| name | psychrometrics |
| description | HVAC psychrometrics — dry/wet bulb, dew point, humidity ratio, relative humidity, enthalpy, psychrometric chart, heating/cooling/dehumidification processes, cooling load. |
| metadata | {"priority":6,"promptSignals":{"phrases":["psychrometric","HVAC","humidity","dew point","wet bulb","dry bulb","cooling load","enthalpy","air conditioning"],"minScore":4}} |
Psychrometrics — Complete Skill
Key Properties
Dry bulb temperature (T_db): Normal air temperature (thermometer in shade)
Wet bulb temperature (T_wb): Temperature with evaporative cooling (wet wick)
Dew point (T_dp): Temperature at which moisture begins to condense
Relationship: T_db ≥ T_wb ≥ T_dp (equality only at 100% RH)
Humidity ratio (W): [kg water/kg dry air or lb water/lb dry air]
W = 0.622 × P_v/(P_atm - P_v)
P_v = partial pressure of water vapor
Relative humidity (φ):
φ = P_v/P_sat(T_db) × 100% = W/W_sat × 100%
P_sat from steam tables at T_db
Saturation humidity ratio:
W_sat = 0.622 × P_sat/(P - P_sat)
At 25°C, P_atm=101.325kPa: P_sat=3.169kPa → W_sat = 0.0201 kg/kg
Enthalpy of Moist Air
h = c_pa × T + W × (h_g)
h = 1.006×T + W×(2501 + 1.86×T) [kJ/kg dry air] (T in °C)
h = 0.240×T + W×(1061 + 0.444×T) [BTU/lb dry air] (T in °F)
At 25°C, φ=50%: W ≈ 0.0100, h = 1.006×25 + 0.010×(2501+1.86×25) = 25.15 + 25.47 = 50.6 kJ/kg
Psychrometric Chart Processes
Sensible heating/cooling (constant W):
ΔQ = ṁ_dry × c_pa × ΔT [kW]
c_pa = 1.006 kJ/(kg·K) for dry air, ≈ 1.02 kJ/(kg·K) for moist air
Humidification (constant T_db):
Water added: Δm_w = ṁ_dry × ΔW [kg/s]
Heat added (steam humidification): ΔQ = ṁ_dry × ΔW × h_steam
Cooling and dehumidification (pass through dew point):
If T_coil < T_dp → moisture condenses
Process: A (entering) → B (leaving coil at saturation)
Sensible heat removed: Q_s = ṁ_dry × c_pa × (T_A - T_B)
Latent heat removed: Q_L = ṁ_dry × (W_A - W_B) × h_fg [h_fg ≈ 2454 kJ/kg at 20°C]
Total: Q_total = ṁ_dry × (h_A - h_B)
Sensible heat ratio: SHR = Q_s/Q_total (typical comfort AC: SHR = 0.70-0.80)
Mixing two air streams (1 and 2, mix to M):
W_M = (ṁ₁W₁ + ṁ₂W₂)/(ṁ₁ + ṁ₂) [mass-weighted]
T_M = (ṁ₁T₁ + ṁ₂T₂)/(ṁ₁ + ṁ₂)
h_M = (ṁ₁h₁ + ṁ₂h₂)/(ṁ₁ + ṁ₂)
Evaporative cooling (adiabatic saturation — swamp cooler):
h₁ = h₂ (approximately, adiabatic process)
T_wb = constant along adiabatic saturation line
Effectiveness: ε = (T_in - T_out)/(T_in - T_wb,in) = 0.70-0.90 (indirect: 0.40-0.60)
Works well in dry climates (φ < 40%); ineffective in humid climates
Cooling Load Calculation (ASHRAE)
Design conditions: outdoor + indoor design temperatures
Cooling load components:
- Envelope: q = U×A×(T_out - T_in) [walls, roof, windows]
- Solar gain: q = SHGC × A × I_solar [windows]
- Infiltration: q = ṁ_inf × (h_out - h_in) [latent + sensible]
- Internal gains: people, lighting, equipment [W or BTU/hr]
People: 75W sensible + 55W latent (light office activity)
Lighting: 10-20 W/m² office
Equipment: 5-15 W/m² office
Total cooling load:
Q_total = Q_envelope + Q_solar + Q_infiltration + Q_internal
Air flow to handle sensible load:
ṁ_air = Q_sensible / (c_pa × (T_supply - T_room))
Typical supply: T_supply = 12-14°C (55-58°F), T_room = 24°C (75°F)
Common Values at Standard Conditions
Sea level: P_atm = 101.325 kPa = 14.696 psia
Comfort range: T_db = 22-26°C, φ = 40-60%
Standard air density: ρ ≈ 1.20 kg/m³ at 20°C, 50% RH
Specific volume: v ≈ 0.833 m³/kg dry air (std conditions)
Altitude correction (Denver, 1600m):
P_atm ≈ 83.5 kPa → air is less dense → need more volume flow for same mass flow
Output
Provide: W [kg/kg], φ [%], T_dp [°C], h [kJ/kg], process description on psychrometric chart, Q_sensible and Q_latent [kW or BTU/hr], required airflow [m³/s or CFM].
