Chapter 18, Problem 18.81P

DATA The Dew Point and Clouds. The vapor pressure of water (see Exercise 18.44) decreases as the temperature decreases. The table lists the vapor pressure of water at various temperatures:

Temperature (°C )	Vapor Pressure (Pa)
10.0	1.23 × 103
12.0	1.40 × 103
14.0	1.60 × 103
16.0	1.81 × 103
18.0	2.06 × 103
20.0	2.34 × 103
22.0	2.65 × 10 3
24.0	2.99 × 103
26.0	3.36 × 103
28.0	3.78 × 103
30.0	4.25 × 103

If the amount of water vapor in the air is kept constant as the air is cooled, the dew point temperature is reached, at which the partial pressure and vapor pressure coincide and the vapor is saturated. If the air is cooled further, the vapor condenses to liquid until the partial pressure again equals the vapor pressure at that temperature. The temperature in a room is 30.0°c. (a) A meteorologist cools a metal can by gradually adding cold water. When the can’s temperature reaches 16.0°C, water droplets form on its outside surface. What is the relative humidity of the 30.0°C air in the room? On a spring day in the midwestern United States, the air temperature at the surface is 28.0°C. Puffy cumulus clouds form at an altitude where the air temperature equals the dew point. If the air temperature decreases with altitude at a rate of 0.6 C°/100 m, at approximately what height above the ground will clouds form if the relative humidity at the surface is (b) 35%; (c) 80%?