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Chemistry Everyday for Everyone

Relative Humidity
R. Bruce Martin Chemistry Department, University of Virginia, Charlottesville, VA 22903;

Daily, the weather report tells us the percent relative humidity. What does this mean? A hot day accompanied by high relative humidity causes us to experience a muggy feeling. A sudden switch to a low relative humidity environmentresults in dryness of lips and mucous membranes. Informal polls of students indicate that many do not grasp the concept of relative humidity and claim that they have not had it in school. The absence of material about relative humidity from most middle and high school science texts supports this claim. Here is a science topic about which students hear constantly but which is given little coverage inschool science courses. In this short article I define and describe relative humidity at several levels, discussing the concepts of water vapor pressure in the atmosphere and dew point. There is an opportunity for an instructive application of the ideal gas equation. I finish with a new plot directly illustrating the dependence of relative humidity on temperature. I derive the relationship forthis plot from application of an equation suitable for physical chemistry students, but the results of this original plot are of general interest and access. Relative Humidity For any given temperature there is a maximum or saturation amount of water vapor that the atmosphere can hold. This amount may be expressed in mmHg of a mercury barometer or in atmospheres, where 760 mmHg corresponds to oneatmosphere. The saturation vapor pressure of water in air increases with temperature as a greater fraction of molecules attain the energy to escape the liquid phase. At the freezing point of water (0 °C) the saturation vapor pressure is 4.58 mmHg and it rises to 760 mmHg at the boiling point of water (100 °C). Near room temperature the saturation vapor pressure in mmHg is almost numericallyequivalent to the Celsius degrees, becoming equal at a warm room temperature for 27.4 mmHg at 27.4 °C (81 °F). The uppermost curve for 100% humidity in Figure 1 shows the saturation

vapor pressure rising with increasing temperature. The curve is constructed from tables in handbooks for water saturation vapor pressure versus Celsius temperature. The relative humidity, usually expressed as a percentage,is the ratio of the water vapor pressure in the atmosphere to the saturation vapor pressure at the same temperature. In other words, the relative humidity is the amount of water vapor in the atmosphere divided by the maximum amount the air may hold at that temperature (multiplied by 100). At 27.4 °C a vapor pressure of 13.7 mmHg corresponds to 50% humidity. The three lower curves in Figure 1 showwater vapor pressure at the indicated relative humidities. These three curves were constructed by multiplying the saturation vapor pressure at each temperature by the corresponding decreasing fractional relative humidity. Relative humidity is often measured by a hygrometer–– an instrument in which a hair under tension slightly alters its length owing to humidity changes. The instrument dial iscalibrated to read relative humidity directly from the hair length. Relative humidity may also be determined by comparing the temperatures of dry-bulb and wet-bulb thermometers, the temperature of the latter being lowered by evaporative cooling of water from a cloth surrounding the bulb. The lower the relative humidity the greater the cooling effect. The relative humidity is then read from a tablecontaining the dry bulb temperature and the depression of the wet-bulb thermometer. The area above the curve for 100% humidity in Figure 1 corresponds to an atmosphere saturated with water vapor. The dew point is the temperature at which condensation of water vapor occurs owing to saturation at a given water content. Reading off the curve labeled 100 in Figure 1, we see that for a water vapor...
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