11.3 Psychrometric Chart Analysis & Enthalpy
Key Takeaways
- The standard psychrometric chart graphically correlates seven moist air thermodynamic properties at standard sea-level barometric pressure (29.92 in. Hg / 14.696 psia), where identifying any two independent properties fixes the state point.
- On the psychrometric chart, dry-bulb lines run vertically, humidity ratio lines run horizontally to the right, dew point lines extend horizontally to the saturation curve, wet-bulb lines slope diagonally downward to the right, and enthalpy is read along the outer diagonal boundary scale.
- Specific enthalpy (h) measures total heat content in BTU per pound of dry air; total cooling capacity across an evaporator coil is determined using the universal air formula: Q_total = 4.5 * CFM * delta_h.
- The 4.5 air-side multiplier derives directly from standard air density: (60 min/hr) * (0.075 lb/cu ft) = (60 min/hr) / (13.33 cu ft/lb) = 4.5 lb-min / (cu ft-hr).
- Sensible Heat Ratio (SHR = Q_sensible / Q_total) defines the fraction of cooling capacity devoted to temperature drop versus moisture removal, typically ranging from 0.70 to 0.80 in residential comfort cooling.
11.3 Psychrometric Chart Analysis & Enthalpy
The Psychrometric Chart Architecture: The Seven Thermodynamic Properties
The psychrometric chart is the master graphical calculator of HVAC engineering. By plotting thermodynamic relationships at standard atmospheric pressure (29.92 in. Hg = 14.696 psia at sea level), the chart transforms complex partial pressure thermodynamics into an intuitive visual format. According to the Gibbs Phase Rule, knowing any two independent psychrometric properties fixes the state point of the air mixture, enabling instantaneous identification of the remaining five properties.
Psychrometric Chart Line Orientations:
+-------------------------------------------------------------------------+
| [ 100% Saturation Curve ] |
| . - ' ' ' |
| . - ' / / -------------------- |
| . - ' / / (Enthalpy Scale: BTU/lb) |
| . - ' / / |
| . - ' / / |
| . - ' / / (Wet-Bulb Lines: Diagonal) |
| . - ' / / |
| . - ' / / |
| [Dew Point Lines: Horizontal] / / |
| <---------------------------- / / -------------------> [Humidity Ratio |
| / / W: Grains/lb] |
| / / |
| / / (RH Curves: Sweeping) |
| / / |
| / / |
| | | | | | | | |
| | | | | | | | |
| [Dry-Bulb Lines: Vertical] v v v v v v |
| ----------------------------------------------------------------------- |
| 30°F 40°F 50°F 60°F 70°F 80°F 90°F |
+-------------------------------------------------------------------------+
The Seven Thermodynamic Properties of Moist Air
- Dry-Bulb Temperature (T_db): Represented by vertical lines originating from the horizontal axis along the bottom of the chart. Values increase from left to right, calibrated in degrees Fahrenheit (°F).
- Wet-Bulb Temperature (T_wb): Represented by diagonal lines sloping moderately downward from upper-left to lower-right, originating along the curved saturation boundary line.
- Relative Humidity (RH): Represented by curved lines sweeping upward from the lower-left to the upper-right. The uppermost bounding curve represents 100% Relative Humidity (the Saturation Curve). Additional curves represent 90%, 80%, down to 10% RH.
- Dew Point Temperature (T_dp): Represented by horizontal lines extending to the left edge of the chart to intersect the 100% saturation curve. When following any horizontal line left to the saturation curve, dry-bulb, wet-bulb, and dew point are identical.
- Humidity Ratio / Specific Humidity (W): Represented by horizontal lines extending across the chart to the vertical scale on the far right. Humidity ratio measures the absolute weight of water vapor per unit weight of dry air:
- Expressed either as pounds of moisture per pound of dry air (lb_w / lb_da) or grains of moisture per pound of dry air (gr/lb).
- Technicians must memorize the fundamental conversion factor: 7,000 grains = 1 pound of water.
