12.10

*Humidity

Air is a mixture of gases, including nitrogen, oxygen, and water vapor. The total pressure of the mixture is the sum of the partial pressures of the component gases. The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume at the same temperature as the mixture. The partial pressure of water vapor in air depends on weather conditions. It can be as low as zero or as high as the equilibrium vapor pressure of water at the given temperature.
To provide an indication of how much water vapor is in the air, weather forecasters usually give the relative humidity. If the relative humidity is too low, the air contains such a small amount of water vapor that skin and mucous membranes tend to dry out. If the relative humidity is too high, especially on a hot day, we become very uncomfortable and our skin feels “sticky.” Under such conditions, the air holds so much water vapor that the water exuded by sweat glands cannot evaporate efficiently. The relative humidity is defined as the ratio (expressed as a percentage) of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature.

| (12.6)

The term in the denominator on the right of Equation 12.6 is given by the vaporization curve of water and is the pressure of the water vapor in equilibrium with the liquid. At a given temperature, the partial pressure of the water vapor in the air cannot exceed this value. If it did, the vapor would not be in equilibrium with the liquid and would condense as dew or rain to reestablish equilibrium.

The physics of relative humidity.

When the partial pressure of the water vapor equals the equilibrium vapor pressure of water at a given temperature, the relative humidity is 100%. In such a situation, the vapor is said to be saturated because it is present in the maximum amount, as it would be above a pool of liquid at equilibrium in a closed container. If the relative humidity is less than 100%, the water vapor is said to be unsaturated. Example 17 demonstrates how to find the relative humidity.

| Example 17 | | | Relative Humidities

One day, the partial pressure of water vapor in the air is . Using the vaporization curve for water in Figure 12-37, determine the relative humidity if the temperature is (a) 32 °C and (b) 21 °C.

Figure 12-37 The vaporization curve of water.

Reasoning and Solution

a. | According to Figure 12-37, the equilibrium vapor pressure of water at 32 °C is . Equation 12.6 reveals that the relative humidity is

b. | A similar calculation shows that

When air containing a given amount of water vapor is cooled, a temperature is reached in which the partial pressure of the vapor equals the equilibrium vapor pressure.
This temperature is known as the dew point. For instance, Figure 12-38 shows that if the partial pressure of water vapor is , the dew point is 25 °C. This partial pressure would correspond to a relative humidity of 100%, if the ambient temperature were equal to the dew-point temperature. The physics of fog formation. Hence, the dew point is the temperature below which water vapor in the air condenses in the form of liquid drops (dew or fog). The closer the actual temperature is to the dew point, the closer the relative humidity is to 100%. Thus, for fog to form, the air temperature must drop below the dew point. The physics of a home dehumidifier. Similarly, water condenses on the outside of a cold glass when the temperature of the air next to the glass falls below the dew point. And the cold coils in a home dehumidifier (see Figure 12-39) function very much in the same way that the cold glass does. The coils are kept cold by a circulating refrigerant. When the air blown across them by the fan cools below the dew point, water vapor condenses in the form of droplets, which collect in a receptacle.

Figure 12-38 On the vaporization curve of water, the dew point is the temperature that corresponds to the actual partial pressure of water vapor in the air.

Figure 12-39 The cold coils of a dehumidifier cool the air blowing across them to below the dew point, and water vapor condenses out of the air.

Test your understanding of the material in Sections 12.6–12.10:

· | Heat and Specific Heat Capacity
· | Latent Heat
· | Phase Equilibrium and Humidity

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