7.1 The Psychrometric Chart: Dry-Bulb, Wet-Bulb, Relative Humidity, Enthalpy & Dew Point

7.1 The Psychrometric Chart: Dry-Bulb, Wet-Bulb, Relative Humidity, Enthalpy & Dew Point

Psychrometrics is the branch of thermodynamic engineering that studies the physical and thermal properties of moist air—a binary mixture of dry atmospheric gas and water vapor. In air conditioning and refrigeration design, air is both the convective transport medium and the thermal heat sink.

Every comfort cooling, heating, dehumidification, and evaporative cooling process involves thermodynamic transformations that can be precisely mapped, analyzed, and quantified using the Psychrometric Chart. For HVAC contractors in Arizona's low-humidity desert climate, mastering psychrometric properties is essential for sizing equipment, calculating air-side capacities, diagnosing airflow deficiencies, and preventing catastrophic coil freezing or capacity derating.

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1. Standard Atmospheric Baseline & Chart Geometry

The standard psychrometric chart developed by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) is constructed for a standard sea-level barometric pressure of 29.921 in. Hg (14.696 psia / 101.325 kPa).

Under these standard conditions, air exhibits a standard density of:

ρ_air = 0.075 lb/cu ft (Specific volume v = 1 / ρ = 13.33 cu ft/lb dry air at 70°F)

                    PSYCHROMETRIC CHART GEOMETRY & COORDINATE AXES

      Enthalpy Scale (h)
      [BTU/lb dry air]            Saturation Curve (100% Relative Humidity)
             /                           /
            /                           /
           /                           /       Constant Wet-Bulb (T_wb)
          ┌───────────────────────────┐       & Enthalpy (h) Lines (Diagonal)
          │                           │      /
          │                           │     /   Relative Humidity Curves (% RH)
          │                           │    /   /
          │                           │   /   /    Constant Specific Volume (v)
          │                           │  /   /     [cu ft / lb] (Steep Diagonal)
          │                           │ /   /     /
          │                           │/   /     /     Humidity Ratio Scale (W)
          └───────────────────────────┴───┴─────┴──►  [Grains of moisture / lb]
           30°F    50°F    70°F    90°F   110°F       (Right-Hand Vertical Axis)
           ◄──────── Dry-Bulb Temperature (T_db) ────────►
                    (Horizontal Bottom Axis)

The State Point Rule

According to Gibbs' Phase Rule for a two-component, single-phase mixture, establishing any two independent psychrometric properties (e.g., dry-bulb temperature and wet-bulb temperature, or dry-bulb temperature and relative humidity) definitively fixes the thermodynamic state point. Once this state point is plotted, all remaining five properties can be read directly from the intersecting coordinate lines.

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2. The Seven Fundamental Psychrometric Properties

3. Sling Psychrometer Mechanics & Wet-Bulb Depression

A sling psychrometer consists of two matched mercury or spirit-filled thermometers mounted side-by-side on a swiveling frame: a dry-bulb thermometer that measures ambient air temperature, and a wet-bulb thermometer enclosed in a wetted, clean cotton wick.

                      SLING PSYCHROMETER THERMODYNAMICS

         Dry Thermometer                       Wetted Wick Thermometer
       ┌─────────────────┐                       ┌─────────────────┐
       │ Reads: T_db     │                       │ Reads: T_wb     │
       │ (Sensible Temp) │                       │ (Evaporative)   │
       └────────┬────────┘                       └────────┬────────┘
                │                                         │
                ▼                                         ▼
         80°F Ambient Air                          60°F Depressed Temp
                │                                         │
                └───────────────────┬─────────────────────┘
                                    │
                                    ▼
                  Wet-Bulb Depression = T_db - T_wb
                  80°F - 60°F = 20°F Depression
                  (Indicates very dry, low-humidity air)

Wet-Bulb Depression Mechanics

1. Aspiration & Evaporation: When whirled through the air at an airspeed of at least 900 FPM (10 to 15 ft/s), water evaporates from the wetted wick into the passing air stream.

2. Latent Heat Extraction: Evaporation requires latent heat of vaporization (h_fg ≈ 1,061 BTU/lb at room temperature), which is extracted directly from the thermometer bulb, causing its temperature to drop below the ambient dry-bulb temperature.

3. Wet-Bulb Depression Definition: The mathematical difference between the dry-bulb and wet-bulb temperatures is defined as the Wet-Bulb Depression:

   Wet-Bulb Depression = T_DB - T_WB

4. Saturation Dynamics:

   • In bone-dry desert air (0% RH), water evaporates rapidly, yielding a large wet-bulb depression (25°F to 35°F).
   • In fully saturated air (100% RH), no net evaporation can occur (p_w = p_ws), meaning the wet-bulb depression is zero. At 100% RH:

   T_DB = T_WB = T_DP

[!NOTE] Diagnostic Protocol: Always use distilled or deionized water on the psychrometer wick. Mineral salts present in tap water deposit on the wick fibers upon evaporation, creating an insulating crust that retards moisture transfer and causes falsely high wet-bulb readings.

4. Derivations of the Three Fundamental HVAC Air Formulas

In forced-air HVAC systems, calculating the capacity of heating coils, cooling coils, and heat pumps requires converting volumetric airflow (measured in Cubic Feet per Minute, CFM) and thermodynamic property changes into heat transfer rates (measured in BTU/hr).

