Specific Relative Humidity Air

Overview

Engineering reference data for Specific Relative Humidity Air in air psychrometrics.

Key Formulas

Humidity Ratio

$\omega = 0.622 \frac{P_v}{P_a}$

Mass of water vapor per mass of dry air.

Relative Humidity

$\phi = \frac{P_v}{P_{vs}} \times 100\%$

Ratio of actual to saturation vapor pressure.

Wet Bulb Temperature

$T_{wb} = T_{db} - \frac{P_{vs} - P_v}{\gamma}$

Temperature measured by wet-bulb thermometer.

Enthalpy of Moist Air

$h = c_p T + \omega h_g$

Sensible + latent heat per unit mass of dry air.

Variables

Symbol	Description	Unit
$\omega$	Humidity ratio	kg/kg
$\phi$	Relative humidity	%
$P_v$	Vapor pressure	Pa
$P_{vs}$	Saturation vapor pressure	Pa
$T_{db}$	Dry bulb temperature	°C
$T_{wb}$	Wet bulb temperature	°C

Calculation Example

To determine specific humidity from known air properties, use the relationship between relative humidity and vapor density:

$x = \frac{0.622 \cdot \phi \cdot \rho_{ws}}{(\rho - \rho_{ws}) \cdot 100\%}$

Example: Given moist air at 20°C with:

• Relative humidity φ = 60%
• Water vapor density ρ_ws = 0.0173 kg/m³
• Moist air density ρ = 1.204 kg/m³

$x = \frac{0.622 \times 60 \times 0.0173}{(1.204 - 0.0173) \times 100}$

$x = \frac{0.647}{118.67} = 0.00545 \text{ kg}_{H_2O}/\text{kg}_{dry\_air}$

Converting to g/kg: x ≈ 5.45 g/kg

Conversion Factors

Parameter	Value	Description
0.622	Ratio M_w/M_a	Molecular weight ratio of water (18.015) to dry air (28.97)
100%	Denominator factor	Converts relative humidity from percentage to decimal

Physical Interpretation

The constant *0.622 represents the ratio of the molecular mass of water vapor to that of dry air. This factor arises from the ideal gas law applied to gas mixtures, where:

• Specific humidity equals the mass ratio of water vapor to dry air
• The conversion accounts for the different molecular weights of H₂O and the N₂/O₂ mixture comprising dry air

References

• Original Source