Psychrometric Properties

Psychrometric properties define the thermodynamic state of moist air. Understanding these properties and their interrelationships enables accurate analysis of HVAC systems and processes.

Dry-Bulb Temperature (DBT)

Dry-bulb temperature represents the actual air temperature measured by a standard thermometer shielded from radiation and moisture. It indicates the sensible heat content of air.

Measurement: Standard mercury or digital thermometer with dry sensing element, protected from direct solar radiation and precipitation.

Physical Significance: DBT directly relates to the kinetic energy of air molecules. Higher temperatures indicate greater molecular motion and higher sensible heat content.

The sensible heat content of dry air:

$$q_s = m c_p (T_2 - T_1)$$

where $c_p = 1.006$ kJ/(kg·K) at 20°C.

HVAC Applications:

• Space temperature control setpoints
• Outdoor design temperatures for load calculations
• Energy balance calculations
• Thermal comfort assessment (operative temperature)

Typical Ranges:

• Comfort cooling: 22-26°C (72-78°F)
• Comfort heating: 20-22°C (68-72°F)
• Outdoor design: -30°C to +45°C (-22°F to +113°F) depending on climate

Wet-Bulb Temperature (WBT)

Wet-bulb temperature is the lowest temperature achievable through evaporative cooling at constant pressure. It represents the temperature indicated by a thermometer with wetted wick in moving air.

Measurement Principle: As water evaporates from the wick, it absorbs latent heat from the air, cooling the thermometer. Equilibrium is reached when heat transfer to the wick equals evaporative cooling.

Theoretical Foundation: Wet-bulb temperature approximates the adiabatic saturation temperature for air-water vapor mixtures:

$$h_1 + (W_{sat} - W_1) h_f = h_{sat}$$

where $h_f$ is enthalpy of liquid water at wet-bulb temperature.

Relationship to Dry-Bulb:

$$T_{wb} \leq T_{db}$$

Equality occurs only at saturation (100% RH). The wet-bulb depression $(T_{db} - T_{wb})$ indicates moisture content and evaporative cooling potential.

Psychrometric Equation: Relating wet-bulb to other properties:

$$W = W_{sat}(T_{wb}) - \frac{(T_{db} - T_{wb})(c_p + W_{sat} c_{pw})}{h_{fg}}$$

where $h_{fg}$ is latent heat of vaporization.

HVAC Applications:

• Cooling tower design and performance
• Evaporative cooling system analysis
• Enthalpy determination on psychrometric charts
• Outdoor air condition characterization

Practical Measurement:

• Sling psychrometer: Manual instrument with two thermometers
• Aspirated psychrometer: Motorized air movement over wet bulb
• Digital psychrometers: Electronic sensing with built-in ventilation

Dewpoint Temperature (Td)

Dewpoint temperature is the temperature at which air becomes saturated (100% RH) when cooled at constant pressure and humidity ratio. At dewpoint, water vapor begins condensing.

Fundamental Relationship:

$$p_v = p_{ws}(T_d)$$

The water vapor pressure equals saturation pressure at the dewpoint temperature.

Calculation from Humidity Ratio:

$$T_d = T_{sat}\left(\frac{p_{atm} W}{0.622 + W}\right)$$

Physical Significance: Dewpoint indicates absolute moisture content independent of temperature. Unlike relative humidity, dewpoint changes only when moisture is added or removed.

