ATMOSPHERIC MOISTURE

Vocabulary

absolute humidity; relative humidity; evaporation; saturation; condensation; sublimation; latent heat of vaporization; dew point temperature; sling psychrometer; dry-bulb thermometer; dry-bulb temperature; air temperature; wet-bulb thermometer; wet-bulb temperature; depression

Behavioral Objectives

The student will be able to determine the relative humidity of the air given the temperature, water vapor content, and capacity.

The student will be able to determine the relative humidity given the air temperature (dry-bulb temperature), the wet-bulb temperature, and the table.

The student will be able to determine the dew point temperature given the air temperature (dry-bulb temperature), the wet-bulb temperature, and the table.

The student will be able to calculate when the air will be saturated given sufficient data.

Introduction

The amount of water present in the air, whether it is in the solid, liquid, or gaseous state, plays an important role in the weather experienced on earth. This amount of water varies considerably and, therefore, its measurement must be reported. One method of stating how much water vapor, water in its gaseous state, is in the air is to state the actual measured weight of water vapor in a given amount of air. This is called the absolute humidity. The absolute humidity, however, does not fully indicate the moisture quality of the air because as the the temperature of the air changes, the amount of water vapor that it can hold (its capacity) changes. Examine the Water Vapor Capacity Table. At higher temperatures the air can hold more water vapor than at lower temperatures, so as the temperature of the air increases, the water vapor capacity also increases. As a result, the absolute humidity alone does not tell the full story about the moisture conditions of the atmosphere. A more complete method of reporting it is by the use of relative humidty. The relative humidity is the amount of water vapor the air actually has (the absolute humidity) compared to the amount of moisture the air can hold at that temperature. Relative humidity is always stated as a percentage, so the formula would be:

Relative Humidity % = (absolute humidity/capacity) x 100

OR

Relative Humidity % = (amount of moisture in the air/maximum amount of water vapor the air can hold at that temperature) x 100

See the sample problem 1. As the amount of water vapor in the air increases, it approaches the capacity or the total amount it can hold. When it reaches this point, the air is said to be saturated, and the relative humidity will be 100%.

One instrument which is used to determine relative humidity is the sling psychrometer. This is an instrument consisting of two thermometers, one of which is plain (the dry-bulb thermometer) and the other of which has a wick or piece of cloth wrapped around the bulb or bottom (the wet-bulb thermometer). The amount of moisture in the air and the temperature of the air both influence how rapidly water will evaporate or change into water vapor and enter the air. As water evaporates, it removes heat to make this change of state. This heat is then stored in the water vapor in the air to be released later when the water vapor returns to its liquid or its solid state by the processes of either condensation or sublimation respectively. The sling psychrometer makes use of these principles. The wick is dampened and as water evaporates from this cloth, heat is taken with it. Thus, the wet-bulb thermometer will register the wet-bulb temperature which is usually lower than the air temperature (the dry-bulb temperature), registered by the dry-bulb thermometer where no evaporation has taken place. This difference in temperature is called the depression. The dry-bulb temperature is always higher than the wet-bulb temperature except for when the air is saturated or the relative humidity is 100%. In this situation, as water evaporates from the wet-bulb, an equal amount of condensation is returning the heat which was lost. Therefore, the two temperatures will be the same. After both thermometers have registered their temperatures and the depression has been determined, tables can be used to find the relative humidity.

As air is cooled and no moisture is added, the relative humidity will increase until the air reaches saturation (100% RH). The temperature of the air when this occurs is called the dew point temperature. Further cooling of the air will result in condensation because the air is no longer capable of holding all of that moisture. Once this air begins to warm again, though, it will no longer have as much water vapor in it as previously, so the relative humidity and dew point temperature will have changed. It is possible to find the dew point temperature of the air by using a sling psychrometer and a table similar to the one used to find the relative humidity. See the sample problem 2.

Review Questions

As air temperature increases, the amount of water vapor the air can hold __________.

The ______________ humidity compares the _________________ humidity to the _______________ and is always stated as a _______________.

Evaporation is a ______________ process and condensation is a _______________ process.

The _______________ is the temperature difference between the _____________ temperature, which is usually higher, and the ____________________ temperature.

When the relative humidity is 100%, the depression will be ____________.

As the air temperature rises and no evaporation occurs, the relative humidity will _______________.

As moisture is added to the air and the temperature remains the same, the relative humidity will ____________.

If the air temperature drops enough, it will reach saturation at the __________________ temperature and as it continues to drop, __________________ will occur.

Answers: increases; relative, absolute, capacity, percentage; cooling, warming; depression, dry-bulb (air), wet-bulb; zero; decrease; increase; dew point, condensation.

Sample Problem 1

What is the relative humidity of the air if the air temperature is 50°F and it contains 2.46 grains of water vapor?

