Psychrometric Moist Air Enthalpy & Dew Point Calculator

Thermodynamics of Moist Atmospheric Air

Psychrometrics is the specialized branch of engineering thermodynamics dedicated to investigating the physical and thermal properties of gas-vapor mixtures, predominantly moist air consisting of atmospheric dry air and water vapor ($H_2O$). Conceived systematically by Willis Carrier in 1911 through his seminal formulation of the rational psychrometric formulae, this science governs the thermal design of modern heating, ventilation, air conditioning, and refrigeration (HVAC&R) systems, industrial drying ovens, evaporative cooling towers, meteorology, agricultural greenhouse environmental control, and cleanroom aerospace manufacturing.

In atmospheric psychrometrics, moist air is treated as a binary mixture of two ideal gases: bone-dry air (a homogeneous mixture of 78.08% nitrogen, 20.95% oxygen, 0.93% argon, and trace gases with an apparent molar mass $M_a = 28.966 text{ g/mol}$) and superheated water vapor ($M_w = 18.015 text{ g/mol}$). According to Dalton's Law of Partial Pressures, the total barometric pressure $P$ exerted by moist air is the exact sum of the partial pressure of the dry air constituent $p_a$ and the partial pressure of water vapor $p_v$:

Fundamental Psychrometric Equations and Derivations

1. Water Vapor Saturation Pressure ($p_{ws}$)

The maximum equilibrium pressure that water vapor can exert in equilibrium with a plane surface of pure liquid water at temperature $T$ (°C) is modeled with high fidelity using the extended Magnus-Tetens Equation (recommended by the World Meteorological Organization and ASHRAE):

2. Relative Humidity ($phi$ or $text{RH}$) & Partial Vapor Pressure ($p_v$)

Relative humidity is defined as the mole fraction of water vapor in a moist air sample relative to the mole fraction in a saturated sample at the identical temperature and total pressure:

3. Humidity Ratio / Moisture Content ($W$)

The humidity ratio $W$ (also denoted specific humidity or absolute moisture content) quantifies the exact mass of water vapor associated with each unit mass of dry air. Invoking the ideal gas law ($m_v = p_v V / R_w T$ and $m_a = p_a V / R_a T$):

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

The specific enthalpy of moist air is referenced per kilogram of dry air ($h = H / m_a$). It combines the sensible heat of the dry air and the combined sensible and latent heat of the entrained water vapor:

where $c_{pa} = 1.006 text{ kJ/kg}cdottext{K}$ is the isobaric specific heat capacity of dry air, $h_{we} = 2,501 text{ kJ/kg}$ is the latent heat of vaporization of water at 0 °C, and $c_{pv} = 1.86 text{ kJ/kg}cdottext{K}$ is the specific heat capacity of superheated water vapor.

5. Dew Point Temperature ($T_{text{dp}}$)

The dew point temperature is the temperature to which a given parcel of moist air must be sensibly cooled at constant total pressure and constant humidity ratio for water vapor to condense. Inverting the Magnus equation using the actual partial vapor pressure $p_v$ yields:

6. Wet-Bulb Temperature ($T_{text{wb}}$) & The Lewis Relation

A wet-bulb thermometer measures the dynamic equilibrium temperature achieved when a water-wetted porous wick is exposed to an air stream moving at velocities exceeding 3 to 5 m/s. Convective heat transferred from the warm air into the wick is precisely counterbalanced by the latent heat lost through evaporative mass transfer:

Because the Lewis number $Le = alpha / D_{AB} approx 1.0$ for water vapor diffusing in atmospheric air, the convective heat transfer coefficient $h_c$ and mass transfer coefficient $h_m$ satisfy the Lewis relation $h_c / h_m approx c_{pm}$. Consequently, the wet-bulb temperature indicated by a sling psychrometer matches the thermodynamic adiabatic saturation temperature with exceptional accuracy.

7. Specific Volume and Density

The specific volume $v$ represents the total volume of the moist air mixture per kilogram of dry air:

Step-by-Step Numerical Calculation Example

Suppose an air handling unit (AHU) conditions outdoor ambient air at summer design conditions:

• Dry Bulb Temperature: $T_{text{dry}} = 32.0,^circtext{C}$
• Relative Humidity: $phi = 60.0%$
• Barometric Pressure: Standard sea-level $P = 101.325 text{ kPa}$
• Volumetric Supply Flow: $dot{V} = 5,000 text{ m}^3/text{h}$

Step 1: Calculate Saturation Vapor Pressure ($p_{ws}$)

Step 2: Calculate Partial Vapor Pressure ($p_v$)

Step 3: Calculate Humidity Ratio ($W$)

Step 4: Calculate Dew Point Temperature ($T_{text{dp}}$)

Step 5: Calculate Specific Enthalpy ($h$)

Step 6: Calculate Specific Volume, Density, and Mass Flow Rate

Step 7: Cooling Coil Thermal Load to Reach Indoor Setpoint

If the cooling coil cools and dehumidifies this air to off-coil apparatus dew point $T_2 = 13.0,^circtext{C}$ and saturation $phi_2 = 95%$ ($h_2 = 35.8 text{ kJ/kg}$):

Standard Indoor and Industrial Psychrometric Regimes