Condensation Analysis: Condensation occurs on any surface below dewpoint temperature:

$$\dot{m}{condensate} = \dot{m}{air}(W_1 - W_2)$$

where $W_2 = W_{sat}(T_{surface})$

HVAC Applications:

• Determining when condensation occurs on windows, pipes, ducts
• Mold growth prevention (maintain surfaces above dewpoint)
• Dehumidification requirements
• Absolute humidity measurement

Typical Values:

• Dry climates: -10°C to +5°C (14°F to 41°F)
• Moderate climates: +5°C to +15°C (41°F to 59°F)
• Humid climates: +15°C to +25°C (59°F to 77°F)

Dewpoint Depression: The difference $(T_{db} - T_d)$ correlates inversely with relative humidity:

• Small depression: High RH
• Large depression: Low RH

Relative Humidity (φ or RH)

Relative humidity is the ratio of actual water vapor pressure to saturation pressure at the same dry-bulb temperature:

$$\phi = \frac{p_v}{p_{ws}(T_{db})} \times 100%$$

Alternatively expressed as ratio of humidity ratios:

$$\phi \approx \frac{W}{W_{sat}(T_{db})} \times 100%$$

Temperature Dependency: Unlike humidity ratio and dewpoint, relative humidity varies with temperature even when absolute moisture content remains constant.

Example: Air at 20°C, 50% RH heated to 30°C:

• Humidity ratio: Unchanged
• Dewpoint: Unchanged
• Relative humidity: Drops to approximately 25%

Comfort Implications: ASHRAE Standard 55 recommends:

• Winter: 30-60% RH (prevents static electricity, dry skin)
• Summer: 40-60% RH (prevents excessive perspiration)

Material Effects:

• Wood movement: ±1% dimension change per 5% RH change
• Paper dimensional stability: Critical at 40-60% RH
• Electronics reliability: Optimal 40-50% RH

Limitations: RH alone doesn’t indicate moisture content. Air at 10°C, 100% RH contains less moisture than air at 30°C, 50% RH.

Humidity Ratio (W)

Humidity ratio (mixing ratio, moisture content) is the mass of water vapor per unit mass of dry air:

$$W = \frac{m_{vapor}}{m_{dry,air}} \text{ kg/kg or lb/lb}$$

Calculation from Vapor Pressure:

$$W = 0.622 \frac{p_v}{p_{atm} - p_v}$$

The constant 0.622 derives from molecular weight ratio:

$$0.622 = \frac{M_{H_2O}}{M_{air}} = \frac{18.015}{28.965}$$

Range of Values:

• Minimum: 0 kg/kg (perfectly dry air, theoretical)
• Cold/dry: 0.001-0.003 kg/kg
• Moderate: 0.005-0.010 kg/kg
• Warm/humid: 0.015-0.025 kg/kg
• Maximum at 35°C: ~0.036 kg/kg at saturation

Imperial Units: Often expressed in grains per pound:

$$W_{gr/lb} = W_{kg/kg} \times 7000$$

Latent Heat Calculations: Humidity ratio directly determines latent cooling or heating:

$$q_l = \dot{m}{air} \times (W_1 - W_2) \times h{fg}$$

where $h_{fg} \approx 2501$ kJ/kg at 0°C.

Conservation in Processes:

• Sensible heating/cooling: W constant
• Humidification: W increases
• Dehumidification: W decreases
• Adiabatic mixing: $W_{mix} = \frac{m_1 W_1 + m_2 W_2}{m_1 + m_2}$

Specific Enthalpy (h)

Specific enthalpy represents total heat content per unit mass of dry air, combining sensible and latent components:

$$h = h_{dry,air} + W \times h_{water,vapor}$$

Expanded Form:

$$h = c_p T + W(h_{fg,0} + c_{pw} T)$$

where:

• $c_p$ = specific heat of dry air = 1.006 kJ/(kg·K)
• $h_{fg,0}$ = latent heat at 0°C = 2501 kJ/kg
• $c_{pw}$ = specific heat of water vapor = 1.86 kJ/(kg·K)

Numerical Equation (SI):

$$h = 1.006 T + W(2501 + 1.86 T) \text{ kJ/kg}$$

Numerical Equation (IP):

$$h = 0.24 T + W(1061 + 0.444 T) \text{ Btu/lb}$$

Energy Balance Applications: Enthalpy enables direct energy calculations:

$$\dot{Q} = \dot{m}_{air}(h_1 - h_2)$$

Process Analysis:

