Humidity Institute Theory 5 - Influence of Temperature and Pressure on Percentage rh

Part 5 of the Basic Theory about Humidity - Important Parameters to be Measured and Monitored in Various Applications

The Influence of Temperature and Pressure on %rh

The saturated vapor pressure depends only on temperature and is not affected by the total pressure. There is no difference between the situation in an open space and that in a closed container.

In an open space, at a constant humidity and temperature, %rh is directly proportional to the total pressure. However, the value of %rh is limited to 100% because p cannot be greater than ps.

In a closed container with a fixed volume, %rh decreases as the temperature rises, but not as strongly as in an open space.

Examples

A) Office Building

In practical applications, an office building can be regarded as an open environment.

For example, a local temperature increase caused by a heater or office equipment does not change the local pressure value of water vapor, so the local vapor pressure throughout the building remains the same. However, the local saturated vapor pressure will increase. Therefore, the relative humidity near the heat source will decrease.

If we assume that the temperature elsewhere in the building is 25°C with a relative humidity of 50%, a local temperature increase to 30°C will decrease the relative humidity as follows:

ps at 25°C=3.17kPa

ps at 30°C=4.24kPa

p=0.5x3.17kPa=1.585kPa, corresponding to 50% rh

Localized % rh=100x1.585/4.24=37.4%

B) Dew on a Cold Mirror

If the temperature of a mirror is lowered to the exact value at which the dew point appears on the surface, the value of the mirror temperature is called the dew point. Using the previous example, the dew point corresponding to the conditions of 50% rh and 25°C can be found as follows:

ps at 25°C=3.17kPa

p=0.5x3.17kPa=1.585kPa, corresponding to 50% rh

If there is an equilibrium between the dew on the mirror and the environment, then ps must be equal to the vapor pressure p at the temperature of the cooled mirror. Based on a simple interpolation of the values in the saturated vapor table, we find that the ps value of 1.855 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 a saturated vapor table.

C) Compression in a Sealed Chamber

If the total pressure in a sealed chamber is increased from one atmosphere to one - and - a - half atmospheres while the temperature remains constant, the partial pressure of water vapor will increase by 1.5 times. Since the temperature is the same, the saturated pressure ps also remains the same. If we assume the conditions before compression are 50% rh and 25°C, the conditions after compression are 75% rh and 25°C.

D) Injection of Dry Gas in a Sealed Chamber

If dry nitrogen is injected into a closed chamber that already contains air at 50% RH and the temperature remains constant, the total pressure in the chamber will increase. However, the partial water vapor pressure p remains constant because the decrease in the mole fraction of water vapor in the chamber exactly balances the increase in the total pressure (see Dalton's Law). Since the temperature remains constant, the "saturated vapor pressure Ps" also remains constant. Therefore, the relative humidity remains at 50% despite the injection of dry gas into the chamber.

Rules: Rules-of-Thumb for Relative Humidity in Moist Air Applications

Recall that % rh =p/ps x100

1. As the temperature of the system increases, the relative humidity decreases because ps increases while p remains constant. Similarly, as the temperature of the system decreases, the relative humidity increases because ps decreases while p remains constant. As the temperature decreases, the system will eventually reach saturation where p = ps and the air temperature = dew point temperature.

2. When the total pressure of the system decreases, the relative humidity decreases because p decreases, but ps does not change since the temperature is unchanged. Similarly, when the total pressure of the system increases, the relative humidity increases until it eventually reaches saturation.