Humidity Academy Theory 5 - Effect of Temperature and Pressure on % rh

Effect of Temperature and Pressure on %rh

Saturation vapor pressure depends only on temperature. There is no effect of total pressure, and there is no difference between the situation in an open space and that in a closed container.

• In an open space, at constant moisture level and temperature, %rh is directly proportional to the total pressure. However, the value of %rh is limited to 100 % as p cannot be greater than ps.
• In a closed container of fixed volume, %rh decreases as temperature increases, but not quite as strongly as in 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, doesn’t 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, corresponding 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 ps of 1.585 kPa corresponds to a temperature of 13.8 °C. This temperature is the dew point.The example above shows that converting relative humidity into 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 in 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: “Relative Humidity Measurement Explained”

See previous blog posts:
Humidity Academy Theory 1
Humidity Academy Theory 2
Humidity Academy Theory 3
Humidity Academy Theory 4
Watch out for Humidity Academy Theory part 6 on the PST Blog