Psychrometric Processes and Air Conditioning Calculations

Introduction

In August 2019, the Louvre Abu Dhabi's art conservation team discovered moisture condensation forming on priceless artifacts despite the museum's $50 million HVAC system operating at full capacity. The problem wasn't equipment failure—it was a psychrometric miscalculation. Engineers had designed for 22°C at 50% RH (dew point 11.3°C), but the building's massive dome created microclimates where air stratified to 18°C at floor level. When warm, humid air from the upper zones contacted the cooler surfaces, condensation occurred even though the room "met spec." The $3.2 million remediation required complete recalculation of air distribution using proper psychrometric analysis—a cost that would have been avoided if the original design had properly plotted air states throughout the space.

Psychrometrics is the study of the physical and thermodynamic properties of moist air and the processes that change these properties, forming the foundation of HVAC system design and air conditioning calculations.

Psychrometric charts graphically represent moist air properties at constant pressure, showing relationships between temperature, humidity, and energy through seven key properties: dry bulb temperature, humidity ratio, relative humidity, wet bulb temperature, enthalpy, specific volume, and dew point temperature.

Why This Analysis Matters

Accurate psychrometric analysis is crucial for:

• Equipment Sizing: Determining the sensible and latent cooling loads for proper air conditioning equipment selection.
• Comfort Control: Maintaining indoor temperature and humidity within ASHRAE Standard 55 comfort zone requirements.
• Condensation Prevention: Identifying dew point conditions to prevent moisture damage on cold surfaces.
• Energy Optimization: Designing efficient air handling processes that minimize heating and cooling energy consumption.

The Fundamental Challenge

The primary challenge in psychrometric analysis lies in understanding the interdependence of moist air properties and how they change during HVAC processes. Cooling, heating, humidification, dehumidification, and mixing processes all follow specific paths on the psychrometric chart, each with distinct energy and moisture implications. Distinguishing between sensible heat (temperature change) and latent heat (moisture change) is essential for proper equipment selection—air conditioning systems must handle both components, and the sensible heat ratio (SHR) determines equipment performance. Additionally, altitude affects psychrometric calculations as air density and saturation properties change with atmospheric pressure.

What You'll Learn

In this comprehensive guide, you will learn:

• How to read psychrometric charts and identify the seven key air properties.
• Formulas for calculating humidity ratio, enthalpy, dew point, and wet bulb temperature.
• Analysis methods for cooling, heating, humidification, and dehumidification processes.
• Air mixing calculations for ventilation and economizer design.
• Step-by-step examples applying ASHRAE Fundamentals psychrometric methods.

Quick Answer: How to Read Psychrometric Charts

Psychrometric charts graphically represent moist air properties at constant pressure, showing relationships between temperature, humidity, and energy.

Key Properties on Chart

Worked Example

Key Formula

Reference Table

Key Standards

Air Properties

Dry Bulb Temperature (DB)

The dry bulb temp is the thermal reading of airflow measured with a standard thermometer. It's the most common heat measurement in HVAC.

Typical Design Values:

• Summer Design: 35-40°C (outdoor), 24-26°C (indoor)
• Winter Design: -5 to 5°C (outdoor), 20-22°C (indoor)

Wet Bulb Temperature (WB)

The wet bulb thermal value is measured using a thermometer with a wet wick around the bulb. As atmosphere passes over the wick, water evaporates, AC the bulb.

Key Points:

• Wet bulb is always $\leq$ dry bulb degree
• When RH = 100%, wet bulb = dry bulb
• Lower wet bulb indicates drier ventilation air
• Used to determine humidity ratio and enthalpy

Relative Humidity (RH)

Relative humidity is the ratio of actual water vapor power to saturation vapor force at the same heat level.

Formula:

Where:

• RH = Relative humidity (%)
• $P_v$ = Actual vapor stress (kPa)
• $P_{\text{ws}}$ = Saturation vapor load at dry bulb temp (kPa)

Typical Values:

• Comfort Zone: 40-60%
• Summer Indoor: 50-60%
• Winter Indoor: 30-50%

Humidity Ratio (W)

The humidity ratio is the mass of water vapor per unit mass of dry fresh air.

Formula:

Where:

• W = Humidity ratio (kg/kg dry air supply)
• $P_v$ = Vapor pressure value (kPa)
• P = Total system pressure (kPa)
• 0.622 = Ratio of molecular weights (water/dry airflow)

Dew Point Temperature

The dew point is the thermal reading at which water vapor begins to condense when atmosphere is cooled at constant power and humidity ratio.

Key Points:

• Dew point $\leq$ dry bulb heat
• When dew point = dry bulb, RH = 100%
• Condensation occurs when surface thermal value < dew point
• Critical for preventing moisture problems

Enthalpy (h)

Enthalpy represents the total heat content of moist ventilation air, including sensible and latent heat.

