Psychrometric Calculator

Psychrometrics and Moist Air Thermodynamics

Psychrometrics is the branch of applied thermodynamics that investigates the physical, thermal, and psychrometric properties of atmospheric gas mixtures comprising dry air and water vapor. In heating, ventilation, air conditioning (HVAC), industrial drying, cleanroom environmental control, and meteorology, precise evaluation of moist air thermodynamic properties is essential to size air handling units, cooling towers, dehumidifiers, and thermal comfort systems per standards such as ASHRAE 55 and ASHRAE 62.1.

Atmospheric air is not a single uniform chemical species; rather, it behaves as a binary mixture of dry air (predominantly nitrogen, oxygen, argon, and carbon dioxide with an average molar mass $M_{da} = 28.966\text{ g/mol}$) and gaseous water vapor ($M_w = 18.01528\text{ g/mol}$). According to Dalton's Law of Partial Pressures, the total barometric atmospheric pressure ($P_{atm}$) is the sum of dry air partial pressure ($P_a$) and water vapor partial pressure ($P_w$):

Key Psychrometric State Parameters & Governing Equations

Under the formulation outlined in the ASHRAE Handbook: Fundamentals (Chapter 1), the state of moist air at any given barometric pressure is uniquely determined by any two independent thermodynamic properties (most commonly dry-bulb temperature and relative humidity).

1. Saturation Vapor Pressure ($P_{ws}$)

Saturation vapor pressure represents the maximum partial pressure exerted by water vapor in equilibrium with pure liquid water at temperature $T$ (°C). Using the highly accurate Magnus-Tetens empirical formulation (valid between $-40^\circ\text{C}$ and $+50^\circ\text{C}$):

2. Actual Vapor Pressure ($P_w$) and Relative Humidity ($RH$)

Relative humidity ($RH$) is defined as the ratio of actual water vapor partial pressure to saturation vapor pressure at the identical dry-bulb temperature:

3. Humidity Ratio ($W$, Specific Humidity)

The humidity ratio ($W$), also referred to as absolute or specific humidity, expresses the mass of water vapor associated with each unit mass of bone-dry air. Derived from the ideal gas law:

4. Dew Point Temperature ($T_{dp}$)

The dew point is the temperature at which water vapor in moist air begins to condense into liquid droplets at constant total atmospheric pressure. Inverting the Magnus-Tetens relationship with respect to actual vapor pressure $P_w$:

5. Wet-Bulb Temperature ($T_{wb}$)

The wet-bulb temperature corresponds to the temperature indicated by a thermometer enveloped in a wetted wick exposed to rapid air currents. It denotes the thermodynamic limit of evaporative cooling. A widely utilized and continuous numerical approximation developed by Stull (2011) evaluates $T_{wb}$ directly from dry-bulb temperature and relative humidity:

6. Specific Enthalpy of Moist Air ($h$)

Specific enthalpy ($h$) quantifies the total thermal energy content per kilogram of dry air, incorporating sensible thermal energy of dry air plus the latent and sensible heat of the associated water vapor (reference datum at $0^\circ\text{C}$ dry air and liquid water):

Where $c_{pa} = 1.006\text{ kJ/(kg}\cdot\text{K)}$ is the specific heat capacity of dry air, $h_{we} = 2501\text{ kJ/kg}$ is the latent heat of vaporization of water at $0^\circ\text{C}$, and $c_{pw} = 1.86\text{ kJ/(kg}\cdot\text{K)}$ is the specific heat of water vapor.

7. Specific Volume ($v$) and Moist Air Density ($\rho$)

Specific volume represents the cubic meters of moist air mixture space occupied per kilogram of dry air:

Where $R_a = 0.287042\text{ kJ/(kg}\cdot\text{K)}$ is the specific gas constant of dry air, and $P_{atm}$ is in $\text{kPa}$. Moist air mixture mass density ($\rho$) is subsequently computed as:

Psychrometric Process Reference Matrix

Every HVAC conditioning process traces a distinct directional path across the psychrometric diagram:

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