Analyzing Relative Humidity Change During Heating and Humidification

Understanding how relative humidity changes during different air conditioning processes like heating and humidification is important in thermodynamics and HVAC systems. Let's break down this specific process.

What is Heating and Humidification?

This process involves simultaneously:

• Adding heat to the air, which increases its dry-bulb temperature.
• Adding moisture to the air, which increases its humidity ratio (specific humidity).

Common examples include passing air through a heating coil followed by a humidifier or spray chamber where water is added.

Effect on Relative Humidity

Relative humidity ($\phi$) is a measure of the amount of water vapor in the air compared to the maximum amount of water vapor the air can hold at that temperature. It is calculated as:

$\phi = \frac{Partial \ Pressure \ of \ Water \ Vapor (p_v)}{Saturation \ Pressure \ of \ Water \ Vapor \ at \ the \ Air \ Temperature (p_{vs})} \times 100\%$

or conceptually related to the humidity ratio ($W$) and the saturation humidity ratio ($W_s$) at the same temperature:

$\phi \approx \frac{W}{W_s} \times 100\%$

Let's consider the individual effects:

• Heating Alone: If you only heat air (dry heating), the humidity ratio ($W$) remains constant, but the temperature increases. A higher temperature means the air can hold more moisture, so the saturation pressure ($p_{vs}$) or saturation humidity ratio ($W_s$) increases. With $p_v$ (or $W$) constant and $p_{vs}$ (or $W_s$) increasing, the relative humidity ($\phi$) decreases.
• Humidification Alone (Isothermal): If you only add moisture to air at a constant temperature (isothermal humidification), the temperature remains constant, but the humidity ratio ($W$) increases. The saturation pressure ($p_{vs}$) or saturation humidity ratio ($W_s$) remains constant (as temperature is constant). With $p_v$ (or $W$) increasing and $p_{vs}$ (or $W_s$) constant, the relative humidity ($\phi$) increases.

In the combined heating and humidification process, both temperature (affecting $p_{vs}$ or $W_s$) and humidity ratio (affecting $p_v$ or $W$) are changing. The final relative humidity depends on the balance between the amount of heat added and the amount of moisture added.

• If a relatively large amount of heat is added compared to the amount of moisture, the temperature increase will significantly raise the air's moisture holding capacity ($W_s$). Even though $W$ increases, $W_s$ might increase faster, leading to a decrease in the final relative humidity compared to the initial relative humidity.
• If a relatively large amount of moisture is added compared to the amount of heat, the increase in $W$ will be substantial relative to the increase in $W_s$ (which is less affected due to a smaller temperature rise). This can lead to an increase in the final relative humidity compared to the initial relative humidity.
• In some specific cases, the relative humidity might even end up close to the initial value, or it could increase significantly towards saturation, or decrease significantly depending on the process path on a psychrometric chart.

Conclusion

Because the final relative humidity depends on the ratio of heat addition to moisture addition, it is not fixed. The final relative humidity during a heating and humidification process can either increase or decrease compared to the initial relative humidity.