Absolute Humidity Air

Overview

Engineering reference data for Absolute 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

Units and Measurement

Absolute humidity is expressed as the mass of water vapor per unit volume of the mixture. The common units and their typical applications are:

• SI Units:

  • kg/m³ (kilograms per cubic meter) - Used in scientific and precise engineering calculations.
  • g/m³ (grams per cubic meter) - A more common unit for everyday and HVAC applications.

• Imperial Units:

  • lbs/ft³ (pounds per cubic foot) - Used in some engineering contexts in the US.
  • gr/ft³ (grains per cubic foot) - A specialized unit common in psychrometry and industrial process control.

Practical Significance

Unlike relative humidity, which is temperature-dependent and a ratio, absolute humidity provides a direct measure of the actual water content in the air. This makes it particularly useful for:

• Material Processing: Calculating moisture loads in industries like food production, pharmaceuticals, and paper manufacturing.
• HVAC Engineering: Determining the amount of water that needs to be added or removed from air to achieve a desired condition.
• Combustion Analysis: Assessing the effect of water vapor on the properties of air-fuel mixtures.

It is important to note that absolute humidity changes if the volume of the air parcel changes (e.g., due to pressure or temperature changes), even if no moisture is added or removed. For applications where the amount of water vapor per unit mass of dry air is more relevant, specific humidity is often used.

References

• Original Source

Calculation Example

To calculate the absolute humidity of air, you can use the following procedure with the ideal gas law. Assume you have measured the vapor pressure ($e$) and the air temperature ($T$).

Given:

• Vapor pressure, $e = 2.34 \, \text{kPa}$
• Air temperature, $T = 25^\circ\text{C}$

Step 1: Convert Temperature to Kelvin $T(K) = 25 + 273.15 = 298.15 \, K$

Step 2: Apply the Ideal Gas Law for Water Vapor The formula for absolute humidity ($\rho_w$) is: $\rho_w = \frac{e}{R_w \cdot T}$ where $R_w$ is the specific gas constant for water vapor, $461.5 \, \text{J/(kg·K)}$.

Step 3: Calculate $\rho_w = \frac{2340 \, \text{Pa}}{461.5 \, \text{J/(kg·K)} \times 298.15 \, \text{K}} \approx 0.017 \, \text{kg/m}^3$

This result, $0.017 \, \text{kg/m}^3$, is the mass of water vapor per cubic meter of air under these specific conditions. This value increases as vapor pressure increases or as temperature decreases.

Definition

Absolute humidity is defined as the mass of water vapor present in a unit volume of moist air. It provides a direct measurement of the water vapor content without reference to the air's temperature or pressure.

$$\rho_v = \frac{m_{H_2O}}{V}$$

Where:

• $\rho_v$ = absolute humidity (kg/m³ or g/m³)
• $m_{H_2O}$ = mass of water vapor (kg or g)
• $V$ = volume of the moist air mixture (m³)

Relationship to Vapor Pressure

Absolute humidity can be calculated from the partial pressure of water vapor ($e$) and the absolute temperature ($T$) using the ideal gas law.

$$\rho_v = \frac{e \cdot M_w}{R \cdot T}$$

Where:

• $e$ = partial pressure of water vapor (Pa)
• $M_w$ = molar mass of water (0.018015 kg/mol)
• $R$ = universal gas constant (8.314 J/(mol·K))
• $T$ = absolute temperature (K)

Key Distinction

Absolute humidity differs from specific humidity (the mass of water vapor per unit mass of moist air) and relative humidity (the ratio of the current absolute humidity to the maximum possible absolute humidity at that temperature). Its value changes with temperature and pressure even if no moisture is added or removed, as the volume of the air changes.

Notes on Terminology and Units

• The notation "mh20" in the source text likely refers to the mass of water vapor, typically denoted as $m_{H_2O}$ in engineering contexts.
• Absolute humidity can be expressed in various unit systems, but consistency is key: SI units (kg/m³ or g/m³) are standard in scientific calculations, while imperial units (lbs/ft³ or gr/ft³) are common in some HVAC and industrial applications.
• When converting between unit systems, use precise conversion factors to maintain accuracy in engineering designs and analyses.

Summary of Humidity Types and Units

The following table summarizes the primary expressions of humidity and their corresponding measurement units.