At 50°F the air can hold 4.1 grains of water vapor (from the table)

RH% = 2.46/4.1 X 100 = 0.6 X 100 = 60%

Sample Problem 2

The dry-bulb temperature is 80°F and the wet-bulb temperature is 74°F. What is the depression, the relative humidity, and the dew point temperature?

The depression is the difference between the dry-bulb temperature and the wet-bulb temperature. 80°F - 74° = 6° depression

Using the relative humidity table, find the air temperature of 80° in the left hand column and intersect that horizontal line with the vertical column for a depression of 6° to find the relative humidity. The number at the intersection of the two lines is 75, so the relative humidity is 75%.

Using the dew point table, find the air temperature of 80° and intersect that horizontal line with the vertical column for a depression of 6° to find the dew point temperature. The number at the intersection of those two columns is 72°, so the dew point temperature is 72°F. This means that if the air were to be cooled to 72°F, condensation would begin and the relative humidity would then be 100%.

Sample Problem 3

If the air temperature is 60°F and the relative humidity is 70%, how many grains of moisture does the air presently have? How many must be added for it to reach saturation?

At 60°F the air can hold 5.7 grains of moisture (from table 1). It has 70% of its capacity or (5.7 X .70 =) 3.99 grains of water vapor. It can hold 5.7 but it has only 3.99, so to become saturated (5.7 - 3.99 =) 1.71 grains must be added.

Problems

Complete the tables below.

air temperature water vapor content capacity RH%
40°F 2.9

70°F 4.0

60°F 1.71

90°F 10.29

Air Temperature Wet-Bulb Depression RH Dew Point
25°F 21°F __________ __________ __________
60°F 40°F __________ __________ __________
40°F 37°F __________ __________ __________
80°F 80°F __________ __________ __________
65°F 51°F __________ __________ __________
50°F 50°F __________ __________ __________
15°F 12°F __________ __________ __________
90°F 65°F __________ __________ __________

If air contains one fourth of the total water vapor it could hold, the RH is __________.

The air temperature is 55°F and the depression is 10F. The RH is __________ and the dew point is __________.

The air temperature is 30°F and the RH is 20%. The air contains __________ grains of water vapor.

The air temperature is 50°F and the air contains 2.87 grains of water vapor. The RH is __________. If the temperature drops 10°F, __________ grains of moisture must condense out of the air. If the temperature drops from 50°F to 30°F, __________ grains of moisture must be lost.

The air temperature is 70°F and the relative humidity is 40%. The air contains __________ grains of water vapor. Will adding four grains of moisture saturate the air? __________ How many grains minimum must be added to bring the air just to saturation? __________

Answers: 100%; 50%; 30%; 70%; 4°F, 49%, 10°F; 20°F, 5%, -8°F; 3°F, 75%, 33°F; 0°F, 100%, 80°F; 14°F, 35%, 37°F; 0°F, 100%, 50°F; 3°F, 46%, 0°F; 25°F, 24%, 48°F. 25%; 43%, 33°F; 0.38; 70%, zero, 0.97; 3.2, no, 4.8.

More Practice

Determine the relative humidity if:

the temperature is 30°F and it contains 1.9 grains of water vapor.

the temperature is 50°F and it contains 1.64 grains of water vapor.

the temperature is 70°F and it contains 1.6 grains of water vapor.

the temperature is 80°F and it contains 5.45 grains of water vapor.

the temperature is 80°F and it contains 3.27 grains of water vapor.

the temperature is 50°F and it contains 1.845 grains of water vapor.

the temperature is 40°F and it contains 0.783 grains of water vapor.

the temperature is 60°F and it contains 3.876 grains of water vapor.

the temperature is 30°F and it contains 0.209 grains of water vapor.

the temperature is 70°F and it contains 7.28 grains of water vapor.

the temperature is 30°F and the absolute humidity is 1.9.

the temperature is 70°F and the absolute humidity is 4.0.

the temperature is 70°F and the absolute humidity is 3.20

the temperature is 40°F and the absolute humidity is 0.87

the temperature is 80°F and the absolute humidity is 7.63.

the temperature is 50°F and the absolute humidity is 4.1.

the temperature is 100°F and the absolute humidity is 3.94.

the temperature is 90°F and the absolute humidity is 1.47.

the temperature is 60°F and the absolute humidity is 3.42.

the temperature is 40°F and the absolute humidity is 2.61.

the temperature is 70°F and the absolute humidity is 4.8.

the temperature is 100°F and the absolute humidity is 7.88.

the temperature is 50°F and the absolute humidity is 1.435.

the temperature is 90°F and the absolute humidity is 7.35.

the temperature is 40°F and the absolute humidity is 1.74.

the temperature is 40°F and the absolute humidity is 0.87.

the temperature is 80°F and the absolute humidity is 2.18.

the temperature is 30°F and the absolute humidity is 1.71.

the temperature is 70°F and the absolute humidity is 1.60.

the temperature is 60°F and the absolute humidity is 4.56.