- Specific Volume (v): Represented by steep diagonal lines extending across the chart from lower-right to upper-left (with steeper angles than wet-bulb lines). Values span from approximately 12.5 to 15.0 cu ft/lb of dry air. Standard dry air at 70°F and 29.92 in. Hg has a specific volume of 13.33 cu ft/lb (density ρ = 1 / 13.33 = 0.075 lb/cu ft).
- Enthalpy (h): Represented on an outer diagonal scale located beyond the saturation curve on the upper-left margin. Enthalpy measures the total heat energy contained in the moist air mixture per unit mass of dry air, calibrated in BTU per pound of dry air (BTU/lb_da). Enthalpy lines run nearly parallel to wet-bulb lines.
Enthalpy and the Universal Air-Side Heat Equations
Calculating the real-world thermal performance of heating and cooling coils requires converting volumetric airflow (CFM—cubic feet per minute) into mass flow rate (pounds of dry air per hour). In the Imperial engineering system, this transformation is accomplished using standard air multipliers.
Derivation of the Total Heat Multiplier (4.5)
To compute the total cooling or heating capacity across a coil, technicians use the master enthalpy equation:
Q_total = 4.5 * CFM * delta_h
Where:
- Q_total is total cooling capacity in BTU/hr.
- CFM is volumetric air volume flow rate in cubic feet per minute.
- delta_h is the enthalpy change between entering and leaving air (h_entering - h_leaving) in BTU/lb.
The constant 4.5 is derived directly from the physical density of standard air and unit conversions:
Mass Flow Rate (m_dot) = CFM * (60 min/hr) * rho_air
Substituting the density of standard air (rho = 0.075 lb/cu ft, corresponding to standard specific volume v = 13.33 cu ft/lb):
Constant = (60 min/hr) * (0.075 lb/cu ft) = (60 min/hr) / (13.33 cu ft/lb) = 4.5 lb-min / (cu ft-hr)
Derivation of the Sensible Heat Multiplier (1.08)
To calculate purely sensible heat transfer (temperature change with zero phase change):
Q_sensible = 1.08 * CFM * delta_T_db
Where specific heat capacity of standard air is c_p = 0.24 BTU/(lb-°F):
Constant = (60 min/hr) * (0.075 lb/cu ft) * 0.24 BTU/(lb-°F) = 4.5 * 0.24 = 1.08
Derivation of the Latent Heat Multiplier (0.68)
To calculate latent heat removal based on grains of moisture condensed:
Q_latent = 0.68 * CFM * delta_W_grains
Where the latent heat of vaporization is h_fg ≈ 1,060 BTU/lb, and 1 lb = 7,000 grains:
Constant = 4.5 lb-min / (cu ft-hr) * (1,060 BTU/lb / 7,000 grains/lb) = 4.5 * 0.1514 = 0.681 ≈ 0.68
Summary of Fundamental Air-Side Capacity Formulas:
=========================================================================
Total Capacity: Q_total = 4.50 * CFM * (h_in - h_out) [BTU/hr]
Sensible Capacity: Q_sensible = 1.08 * CFM * (T_db,in - T_db,out) [BTU/hr]
Latent Capacity: Q_latent = 0.68 * CFM * (W_gr,in - W_gr,out) [BTU/hr]
Heat Balance: Q_total = Q_sensible + Q_latent [BTU/hr]
Sensible Heat Ratio: SHR = Q_sensible / Q_total
=========================================================================
Worked Psychrometric Cooling Coil Problem: Step-by-Step Analysis
An HVAC service technician conducts a comprehensive cooling performance evaluation on a nominal 3-ton residential split system. An airflow traverse using an electronic anemometer establishes that the blower delivers 1,200 CFM (400 CFM/ton). The technician records the following psychrometric state points across the clean evaporator coil:
- Entering Return Air (State 1):
- Dry-Bulb Temperature (T_db1): 80.0°F
- Wet-Bulb Temperature (T_wb1): 67.0°F
- From Psychrometric Chart: Enthalpy h1 = 31.5 BTU/lb, Humidity Ratio W1 = 78 grains/lb, Relative Humidity ≈ 50%, Dew Point ≈ 60°F.
