6.3 Psychrometric Principles & Chart Analysis

6.3 Psychrometric Principles & Chart Analysis

Psychrometrics is the branch of thermodynamics dedicated to evaluating the physical, thermal, and moisture properties of atmospheric air mixtures. Atmospheric air is not a single elemental gas, but a binary mixture of dry air (principally 78% nitrogen and 21% oxygen by volume) and varying quantities of water vapor. Analyzing this mixture is essential for psychrometric load calculations, coil selection, and indoor humidity control.

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1. Dalton's Law of Partial Pressures & Atmospheric Air

Under Dalton's Law of Partial Pressures, the total barometric pressure exerted by moist air equals the sum of the independent partial pressures exerted by each individual gas constituent:

$P_{\text{total}} = P_{\text{dry air}} + P_{\text{water vapor}}$

Under standard sea-level conditions adopted by ASHRAE:

• Standard atmospheric pressure = $14.696\text{ psia} = 29.921\text{ in. Hg} = 101.325\text{ kPa}$.
• Standard air density ($\rho$) = $0.075\text{ lb/ft}^3$ at 70°F dry-bulb.
• Standard specific volume ($v$) = $1 / 0.075 = 13.33\text{ ft}^3/\text{lb}$.

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2. The Seven Interdependent Psychrometric Properties

The thermodynamic state of moist air is fully defined by seven physical properties:

1. Dry-Bulb Temperature ($DB$): The true thermodynamic temperature of the air mixture measured by a standard thermometer shielded from direct thermal radiation. On the standard psychrometric chart, dry-bulb temperature is plotted along the horizontal bottom axis, with lines of constant dry-bulb extending vertically straight upward.
2. Wet-Bulb Temperature ($WB$): The temperature registered by a thermometer whose sensing bulb is covered by a clean, water-saturated fabric wick and exposed to high-velocity airflow (at least 700 to 900 ft/min). Evaporation of water from the wick draws latent heat from the bulb, depressing the temperature. Wet-bulb temperature reflects the dynamic limit of direct evaporative cooling. On the psychrometric chart, constant wet-bulb lines run diagonally downward to the right.
3. Dew Point Temperature ($DP$): The temperature at which moist air reaches 100% saturation (holding the maximum possible quantity of water vapor for that temperature) and water vapor begins condensing into liquid droplets. Dew point depends strictly on the moisture mass present in the air ($W$), remaining unchanged during pure sensible heating or cooling. Traced horizontally to the 100% saturation curve.
4. Relative Humidity ($RH$): The dimensionless ratio (expressed as a percentage) of the actual partial pressure of water vapor in the air mixture ($P_v$) to the saturation water vapor pressure ($P_{vs}$) at the same dry-bulb temperature: $RH = \frac{P_v}{P_{vs}} \times 100\%$ Plotted on the chart as curved lines arching upward and to the right. The outermost curve is the 100% RH Saturation Line, where $DB = WB = DP$.
5. Humidity Ratio ($W$, Specific Humidity): The actual mass of water vapor held in the air per pound of dry air. Expressed in grains of moisture per pound of dry air ($\text{gr/lb}_{\text{da}}$) or pounds of water per pound of dry air ($\text{lb}w/\text{lb}{\text{da}}$). A fundamental conversion constant is: $7,000\text{ grains of moisture} = 1.0\text{ pound of liquid water}$ Plotted on the vertical scale along the right-hand margin of the psychrometric chart, with lines of constant humidity ratio running horizontally straight across.
6. Specific Volume ($v$): The space occupied per unit mass of dry air and its associated moisture, expressed in cubic feet per pound ($\text{ft}^3/\text{lb}_{\text{da}}$). Lines of constant volume run diagonally with a steep downward slope (~60°).
7. Enthalpy ($h$): The total thermal energy content of moist air per unit mass of dry air, measured in BTU per pound ($\text{BTU/lb}_{\text{da}}$) above a reference baseline of 0°F dry air and 32°F liquid water. Enthalpy lines run diagonally downward to the right, nearly parallel to wet-bulb temperature lines.

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3. The Two-Property Rule & State Point Plotting

A foundational axiom of psychrometric analysis is the Two-Property Rule:

Core Exam Rule: The thermodynamic state point of moist air is completely fixed by identifying any two independent psychrometric properties. Once this intersection point is located on the chart, the remaining five properties can be read directly without further calculation.

Worked Example: Locating an Indoor Design State Point

Consider a standard ACCA Manual J indoor summer comfort design condition: 75°F Dry-Bulb ($DB$) and 50% Relative Humidity ($RH$).

1. Locate 75°F along the horizontal bottom axis; follow the vertical line upward.
2. Locate the curved 50% relative humidity line; identify the intersection.
3. Read the remaining five properties at this exact state point:
   • Wet-Bulb Temperature ($WB$): Follow the diagonal wet-bulb line up to the saturation curve = 62.5°F.
   • Dew Point Temperature ($DP$): Follow a horizontal line left to the 100% saturation curve = 55.1°F.
   • Humidity Ratio ($W$): Follow the horizontal line right to the vertical moisture axis = 65.0 grains/lb ($0.00928\text{ lb}w/\text{lb}{\text{da}}$).
   • Specific Volume ($v$): Interpolate between the steep volume lines = 13.68 ft³/lb.
   • Enthalpy ($h$): Follow the diagonal enthalpy scale = 28.1 BTU/lb.

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4. Tracing Fundamental HVAC Thermodynamic Processes

Every air conditioning, heating, ventilation, or dehumidification process traces a distinct vector path across the psychrometric chart:

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5. Sensible Heat Ratio (SHR) & Coil Load Matching

In comfort air conditioning, cooling coils must simultaneously remove sensible heat (lowering space dry-bulb temperature) and latent heat (condensing moisture vapor):

• Total Cooling Load ($Q_t$): The sum of sensible and latent cooling: $Q_t = Q_s + Q_l$
• Sensible Heat Ratio ($SHR$): The fraction of total cooling capacity dedicated to sensible cooling: $SHR = \frac{Q_s}{Q_t} = \frac{Q_s}{Q_s + Q_l}$

Field Significance of SHR in Maryland Climate

The Sensible Heat Ratio determines the slope of the coil condition line on the psychrometric chart connecting entering air to the coil Apparatus Dew Point (ADP).

• High-Sensible Applications (SHR 0.85–0.95): Data centers, arid desert climates (e.g., Phoenix, AZ), where sensible gains dominate and moisture removal is negligible.
• Load-dependent SHR: A dwelling or commercial space can have a higher or lower SHR depending on envelope, people, ventilation, and moisture sources. Calculate it from the project loads.
• High latent loads: Restaurants, gyms, auditoriums, and humid outdoor-air systems often have lower SHR, but no occupancy name fixes a universal range.

Contractor Warning: If an air conditioner with an SHR of 0.85 is installed in a Maryland home requiring an SHR of 0.72, the unit will satisfy the thermostat (sensible cooling) very quickly and cycle off before extracting sufficient latent moisture. This results in an uncomfortably damp, clammy indoor environment ($RH > 60%$), fostering dust mites, microbial growth, and indoor air quality complaints.