All three universal HVAC air equations originate from the fundamental mass flow rate equation for air under standard atmospheric density:

m_dot_air = CFM × (60 min/hr) × ρ_air = CFM × 60 × 0.075 lb/cu ft = 4.5 × CFM [lb dry air / hr]

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1. Sensible Heat Equation (Q_s)

Sensible heat exchange changes the dry-bulb temperature of the air without altering its absolute moisture content (W remains constant):

Q_s = m_dot_air × c_p × ΔT_DB

Where c_p is the specific heat capacity of dry air (0.24 BTU / (lb·°F)):

Q_s = (4.5 × CFM) × 0.24 × ΔT_DB

Q_s = 1.08 × CFM × ΔT_DB [BTU/hr]

• Constant 1.08 = 60 min/hr × 0.075 lb/cu ft × 0.24 BTU/lb·°F
• ΔT_DB = |T_DB,entering - T_DB,leaving| (°F)

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2. Latent Heat Equation (Q_l)

Latent heat exchange changes the moisture content of the air through evaporation or condensation without changing the dry-bulb temperature:

Q_l = m_dot_air × h_fg × ΔW_lb

Where:

• h_fg = Latent heat of vaporization of water at room temperature (≈ 1,061 BTU/lb)
• ΔW_grains = Moisture change in grains of water per pound of dry air
• Conversion factor: 1.0 lb H2O = 7,000 grains

Q_l = (4.5 × CFM) × 1,061 BTU/lb × (ΔW_grains / 7,000 grains/lb)

Q_l = ((4.5 × 1,061) / 7,000) × CFM × ΔW_grains = 0.682 × CFM × ΔW_grains

Q_l = 0.68 × CFM × ΔW_grains [BTU/hr]

• Constant 0.68 = (60 × 0.075 × 1,061) / 7,000
• ΔW_grains = |W_entering - W_leaving| (grains/lb dry air)

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3. Total Heat Equation (Q_t)

Total heat exchange accounts for the combined sensible and latent thermal energy transferred across the heat exchanger using specific enthalpy (h in BTU/lb dry air):

Q_t = m_dot_air × Δh

Q_t = (4.5 × CFM) × Δh

Q_t = 4.5 × CFM × Δh [BTU/hr]

• Constant 4.5 = 60 min/hr × 0.075 lb/cu ft
• Δh = |h_entering - h_leaving| (BTU/lb dry air)
• Thermodynamic balance verification: Q_t = Q_s + Q_l

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4. Sensible Heat Ratio (SHR)

The Sensible Heat Ratio (SHR) represents the fraction of total cooling capacity devoted exclusively to lowering sensible dry-bulb temperature:

SHR = Q_s / Q_t = Q_s / (Q_s + Q_l)

                      SENSIBLE HEAT RATIOS BY REGION

     Humid Southeast / Coastal (SHR ≈ 0.65 - 0.75)   Arizona Desert (SHR ≈ 0.85 - 0.95+)
     ┌───────────────────┬──────────────────┐        ┌───────────────────────────────┬───────┐
     │ Sensible (70%)    │ Latent (30%)     │        │ Sensible (90%)                │Lat(10)│
     └───────────────────┴──────────────────┘        └───────────────────────────────┴───────┘

5. Comprehensive Worked Engineering Calculation

Field Scenario

A technician performs a commissioning test on a nominal 3-ton (36,000 BTU/hr) split-system air conditioner in a Phoenix home. Airflow is verified at 1,200 CFM. Psychrometric measurements across the evaporator coil yield the following properties:

Entering Return Air Conditions:

• T_DB,entering = 80.0°F
• T_WB,entering = 67.0°F
• Psychrometric chart lookup: Enthalpy h_entering = 31.6 BTU/lb, Moisture W_entering = 78.0 grains/lb

Leaving Supply Air Conditions:

• T_DB,leaving = 57.0°F
• T_WB,leaving = 55.0°F
• Psychrometric chart lookup: Enthalpy h_leaving = 23.2 BTU/lb, Moisture W_leaving = 61.0 grains/lb

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Step-by-Step Mathematical Solution

1. Calculate Sensible Heat Removal (Q_s):

   • ΔT_DB = 80.0°F - 57.0°F = 23.0°F
   • Q_s = 1.08 × 1,200 CFM × 23.0°F = 1.08 × 27,600 = 29,808 BTU/hr

2. Calculate Latent Heat Removal (Q_l):

   • ΔW = 78.0 gr/lb - 61.0 gr/lb = 17.0 grains/lb
   • Q_l = 0.68 × 1,200 CFM × 17.0 gr/lb = 0.68 × 20,400 = 13,872 BTU/hr

3. Calculate Total Heat Removal using Enthalpy (Q_t):

   • Δh = 31.6 BTU/lb - 23.2 BTU/lb = 8.4 BTU/lb
   • Q_t = 4.5 × 1,200 CFM × 8.4 BTU/lb = 4.5 × 10,080 = 45,360 BTU/hr

4. Verify Energy Summation & Calculate System SHR:

   • Q_s+l = Q_s + Q_l = 29,808 + 13,872 = 43,680 BTU/hr
   • (Note: Minor variance between Q_t via enthalpy and Q_s+Q_l is due to standard rounding of the 1.08, 0.68, and 4.5 constants and chart interpolation).
   • SHR = Q_s / Q_t = 29,808 BTU/hr / 43,680 BTU/hr = 0.682 (68.2% Sensible)

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6. High-Altitude and Density Deration

[!WARNING] Arizona Exam Trap — Altitude Air Density Adjustments: Standard constants (1.08, 0.68, 4.5) assume sea-level air density (ρ = 0.075 lb/cu ft). In Northern Arizona (e.g., Flagstaff at elevation 7,000 ft, barometric pressure ≈ 23.0 in. Hg, density ρ ≈ 0.060 lb/cu ft), air is 20% less dense.

• The sensible constant drops from 1.08 to 0.86 (60 × 0.060 × 0.24 = 0.864).
• The total constant drops from 4.50 to 3.60 (60 × 0.060 = 3.60).
• Failure to derate density constants in high-elevation Arizona designs leads to calculated capacities being overpredicted by 20%.