Chapter 5, Problem 1PA

(a)

To determine

The water vapor capacity of air at $0°,20°\text{ and 30}°$ with reference to Figure 5.6 in the textbook.

Answer to Problem 1PA

The water vapor capacity of air at $0°,20°\text{ and 30}°$ centigrade with reference to Figure 5.6 in the textbook is 6, 18, and 30 grams per cubic meter, respectively. All the values are approximated.

Explanation of Solution

Air holds a certain amount of water vapor at any given temperature. When air holds all the water vapor that it can, it is said to be in its saturated condition and to have reached its moisture capacity. The water vapor capacity or moisture capacity of air is the maximum amount of water vapor that the air can store at a given temperature.

Figure 5.6 in the textbook shows a graph of the maximum amount of water vapor that can be contained in a cubic meter of air over a wide range of temperatures. According to the graph, the water vapor capacity of air at $0°$ centigrade is 6 gram/cubic meter, $20°$ centigrade is 18 gram/cubic meter, and $30°$ centigrade is 30 gram/cubic meter. All the values are approximated.

(b)

To determine

The relative humidity of an air parcel if the temperature is given as $30°\text{C}$ and actual water vapor content is given as 20.5 grams per cubic meter.

Answer to Problem 1PA

The relative humidity of an air parcel if the temperature is given as $30°\text{C}$ and actual water vapor content is given as 20.5 grams per cubic meter is 68.3%.

Explanation of Solution

Relative humidity is the ratio of the amount of water vapor of the given air at that temperature and the maximum amount of water vapor that the air can hold at that temperature. It is expressed in percentages.

The temperature of the air parcel is given as $30°\text{C}$ and the actual water vapor content is given as 20.5 grams per cubic meter. According to the graph in Figure 5.6 in the text book, the water vapor capacity of air at $30°\text{C}$ is 30gram per cubic meter.

The formula to calculate relative humidity is given below:

$\text{Relative Humidity}=\left(\frac{\text{Actual water vapor content in air}}{\text{Maximum water vapor that air can hold}}\right)\times 100\%$

Substitute the values of actual water vapor content in air as 20.5 grams per cubic meter and maximum water vapor that air can hold as 30 grams per cubic meter.

$\begin{array}{c}\text{Relative Humidity}=\left(\frac{\text{Actual water vapor content in air}}{\text{Maximum water vapor that air can hold}}\right)\times 100\%\\ =\left(\frac{20.5}{30}\right)\times 100\\ =68.3\%\end{array}$

(c)

To determine

The actual water vapor content of the air with 60% of relative humidity at 5 degrees centigrade and the new relative humidity if the air is heated to 20 degrees centigrade without increase in water vapor content.

The actual water vapor content of the air with 60% of relative humidity at 5 degrees centigrade is 4.8 gram per cubic meter and the new relative humidity if the air is heated to 20 degrees centigrade without increase in water vapor content is 26.6%.

Explanation of Solution

Relative humidity is the ratio of the amount of water vapor of the given air at that temperature and the maximum amount of water vapor that the air can hold at that temperature. It is expressed in percentages.

The temperature of the air parcel is given as $5°\text{C}$. According to the graph in Figure 5.6 in the text book, the water vapor capacity of air at $5°\text{C}$ is approximately 8 gram per cubic meter.

The formula for the actual water vapor content is given below:

$\text{Actual water vapor content in air}=\left(\frac{\text{Relative Humidity}\times \left\{\begin{array}{l}\text{Maximum water vapor}\\ \text{that air can hold}\end{array}\right\}}{100\%}\right)$

Substitute relative humidity as 60% and maximum water vapor that air can hold as 8 grams per cubic meter.

$\begin{array}{c}\text{Actual water vapor content in air}=\left(\frac{\text{Relative Humidity}\times \left\{\begin{array}{l}\text{Maximum water vapor}\\ \text{that air can hold}\end{array}\right\}}{100\%}\right)\\ =\left(\frac{60\%\times 8\text{gram per cubic meter}}{100\%}\right)\\ =4.8{\text{g/m}}^3\end{array}$

If the temperature of air parcel is raised to $20°\text{C}$, the maximum water vapor that air can hold at that temperature would be 18 grams per cubic centimeter. It is mentioned that there is no increase in water vapor content.

The formula for the relative humidity is given below:

$\text{Relative Humidity}=\left(\frac{\text{Actual water vapor content in air}}{\text{Maximum water vapor that air can hold}}\right)\times 100\%$

Substitute the maximum water vapor that the air can hold as 18 grams per cubic meter and the actual water vapor content in air as 4.8 grams per cubic meter.

$\begin{array}{c}\text{Relative Humidity}=\left(\frac{\text{Actual water vapor content in air}}{\text{Maximum water vapor that air can hold}}\right)\times 100\%\\ =\left(\frac{4.8{\text{gram/m}}^3}{18{\text{gram/m}}^3}\right)\times 100\%\\ =26.6\%\end{array}$