## Physics Brain Teaser

Question: Can the Relative Humidity exceed 100%?

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“The relative humidity (RH) is the ratio of the amount of water vapor actually in the air to the maximum amount of water vapor required for saturation at that particular temperature (and pressure). It is the ratio of the air's water vapor content to its capacity.”

“Consider a cloud droplet in equilibrium with its environment. The total number of vapor molecules around the droplet remains fairly constant and defines the droplet's saturation vapor pressure. Since the droplet is in equilibrium, the saturation vapor pressure is also called the equilibrium vapor pressure.

[Consider] a cloud droplet and a flat water surface, both of which are in equilibrium. Because more vapor molecules surround the droplet, it has a greater equilibrium vapor pressure. The reason for this fact is that water molecules are less strongly attached to a curved (convex) water surface; hence, they evaporate more readily.

To keep the droplet in equilibrium, more vapor molecules are needed around it to replace those molecules that are constantly evaporating from its surface. Smaller cloud droplets exhibit a greater curvature, which causes a more rapid rate of evaporation. As a result of this process (called the curvature effect), smaller droplets require an even greater vapor pressure to keep them from evaporating away. Therefore, when air is saturated with respect to a flat surface, it is unsaturated with respect to a curved droplet of pure water, and the droplet evaporates. So, to keep tiny cloud droplets in equilibrium with the surrounding air, the air must be supersaturated; that is, the relative humidity must be greater than 100 percent. The smaller the droplet, the greater its curvature, and the higher the supersaturation needed to keep the droplet in equilibrium.”

“…when the droplet's size is less than 2 µm, the relative humidity (measured with respect to a flat surface) must be above 100.1 percent for the droplet to survive. As droplets become larger, the effect of curvature lessens; for a droplet whose diameter is greater than 20 µm; the curvature effect is so small that the droplet behaves as if its surface were flat.

Just as relative humidities less than that required for equilibrium permit a water droplet to evaporate and shrink, those greater than the equilibrium value allow the droplet to grow by condensation.

…we can see that a droplet whose diameter is 1 µm will grow larger as the relative humidity approaches 101 percent. But relative humidities, even in clouds, rarely become greater than 101 percent. How, then, do tiny cloud droplets of less than 1 µm grow to the size of an average cloud droplet?”

Meteorology Today: An Introduction to Weather, Climate, and the Environment

C. DonaldAhrens - Brooks/Cole - 2013

Related demonstration:

http://lecdem.physics.umd.edu/i/i5/i5-12.html

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