psychrometrics

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:

1. Envelope: q = U×A×(T_out - T_in) [walls, roof, windows]
2. Solar gain: q = SHGC × A × I_solar [windows]
3. Infiltration: q = ṁ_inf × (h_out - h_in) [latent + sensible]
4. 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].