Chapter 7, Problem 1E

Consider the air sample denoted by an asterisk (*) in Figure 7-2. Its temperature is –15°C and its vapor pressure is 1.72 mb. What is its relative humidity with respect to water if, at –15°C, the saturation vapor pressure over liquid water is 1.91 mb? (Your answer should be less than 100%, indicating an unsaturated sample.)

To determine

The relative humidity with respect to water if at $-{15}^{\circ }\text{C}$, the saturation vapor pressure over liquid water is 1.91 mb and vapor pressure is 1.72 mb.

Answer to Problem 1E

The relative humidity of air sample is 90%.

Explanation of Solution

$\begin{array}{l}\text{Temperature}\text{=}{\text{-15}}^{\text{o}}\text{C}\\ \text{Vapor pressure}\text{=}\text{1}\text{.72}\text{mb}\\ \text{Saturation}\text{vapor}\text{pressure}\text{=}\text{1}\text{.91}\text{mb}\end{array}$

The expression used to calculate relative humidity is as follows.

$\text{Relative}\text{humidity}\text{=}\frac{\text{Vapor}\text{pressure}}{\text{Saturation}\text{vapor}\text{pressure}}\text{×100}$

Substitute 1.72mb for vapor pressure 1.91mb for saturation vapor pressure to find the relative humidity.

$\begin{array}{c}\text{Relative}\text{humidity}\text{=}\frac{1.72}{1.91}\text{×100}\\ \text{= 0}\text{.9005}\times \text{100}\\ \text{= 90\%}\end{array}$

Therefore, the relative humidity of air sample is 90%.