Question

When the air temperature is high the human body uses sweating followed by evaporative cooling to control its temperature. This works only if the surrounding air is not already saturated with water, i.e., for relative humidities significantly below 100%. As it turns out, a 70.% relative humidity on a 90.ºF summer day in Florida will already feel very uncomfortable in the absence of a breeze.

(a) Calculate the saturation (equilibrium) vapor pressure of water at 90.ºF and the actual vapor pressure

at that temperature when the relative humidity is 70.%.

(b) Calculate the air temperature (inºF) at which the 70.% humidity in the air from part (a) becomes 100.%? This is the so-called dew point.

Hint: The relative humidity is defined as the actual vapor pressure of water divided by the equilibrium

vapor pressure at a given temperature. Consider to use the Clausius-Clapeyron equation to estimate

the vapor pressure of water. The heat of vaporization of water is given as 40.66 kJ/mol and can be

assumed to be constant between 20ºC and 100ºC.

Use the Clausius-Clapeyron equation.

Answer 1

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