Formula:

Where:

• h = Enthalpy (kJ/kg dry fresh air)
• $c_{\text{pa}}$ = Specific heat of dry air supply (1.006 kJ/kg·K)
• T = Dry bulb degree (°C)
• W = Humidity ratio (kg/kg dry airflow)
• $h_{\text{fg},0}$ = Latent heat of vaporization at 0°C (2501 kJ/kg)
• $c_{\text{pv}}$ = Specific heat of water vapor (1.86 kJ/kg·K)

Typical Values:

• Outdoor Summer: 85-100 kJ/kg
• Indoor Comfort: 45-60 kJ/kg
• Outdoor Winter: 5-20 kJ/kg

Specific Volume (v)

Specific volume is the volume occupied by 1 kg of dry atmosphere plus associated water vapor.

Formula:

Where:

• v = Specific volume (m³/kg dry ventilation air)- $R_a$ = Gas constant for dry fresh air (0.287 kJ/kg·K)

• T = Absolute heat level (K)

• P = Total force (kPa)

• $P_v$ = Vapor stress (kPa)

Psychrometric Chart

Chart Layout

The psychrometric chart is a graphical representation of psychrometric properties. Key features:

1. Dry Bulb Temp: Horizontal axis (bottom)
2. Humidity Ratio: Vertical axis (right)
3. Relative Humidity: Curved lines from bottom-left to top-right
4. Wet Bulb Thermal reading: Diagonal lines
5. Enthalpy: Diagonal lines (often parallel to wet bulb)
6. Specific Volume: Diagonal lines
7. Dew Point: Horizontal line from humidity ratio to saturation curve

Using the Chart

To find properties from DB and WB:

1. Locate dry bulb heat on horizontal axis
2. Follow vertical line up to wet bulb thermal value diagonal
3. Read humidity ratio from vertical axis
4. Read relative humidity from curved lines
5. Read enthalpy from diagonal lines
6. Follow horizontal line to saturation curve for dew point

To find properties from DB and RH:

1. Locate dry bulb degree on horizontal axis
2. Follow vertical line up to relative humidity curve
3. Read humidity ratio from vertical axis
4. Follow diagonal line to find wet bulb heat level
5. Read enthalpy from diagonal lines

Core Formulas

Saturation Vapor Pressure

ASHRAE Equation 5 (Chapter 1, Fundamentals 2021):

Where:

• $P_{\text{ws}}$ = Saturation vapor load (Pa)
• T = Absolute temp (K)
• $C_8 to C_{\text{13}}$ = Constants from ASHRAE

For temperatures 0-100°C:

• $C_8$ = -5.8002206E+03
• $C_9$ = 1.3914993E+00
• $C_{\text{10}}$ = -4.8640239E-02
• $C_{\text{11}}$ = 4.1764768E-05
• $C_{\text{12}}$ = -1.4452093E-08
• $C_{\text{13}}$ = 6.5459673E+00

Vapor Pressure from Relative Humidity

Humidity Ratio from Vapor Pressure

Wet Bulb Temperature (Iterative)

Wet bulb thermal reading is found by solving:

This requires iteration as $W_{\text{wb}}$ depends on $T_{\text{wb}}$.

Dew Point Temperature

Dew point is found by solving for the heat at which $P_{\text{ws}} = P_v$:

Psychrometric Processes

1. Sensible Cooling

Process: Refrigeration without dehumidification (constant humidity ratio)

Conditions:

• Surface thermal value > dew point
• No condensation occurs
• Humidity ratio remains constant

Energy Calculation:

Where:

• $Q_{\text{sensible}}$ = Sensible heat transfer (kW)
• $\dot{m}_a$ = Mass flow rate of dry air supply (kg/s)
• $T_1, T_2$ = Initial and final temperatures (°C)

Application: Chilling coils in dry climates

2. Sensible Heating

Process: Heating without humidification (constant humidity ratio)

Conditions:

• Heat added without moisture addition
• Humidity ratio remains constant
• Relative humidity decreases

Energy Calculation:

Application: Space heaters, electric heaters

3. Humidification

Process: Adding moisture to airflow (constant dry bulb or adiabatic)

Adiabatic Humidification:

• Constant enthalpy process
• Water evaporates using sensible heat
• Dry bulb degree decreases
• Humidity ratio increases

Isothermal Humidification:

• Constant dry bulb heat level
• Heat added to maintain temp
• Humidity ratio increases

Energy Computation:

Application: Humidifiers, spray systems

4. Dehumidification

Process: Removing moisture from atmosphere

Conditions:

• Temperature control surface thermal reading < dew point
• Condensation occurs
• Both sensible and latent heat removed

Energy Analysis:

Application: Air conditioning coils, desiccant systems

5. Air Mixing

Process: Mixing two ventilation air streams

Mass Balance:

Energy Balance:

Humidity Ratio:

Dry Bulb Heat:

Application: Return fresh air mixing, economizer systems

Worked Examples

Example 1: Find Air Properties from DB and WB

Given:

• Dry bulb thermal value: 30°C
• Wet bulb degree: 22°C
• Atmospheric pressure value: 101.325 kPa

Find: Relative humidity, humidity ratio, enthalpy, dew point

Solution:

Step 1: Determine saturation vapor arrangement pressure at wet bulb (22°C = 295.15 K)

Step 2: Compute humidity ratio at wet bulb

Step 3: Find humidity ratio at dry bulb

Step 4: Evaluate saturation vapor power at dry bulb (30°C)

Step 5: Measure actual vapor force

Step 6: Assess relative humidity

Step 7: Determine enthalpy

Answer:

• Humidity ratio: 0.0135 kg/kg
• Relative humidity: 50.6%
• Enthalpy: 64.7 kJ/kg
• Dew point: ~18.5°C

Example 2: Cooling and Dehumidification

Given:

• Inlet air supply: 30°C DB, 22°C WB
• Outlet airflow: 15°C DB, 14°C WB
  • Atmosphere flow rate: 2.5 m³/s- Atmospheric stress: 101.325 kPa

Find: Total AC capacity, sensible refrigeration, latent chilling

Solution:

Step 1: Find inlet ventilation air properties (from Example 1)

• Enthalpy $h_1$ = 64.7 kJ/kg
• Humidity ratio $W_1$ = 0.0135 kg/kg
• Specific volume $v_1$ = 0.887 m³/kg

Step 2: Find outlet fresh air properties

• Enthalpy $h_2$ = 39.5 kJ/kg
• Humidity ratio $W_2$ = 0.0098 kg/kg
• Specific volume $v_2$ = 0.827 m³/kg

Step 3: Compute mass current rate

Step 4: Find total temperature control capacity

Step 5: Evaluate sensible air conditioning

Step 6: Measure latent AC

Step 7: Verify

Answer:

• Total refrigeration: 71.0 kW
• Sensible chilling: 42.6 kW (60%)
• Latent temperature control: 26.2 kW (40%)

Example 3: Air Mixing

Given:

• Stream 1: 30°C DB, 50% RH, 1.5 kg/s
• Stream 2: 15°C DB, 90% RH, 1.0 kg/s
• Atmospheric load: 101.325 kPa

Find: Mixed air supply properties

Solution:

Step 1: Find properties of Stream 1

• $h_1$ = 63.8 kJ/kg
• $W_1$ = 0.0133 kg/kg

Step 2: Find properties of Stream 2

• $h_2$ = 38.9 kJ/kg
• $W_2$ = 0.0096 kg/kg

Step 3: Assess total mass movement

Step 4: Determine mixed airflow enthalpy

Step 5: Compute mixed atmosphere humidity ratio

Step 6: Find mixed ventilation air heat level

Answer:

• Mixed fresh air temp: 24°C
• Mixed air supply humidity ratio: 0.0119 kg/kg
• Mixed airflow enthalpy: 54.4 kJ/kg

Design Applications

1. Cooling Load Calculation

Psychrometric analysis is essential for calculating air conditioning loads:

Sensible Load:

Latent Load:

Where:

• V = Atmosphere circulation rate (m³/s)
• $T_{\text{oa}}, T_{\text{ra}}$ = Outdoor and return ventilation air temperatures (°C)
• $W_{\text{oa}}, W_{\text{ra}}$ = Outdoor and return fresh air humidity ratios (kg/kg)

2. Air Conditioning System Sizing

Total AC Capacity:

Where:

• $h_{\text{oa}}$ = Outdoor air supply enthalpy (kJ/kg)
• $h_{\text{sa}}$ = Supply airflow enthalpy (kJ/kg)

3. Ventilation Requirements

Minimum Outdoor Atmosphere:

Typical Values (per person):

• Office: 10 L/s
• Classroom: 8 L/s
• Auditorium: 8 L/s

4. Energy Recovery Systems

Sensible Recovery Efficiency:

Total Recovery Efficiency:

Common Mistakes

1. Ignoring Latent Load

Mistake: Only calculating sensible refrigeration load

Impact: Undersized chilling equipment, high humidity

Solution: Always evaluate both sensible and latent loads

2. Wrong Wet Bulb Temperature

Mistake: Using outdoor dry bulb instead of wet bulb for temperature control load

Impact: Incorrect air conditioning capacity determination

Solution: Use design wet bulb thermal reading from climate data

3. Incorrect Air Mixing

Mistake: Averaging temperatures without considering mass flow rate rates

Impact: Wrong mixed fresh air properties

Solution: Use mass-weighted averages for all properties

4. Neglecting Dew Point

Mistake: Not checking for condensation on surfaces

Impact: Moisture damage, mold growth

Solution: Always verify surface heat > dew point

5. Wrong Enthalpy Reference

Mistake: Using different enthalpy references in calculations

Impact: Incorrect energy calculations

Solution: Use consistent reference state (0°C, dry air supply)

What Are the Best Practices for?

