Psychrometric chart. DBT on the horizontal axis, ω (or vapour pressure) on the vertical; curved lines of constant φ, the saturation curve (φ = 100 %) at the top, inclined lines of constant WBT (nearly parallel to constant-enthalpy lines) and lines of constant specific volume. Any two independent properties fix a state.

Basic processes (each is a line on the chart).

• Sensible heating or cooling: horizontal line (ω constant).
• Cooling and dehumidification: air passes a coil colder than its dew point; it ends between the inlet state and the coil's apparatus dew point (ADP). The bypass factor (BPF) expresses the fraction of air that effectively misses the coil; contact factor = 1 − BPF.
• Heating and humidification (winter air conditioning), with steam or water sprays.
• Evaporative (adiabatic) cooling: water evaporates into air along a constant-WBT line; DBT falls and ω rises. Desert coolers work well in hot, dry climates and poorly in humid ones.
• Adiabatic mixing of two streams: the mixed state lies on the straight line joining them, divided in inverse ratio of the dry-air masses.

Air-conditioning load.

• Sensible heat load: changes air temperature — conduction through walls and roof, solar gain through glass, lights, equipment, the sensible part of occupants' heat, and sensible heat of infiltration and fresh air.
• Latent heat load: moisture added to the space — occupants' breathing and perspiration, cooking, infiltration and fresh air.
• Sensible heat factor (SHF) = sensible ÷ total. The room SHF line drawn through the room state on the chart gives all supply-air states that can meet both loads at once. Unit loads (people, lights, U-values, solar factors) come from design data or codes; take them from your data book.

Formulas

ω = 0.622 p_v / (p − p_v) — kg vapour/kg da; p: total pressure, p_v: vapour partial pressure (same units). φ = p_v / p_s — p_s: saturation pressure of water at the DBT (from steam tables). μ = ω / ω_s = φ (p − p_s) / (p − p_v) h = 1.005 t + ω (2501 + 1.88 t) — kJ/kg da, t in °C (reference: dry air and liquid water at 0 °C). v = R_a T / (p − p_v) — specific volume, m³/kg da; R_a = 0.287 kJ/kg·K, p in kPa, T in K. p_v = p_wb − (p − p_wb)(t − t_wb) / (1527.4 − 1.3 t_wb) — Carrier's equation (p_wb: saturation pressure at the WBT; temperatures in °C). Data books print slightly different constants; use the form in yours. BPF = (t_out − t_ADP) / (t_in − t_ADP) — coil bypass factor. Q_s = ṁ_a c_pma Δt — sensible heat (kW); c_pma = 1.005 + 1.88 ω ≈ 1.02 kJ/kg·K, ṁ_a in kg da/s. Q_L = ṁ_a Δω h_fg — latent heat (kW); h_fg ≈ 2500 kJ/kg. Q_total = ṁ_a (h₁ − h₂) SHF = Q_s / (Q_s + Q_L) ṁ₁ ω₁ + ṁ₂ ω₂ = ṁ₃ ω₃, ṁ₁ h₁ + ṁ₂ h₂ = ṁ₃ h₃ — adiabatic mixing (dry-air masses). 1 TR = 3.517 kW

Worked examples

Example 1 (standard, properties). Air is at 35 °C DBT and 40 % RH at 101.325 kPa. From steam tables, p_s(35 °C) = 5.629 kPa. Find p_v, ω, dew point and enthalpy.

1. p_v = φ p_s = 0.40 × 5.629 = 2.252 kPa.
2. ω = 0.622 p_v/(p − p_v) = 0.622 × 2.252/(101.325 − 2.252) = 1.4005/99.073 = 0.01414 kg/kg da.
3. Dew point = saturation temperature at 2.252 kPa = 19.4 °C (steam tables).
4. h = 1.005 t + ω (2501 + 1.88 t) = 35.18 + 0.01414 × 2566.8 = 35.18 + 36.29 = 71.5 kJ/kg da.
5. The chart gives a WBT of about 23.9 °C, consistent with DPT < WBT < DBT.

p_v ≈ 2.25 kPa, ω ≈ 0.0141 kg/kg da, DPT ≈ 19.4 °C, h ≈ 71.5 kJ/kg da

Example 2 (GATE level, supply-air design). A room is held at 25 °C, 50 % RH (ω_r = 0.00988 kg/kg da). Room sensible load is 20 kW and latent load 5 kW. Supply air enters at 14 °C. Take c_pma = 1.02 kJ/kg·K and h_fg = 2500 kJ/kg. Find the SHF, supply air mass flow, supply humidity ratio and its relative humidity (p_s(14 °C) = 1.599 kPa).

1. SHF = Q_s/(Q_s + Q_L) = 20/25 = 0.80.
2. Sensible balance: ṁ_a = Q_s/(c_pma Δt) = 20/(1.02 × 11) = 1.783 kg da/s.
3. Latent balance: Δω = Q_L/(ṁ_a h_fg) = 5/(1.783 × 2500) = 0.00112 kg/kg da.
4. ω_s = 0.00988 − 0.00112 = 0.00876 kg/kg da.
5. p_v = ω p/(0.622 + ω) = 0.00876 × 101.325/0.63076 = 1.407 kPa; φ_s = 1.407/1.599 = 0.88.
6. The supply state (14 °C, 88 % RH) lies below the room state on the RSHF line; the coil must deliver air at this ω, with ADP below its dew point (about 12 °C).

SHF = 0.80, ṁ_a ≈ 1.78 kg/s, ω_s ≈ 0.0088 kg/kg da, φ_s ≈ 88 %

Example 3 (bypass factor). Air at 32 °C passes a coil with ADP = 10 °C and BPF = 0.15. From t_out = t_ADP + BPF (t_in − t_ADP) = 10 + 0.15 × 22 = 13.3 °C. Leaving DBT ≈ 13.3 °C

Common mistakes

• Using DBT instead of DPT to decide whether a cold surface will sweat; condensation starts below the dew point.
• Taking p_s at the dew point or wet bulb when computing φ. Use the saturation pressure at the DBT.
• Writing properties per kg of moist air instead of per kg of dry air.
• Mixing streams by volume flow instead of dry-air mass flow.
• Treating evaporative cooling as dehumidification. It adds moisture.
• Forgetting the fresh-air (ventilation) load, often the largest latent load in humid climates.
• Using 1.005 kJ/kg·K for moist-air sensible heat when the humid specific heat (≈ 1.02) is intended.

For GATE ME

Questions ask for ω, φ, DPT and enthalpy from given pressures; the state after heating, cooling and dehumidification, evaporative cooling or adiabatic mixing; bypass factor; sensible and latent loads and SHF; and refrigeration capacity of a coil. Steam-table saturation pressures are normally supplied. Practise sketching each process on a skeleton chart before calculating, and keep track of per-kg-dry-air quantities.

Quick check

1. For unsaturated air, order DBT, WBT and DPT.
2. Air at 101.325 kPa has p_v = 1.6 kPa. Find ω.
3. What line does evaporative cooling follow on the chart?
4. Room sensible load 12 kW, latent 3 kW. Find SHF.
5. Two equal dry-air flows at 20 °C and 30 °C mix adiabatically. Approximate mixed DBT?

Answers: 1. DBT > WBT > DPT. 2. 0.622 × 1.6/99.725 ≈ 0.0100 kg/kg da. 3. A constant-WBT (nearly constant-enthalpy) line. 4. 0.80. 5. About 25 °C.