Humidity Academy Theory 5 - Effect of Temperature and Pressure on Relative Humidity (%RH)

Effect of temperature and pressure on relative humidity (%RH)

Saturation vapor pressure depends solely on temperature. Total pressure has no effect, and there is no difference between the situation in an open space and that in a closed container.

• In an open space, with constant humidity and temperature, %RH is directly proportional to total pressure. However, the value of %RH is limited to 100%, since p cannot be greater than ps.
• In a closed container of fixed volume, %RH decreases as the temperature increases, but not as sharply as in an open space.

Examples

A) Office building

For practical purposes, an office building can be considered an open environment.

A localized increase in temperature created by a heater or an office machine, for instance, does modify the value of the partial pressure of water vapor, so the local vapor pressure is the same throughout the building. However, the saturation vapor pressure is locally increased. Consequently, relative humidity in the immediate vicinity of the heat source is lowered.

If we assume that elsewhere in the building the temperature is 25°C and relative humidity is 50%, a localized increase of temperature to 30°C lowers relative humidity as follows:

ps at 25°C = 3.17 kPa
ps at 30°C = 4.24 kPa
p = 0.5 x 3.17 kPa = 1.585 kPa, corresponds to 50%RH
Localized %RH = 100 x 1.585/4.24 = 37.4%

B) Dew on a chilled mirror
If the temperature of a mirror is lowered to precisely the value that makes dew appear on the surface, the value of the mirror temperature is called dew point. Using the previous example, the dew point corresponding to a condition of 50 %RH and 25°C can be found as follows:

ps at 25°C = 3.17 kPa
p = 0.5 x 3.17 kPa = 1.585 kPa, corresponding to 50 % RH.

If there is equilibrium between the dew on the mirror and the environment, it follows that ps at the temperature of the chilled mirror must be equal to the vapor pressure p. Based on a simple interpolation of the values of the saturation vapor tables, we find that a value of psof 1.585 kPa corresponds to a temperature of 13.8°C.

This temperature is the dew point. The above example shows that converting relative humidity to dew point and vice versa requires the use of a thermometer and saturation vapor tables.

C) Compression in a closed chamber
If the total pressure inside a closed chamber is increased from one to one and a half atmospheres and temperature is kept constant, the partial pressure of water vapor is increased 1.5 times. Because temperature is the same, so is the saturation pressure ps. If we assume that we had a condition of 50%RH and 25°C before the compression, the condition afterwards is 75 %RH and 25°C.

D) Injection of a dry gas into a closed chamber
If dry nitrogen is injected in a closed chamber where there is already air at a condition of 50 %RH and temperature is kept constant, total pressure in the chamber increases. However, the partial water vapor pressure p remains constant because the mole fraction of water vapor in the chamber decreases by an amount that exactly balances the increase in total pressure (see Dalton's law). Because temperature is maintained constant, the saturation vapor pressure ps is also unchanged. Therefore, relative humidity stays at 50%, despite the fact that a dry gas was injected in the chamber.

Learn more about humidity in the following video: Explanation of relative humidity measurement

Related Blog Posts

Humidity Academy Theory 1 – What is Humidity?
Humidity Academy Theory 2 – Relative Humidity, Pressure and Temperature
Humidity Academy Theory 3 – Humidity and Vapor Pressure
Humidity Academy Theory 4 – Definitions of Humidity: Vapor Concentration
Humidity Academy Theory 6 – The Capacitive Sensor
Humidity Academy Theory 7 – The Wet Bulb/Dry Bulb Technology (Psychrometer)
Humidity Academy Theory 8 – Chilled Mirror and Aluminum Oxide Technology
Humidity Academy Theory 9 – Choosing the Right Humidity Measurement technology