1. Use ASHRAE Formulas

Always use ASHRAE Fundamentals formulas for accurate calculations. These are based on extensive experimental data.

2. Verify with Psychrometric Chart

Use the psychrometric chart to verify calculations and visualize processes.

3. Consider Altitude

Atmospheric pressure value decreases with altitude, affecting all psychrometric properties. Adjust calculations for high-altitude locations.

4. Account for Process Efficiency

Real processes are not ideal. Account for:

• Coil bypass factor (0.05-0.15)
• Fan heat gain (2-5%)
• Duct heat gain/loss

5. Use Design Conditions

Always use design conditions from local climate data:

• Summer design: 1% or 2.5% dry bulb and mean coincident wet bulb
• Winter design: 99.6% or 97.5% dry bulb

6. Validate Results

Check that calculated values are within reasonable ranges:

• Humidity ratio: 0.002-0.025 kg/kg (typical)
• Enthalpy: 5-100 kJ/kg (typical)
• Relative humidity: 30-70% (comfort zone)

Real-World Case Studies

Case Study 1: Hospital Operating Room Humidity Control

Case Study 2: Data Center Economizer Failure

Case Study 3: Indoor Pool Natatorium Disaster

Quick Reference Card

Psychrometric Process Summary

Critical Dew Points to Remember

Design Checklist

Our cooling load calculations reflect real-world conditions and safety factors.

Our cooling load calculations reflect real-world conditions and safety factors.

Our engineering team developed this methodology based on internal testing and real-world validation.

Conclusion

Psychrometric calculations are fundamental to HVAC system design. By understanding the relationships between temperature, humidity, and energy, engineers can design efficient heating and cooling systems, optimize energy consumption, ensure occupant comfort, and prevent moisture problems.

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Key Takeaways

• Calculate enthalpy using $h = c_{pa} \times T + W \times (h_{fg,0} + c_{pv} \times T)$—enthalpy represents total heat content including sensible and latent heat
• Determine humidity ratio from vapor pressure using $W = 0.622 \times (P_v/(P - P_v))$—humidity ratio is mass of water vapor per unit mass of dry air
• Use psychrometric chart to visualize HVAC processes—chart shows relationships between all air properties enabling process design
• Calculate total cooling load from enthalpy difference—$Q_{total} = \dot{m}_a \times (h_1 - h_2)$ where enthalpy difference includes both sensible and latent components
• Maintain comfort conditions per ASHRAE 55—24°C/50% RH summer, 20-22°C/30-50% RH winter for optimal occupant comfort
• Prevent condensation by keeping surface temperatures above dew point—dew point is temperature where condensation begins, critical for moisture control

Further Learning

• Cooling Load Guide - Cooling load calculations
• Duct Sizing Guide - Air distribution design
• Heat Loss Guide - Building heat loss calculations
• Psychrometric Calculator - Interactive calculator for psychrometric calculations

References & Standards

Primary Standards

ASHRAE Fundamentals Handbook Chapter 1: Psychrometrics. Provides comprehensive psychrometric formulas, property calculations, and chart reading methods. Includes ASHRAE Equation 5 for saturation vapor pressure and all psychrometric property relationships.

ASHRAE Standard 55 Thermal Environmental Conditions for Human Occupancy. Specifies comfort conditions (24°C/50% RH summer, 20-22°C/30-50% RH winter) that guide psychrometric design targets.

ASHRAE Standard 62.1 Ventilation for Acceptable Indoor Air Quality. Specifies minimum ventilation rates (10 L/s per person for offices) that affect psychrometric calculations through ventilation heat gain.

Supporting Standards & Guidelines

ASHRAE Handbook - HVAC Systems and Equipment Chapter 4: Air Handling and Distribution. Provides guidance on air handling system design and psychrometric processes.

Further Reading

• ASHRAE Technical Resources - American Society of Heating, Refrigerating and Air-Conditioning Engineers resources
• McQuiston, Parker, Spitler: Heating, Ventilating, and Air Conditioning Analysis and Design - Comprehensive HVAC textbook
• Stoecker, Jones: Refrigeration and Air Conditioning - Reference for refrigeration and air conditioning principles

Note: Standards and codes are regularly updated. Always verify you're using the current adopted edition applicable to your project's location. Consult with local authorities having jurisdiction (AHJ) for specific requirements.

Disclaimer: This guide provides general technical information based on international HVAC standards. Always verify calculations with applicable local codes and consult licensed professionals for actual installations. HVAC system design should only be performed by qualified professionals. Component ratings and specifications may vary by manufacturer.