• Sensible heating: Enthalpy increases, slope = $c_p + W c_{pw}$
• Humidification with steam: Enthalpy increases, slope = $\Delta h / \Delta W$
• Adiabatic saturation: Nearly constant enthalpy
• Cooling and dehumidification: Enthalpy decreases

Typical Values:

• Cold air: 0-20 kJ/kg (0-8 Btu/lb)
• Moderate: 30-50 kJ/kg (13-21 Btu/lb)
• Warm/humid: 60-100 kJ/kg (26-43 Btu/lb)

Specific Volume (v)

Specific volume is the volume occupied by one unit mass of dry air plus its associated water vapor:

$$v = \frac{V_{total}}{m_{dry,air}}$$

Ideal Gas Relationship:

$$v = \frac{R_a T}{p_a}$$

where $R_a = 287.055$ J/(kg·K) for dry air.

Accounting for Vapor Pressure:

$$v = \frac{R_a T}{p_{atm} - p_v}$$

Numerical Approximation (SI):

$$v \approx \frac{287.055 T}{(p_{atm} - p_v) \times 1000} \text{ m}^3\text{/kg}$$

For standard pressure (101.325 kPa) and moderate humidity:

$$v \approx 0.00283 T \text{ m}^3\text{/kg (T in K)}$$

Volume Flow Conversion: Essential for relating mass and volumetric flow rates:

$$\dot{V} = \dot{m} \times v$$

$$\dot{m} = \frac{\dot{V}}{v}$$

Example: Air at 24°C (297 K), standard pressure:

$$v \approx 0.00283 \times 297 = 0.840 \text{ m}^3\text{/kg}$$

For 1000 m³/h volumetric flow:

$$\dot{m} = \frac{1000}{0.840} = 1190 \text{ kg/h}$$

Temperature and Pressure Effects:

$$\frac{v_2}{v_1} = \frac{T_2}{T_1} \times \frac{p_1}{p_2}$$

Typical Values:

• 0°C: 0.78 m³/kg (12.5 ft³/lb)
• 20°C: 0.84 m³/kg (13.5 ft³/lb)
• 40°C: 0.90 m³/kg (14.4 ft³/lb)

Property Interdependencies

Any two independent properties completely define the state of moist air. Common combinations:

Known: DBT + RH

1. Calculate $p_{ws}(T_{db})$ from saturation tables
2. Calculate $p_v = \phi \times p_{ws} / 100$
3. Calculate $W = 0.622 p_v / (p_{atm} - p_v)$
4. Calculate $T_d$ from $p_v = p_{ws}(T_d)$
5. Calculate $h$ and $v$ from formulas

Known: DBT + WBT

1. Calculate $W_{sat}(T_{wb})$ from saturation conditions
2. Use psychrometric equation to find W
3. Calculate $p_v$ from W
4. Calculate RH, dewpoint, enthalpy, specific volume

Known: DBT + Dewpoint

1. Calculate $p_v = p_{ws}(T_d)$
2. Calculate W from vapor pressure
3. Calculate RH, enthalpy, specific volume
4. WBT requires iterative solution

Measurement Instruments

Dry-Bulb:

• Mercury/alcohol thermometers
• Thermocouples, RTDs, thermistors
• Infrared sensors (surface temperature)

Wet-Bulb:

• Sling psychrometer (manual)
• Aspirated psychrometer (motorized)
• Electronic wet-bulb sensors

Dewpoint:

• Chilled mirror hygrometers (most accurate)
• Capacitive polymer sensors
• Calculated from RH and DBT

Relative Humidity:

• Capacitive polymer sensors
• Resistive sensors
• Hair hygrometers (mechanical)

Humidity Ratio:

• Calculated from other properties
• Direct measurement rare

Summary Table

Understanding these seven fundamental properties enables complete characterization of moist air conditions and accurate analysis of all HVAC processes.