Answers: 100%, 40%, 20%, 50%, 30%, 45%, 27%, 68%, 11%, 91%; 100%, 50%, 40%, 30%, 70%, 100%, 20%, 10%, 60%, 90%, 60%, 40%, 35%, 50%, 60%, 30%, 20%, 90%, 20%, 80%.

Determine the depression, relative humidity, and dew point temperature if the air temperature is:

70°F and the wet-bulb temperature is 60°F.

30°F and the wet-bulb temperature is 26°F.

70°F and the wet-bulb temperature is 69°F.

50°F and the wet-bulb temperature is 42°F.

52°F and the wet-bulb temperature is 52°F.

90°F and the wet-bulb temperature is 65°F.

65°F and the wet-bulb temperature is 65°F.

40°F and the wet-bulb temperature is 28°F.

80°F and the wet-bulb temperature is 66°F.

20°F and the wet-bulb temperature is 16°F.

25°F and the wet-bulb temperature is 24°F.

38°F and the wet-bulb temperature is 38°F.

90°F and the wet-bulb temperature is 76°F.

15°F and the wet-bulb temperature is 11°F.

50°F and the wet-bulb temperature is 47°F.

45°F and the wet-bulb temperature is 45°F.

100°F and the wet-bulb temperature is 94°F.

65°F and the wet-bulb temperature is 55°F.

70°F and the wet-bulb temperature is 56°F.

60°F and the wet-bulb temperature is 60°F.

50°F and the wet-bulb temperature is 47°F.

75°F and the wet-bulb temperature is 75°F.

10°F and the wet-bulb temperature is 6°F.

90°F and the wet-bulb temperature is 74°F.

30°F and the wet-bulb temperature is 30°F.

25°F and the wet-bulb temperature is 19°F.

45°F and the wet-bulb temperature is 33°F.

40°F and the wet-bulb temperature is 40°F.

75°F and the wet-bulb temperature is 71°F.

65°F and the wet-bulb temperature is 57°F.

40°F and the wet-bulb temperature is 36°F.

20°F and the wet-bulb temperature is 17°F.

30°F and the wet-bulb temperature is 30°F.

0°F and the wet-bulb temperature is -2°F.

Answers: 10°F, 55%, 53°F; 4°F, 56%, 18°F; 1°F, 95%, 69F; 8F, 49%, 32°F; 0°F, 100%, 52°F; 25°F, 24%, 48°F; 0°F, 100%, 65°F, 12°F, 7%, -14°F; 14°F, 47%, 58°F; 4°F, 40%, 2°F; 1°F, 87%, 22°F; 0°F, 100%, 38°F; 14°F, 52%, 70°F; 4°F, 29%, -9°F; 3°F, 80%, 44°F; 0°F, 100%, 45°F; 6°F, 80%, 93°F; 10°F, 52%, 47°F; 14°F, 40%, 44°F; 0°F, 100%, 60°F; 3°F, 80%, 44°F; 0°F, 100%, 75°F; 4°F, 13%, -27°F; 16°F, 47%, 67°F; 0°F, 100%, 30°F; 6°F, 25%, -3°F; 12°F, 18%, 7°F; 0°F, 100%, 40°F; 4°F, 82%, 69°F; 8°F, 61%, 51°F; 4°F, 68%, 30°F; 3°F, 55%, 8°F; 0°F, 100%, 30°F; 2°F, 33%, -20°F.

If the air contains 1/2 of the water vapor it could hold, the RH is __________.

The air temperature is 80°F and the RH is 80%. If the temperature drops to 70°F, __________ grains of water vapor will be lost, and if it drops to 60°F, _____________ grains will be lost.

The air temperature is 60°F and the RH is 58%. Will adding two grains of moisture saturate the air? __________ What if three grains are added? __________

When the air temperature is 50°F and it contains 0.41 grains of water vapor, the relative humidity is __________.

When the air temperature is 60°F and it contains 2.85 grains of water vapor, the relative humidity is __________.

The air temperature is 40°F and the RH is 90%. The air contains __________ grains of water vapor.

The air temperature is 80°F and it contains 7.63 grains of water vapor. The addition of __________ grains of water vapor would saturate the air.

The air temperature is 30°F and the RH is 20%. The air needs __________ more grains of water vapor before the RH will reach 100%.

The air temperature is 50°F and the RH is 30%. The air contains __________ grains of water vapor.

The air temperature is 50°F and the air contains 3.28 grains of water vapor. The RH is __________. If the temperature drops 10F, __________ grains of water vapor must condense out of the air. If the temperature drops from 40°F to 30°F, __________ more grains of moisture must be lost.

The air temperature is 30°F and the RH is 30%. The air contains __________ grains of water vapor. Will adding 1.3 grains of moisture saturate the air? __________ How many grains minimum must be added to bring the air just to 100% RH? __________

Answers: 50%; 0.72, 3.02; no, yes; 10%; 50%; 2.61; 3.27; 1.52; 1.23; 80%, 0.38, 1.0; 0.57, no, 1.33.