- Leaving Supply Air (State 2):
- Dry-Bulb Temperature (T_db2): 58.0°F
- Wet-Bulb Temperature (T_wb2): 54.0°F
- From Psychrometric Chart: Enthalpy h2 = 22.6 BTU/lb, Humidity Ratio W2 = 54 grains/lb, Relative Humidity ≈ 78%, Dew Point ≈ 51°F.
Step 1: Calculate Total Cooling Capacity (Q_total)
Calculate the enthalpy differential across the coil: delta_h = h1 - h2 = 31.5 BTU/lb - 22.6 BTU/lb = 8.9 BTU/lb
Apply the total heat formula: Q_total = 4.5 * CFM * delta_h = 4.5 * 1,200 * 8.9 Q_total = 5,400 * 8.9 = 48,060 BTU/hr
In nominal cooling tons (1 ton = 12,000 BTU/hr): Total Tons = 48,060 / 12,000 = 4.005 tons
Step 2: Calculate Sensible Cooling Capacity (Q_sensible)
Calculate the dry-bulb temperature drop across the coil: delta_T_db = T_db1 - T_db2 = 80.0°F - 58.0°F = 22.0°F
Apply the sensible heat formula: Q_sensible = 1.08 * CFM * delta_T_db = 1.08 * 1,200 * 22.0 Q_sensible = 1,296 * 22.0 = 28,512 BTU/hr
Step 3: Calculate Latent Cooling Capacity (Q_latent)
- Method A (Energy Balance): Q_latent = Q_total - Q_sensible = 48,060 BTU/hr - 28,512 BTU/hr = 19,548 BTU/hr
- Method B (Moisture Ratio Formula): delta_W = W1 - W2 = 78 grains/lb - 54 grains/lb = 24 grains/lb Q_latent = 0.68 * CFM * delta_W = 0.68 * 1,200 * 24 = 816 * 24 = 19,584 BTU/hr (Both methods agree within 0.18%, demonstrating mathematical and physical consistency!)
Step 4: Calculate Sensible Heat Ratio (SHR)
The Sensible Heat Ratio defines the proportion of total cooling capacity dedicated to dry-bulb temperature reduction:
SHR = Q_sensible / Q_total = 28,512 BTU/hr / 48,060 BTU/hr = 0.593 ≈ 0.59
An SHR of 0.59 indicates that 59% of the system's active cooling capacity is lowering air temperature, while 41% is actively removing water vapor from the airstream.
Step 5: Calculate Condensate Moisture Removal Rate
To determine the physical rate of liquid water draining from the evaporator coil: Moisture Rate (lb/hr) = Q_latent / h_fg = 19,548 BTU/hr / 1,060 BTU/lb = 18.44 pounds of water per hour
Converting to gallons per hour (where pure water weighs 8.34 lb/gal): Drain Rate (gal/hr) = 18.44 lb/hr / 8.34 lb/gal = 2.21 gallons per hour
This evaporator coil extracts over two gallons of liquid condensate from the indoor living space every operating hour, illustrating the massive magnitude of latent thermal energy in comfort cooling.
A technician performs an air-side capacity test on a commercial air handler. The system delivers 4,000 CFM of air. Return air enthalpy enters the cooling coil at 32.0 BTU/lb of dry air, and supply air enthalpy leaves the coil at 24.0 BTU/lb of dry air. Using the standard total heat formula, what is the total cooling capacity of the unit in BTU/hr and nominal tons?
In the universal total heat equation Q_total = 4.5 * CFM * delta_h, what physical air properties and unit conversions are multiplied together to derive the constant 4.5?
A psychrometric test on a 4-ton split heat pump operating at 1,600 CFM reveals that the sensible heat removed by the cooling coil is 33,600 BTU/hr and the latent heat removed is 14,400 BTU/hr. What is the Sensible Heat Ratio (SHR) of this operating system, and what does it indicate about coil performance?