Lab 7: Humidity

Lab 7 Humidity
The purpose of this lab is to introduce the methods that are used to measure and express humidity. Humidity pertains to the quantity of water vapor in the atmosphere. Recall that water is a variable component of the atmosphere in that amounts vary from place to place and over time. Water vapor is an important component of our atmosphere because it is directly related to cloud formation and precipitation processes.

The amount of water vapor that can exist in a volume of air is dependent on the temperature of the volume of air. The warmer the air, the greater the potential uptake of water vapor into the atmosphere. As the temperature of a volume of air increases, the water vapor capacity also increases.

As a volume of air achieves the maximum uptake of water vapor it becomes saturated. Saturation occurs as the rate of evaporation and the rate of condensation are equal. Any additional uptake of water vapor molecules into the air will result in active condensation (the phase change of water vapor to liquid water). Condensed water droplets in the atmosphere are known as cloud droplets and are very important to the formation of clouds.

A sling psychrometer is an instrument that can measure humidity in the atmosphere. The instrument contains two thermometers that are attached to a swivel and handle. The bulb (base) of one of the thermometers is covered in cloth that has soaked in distilled water and is known as the “wet bulb”. The wet bulb thermometer provides the “wet bulb temperature” (WBT). The other thermometer is not covered with cloth and remains dry. The dry thermometer provides the “dry bulb temperature” (DBT). The dry bulb temperature equates to the actual temperature (slinging the thermometer does not have an effect on the actual temperature).

Once the wet bulb is saturated, the psychrometer is briskly rotated for at least 60 seconds. The temperature of both the wet bulb and the dry bulb are then recorded.

To determine the relative humidity, the temperature of the wet bulb is subtracted from the temperature of the dry bulb. This is known as the “wet bulb depression”. The temperature of the dry bulb and the wet bulb depression are applied to the Relative Humidity table (see Table 1, below).

Table 1. Relative humidity table. Relative humidity (%RH) is determined by intersecting the wet bulb depression (in the ‘X’ axis on the table) with the dry bulb temperature in the ‘Y’ axis.
For example, if the dry bulb temperature (DBT) is 20°C and the wet bulb temperature is 16°C, the wet bulb depression is 4 C°; locate 4 C° in the ‘X’ axis and where the value intersects the dry bulb temperature (20°C) along the ‘Y’ axis, a relative humidity value of 66 (or 66% RH) is indicated.

The temperature of the wet bulb is almost always less than that of the dry bulb because, during the “slinging” of the psychrometer, water evaporates from the saturated cloth that surrounds the wet bulb, which cools the wet bulb. If there is no difference between the wet bulb and the dry bulb temperatures, no water from the wet bulb cloth was able to evaporate into the air because the air would be saturated or 100% RH.

The dew point temperature can also be determined using the same wet and dry bulb readings from the sling psychrometer. Dew point temperature is the temperature at which air becomes saturated and can be determined using Table 2, below.

Table 2. Dewpoint Temperature Table. The dewpoint temperature (°C) is determined by plotting the temperature of the dry bulb in the ‘Y’ axis and the wet bulb depression (dry bulb minus wet bulb) in the ‘X’ axis.

For example, if the dry bulb temperature (DBT) is 20°C and the wet bulb temperature is 16°C, the wet bulb depression is 4 C°; locate 4 C° in the ‘X’ axis and where the value intersects the dry bulb temperature (20°C) along the ‘Y’ axis, the dewpoint temperature of 14°C is indicated.

Using the tables 1 and 2, above, complete the following: Please use the correct annotation (°C, or % RH, for example). Enter your answers into the Lab 7 answer submission sheet that can be found under the Lab 7 module.
1. On a warm summer afternoon the temperature outside is 36°C (97°F). Upon slinging the psychrometer, the wet bulb temperature is 20°C (68°F). What is the relative humidity?
2. Using the psychrometer readings from #1 (above), what is the temperature of dewpoint?
3. Given the information from #s 1 and 2 (above), how many C° must the temperature drop before the air becomes saturated?
4. The temperature is 23°C (73°F) and the wet bulb temperature from your sling psychrometer is 15°C (59°F). What is the relative humidity? The correct answer will require averaging between two humidity values from the table:
(humidity value 1 + humidity value 2) / 2
5. Using the same information from #4 (above), what is the dewpoint temperature? Again, the correct answer will require averaging between the two temperature values from the table:
(temperature 1 + temperature 2) / 2
6. On a warm day, someone suggests that it feels like Florida because of the humidity. You decide to measure the humidity by using your sling psychrometer. The temperature is 30°C (86°F) and the wet bulb temperature is 28°C (82°F). What is the relative humidity?

Another method to measure the humidity in the air involves the Mixing Ratio. The Mixing Ratio, often referred to as the Actual Mixing Ratio (AMR), is the mass of water vapor in a mass of dry air and described as grams of water vapor per kilogram of dry air (g/kg). Do not let the term “mixing ratio” confuse you, the term “ratio” describes the amount of water vapor (in grams) that is proportional to the volume dry air (1 kilogram). Water vapor and other components, including nitrogen, argon, and oxygen, are within a mixture of gasses that we refer to as “air”.

While readings from a sling psychrometer do not immediately provide the mass of water vapor as grams per kilogram of air, the wet and dry bulb temperatures can be applied to tables that, given the temperature, the grams of water vapor per kilogram of dry are identified. The maximum amount of water vaper per kilogram of dry air or Saturation Mixing Ratio (SMR) are well documented.

The formula to calculate relative humidity (RH) is:
AMR / SMR (x100) = % RH
Where:
AMR = Actual Mixing Ratio: the measured grams of water vapor per kilogram of dry (or g/kg)
SMR = Saturation Mixing Ratio: the maximum mass of water vapor that can exist in a kilogram of dry air

Figure 1. Saturation Mixing Ratio of Water Vapor. The graph includes the temperature (°C) on the ‘X’ axis and the maximum amount (or capacity) of water vapor per kilogram of dry air (g/kg) on the ‘Y’ axis.

Depending on the given variables, the saturation curve can be used in the following scenarios:

A. If the actual mixing ratio is known, the temperature at which dew point (or saturation) occurs can be determined by intersecting the number of grams per kilogram (along the y-axis) with the saturation curve then determine the associated dewpoint temperature (along the x-axis).

B. If the actual temperature (also known as the “dry bulb” temperature) is known (along the x-axis) the saturation curve will provide the capacity in grams/kilogram (g/kg) of water vapor (along the y-axis) for the specified temperature.

C. If temperature and relative humidity for a volume of air are known, the actual mixing ratio can be determined: multiply the saturation mixing ratio (g/kg) for the given temperature by the RH value, then divide by 100

Refer to the RH formula and saturation curve (above) to complete the following problems. Do not enter any “naked” numbers, be sure that your answers include either “degrees C”, “k/kg”, or “% RH” as appropriate.
7. What is the water vapor capacity (in g/kg) for a volume of air with a temperature of 30°C?
8. If the air is saturated with at 15 g/kg of water vapor, what is the temperature of the volume of air?
9. What is the relative humidity for a volume of air if the AMR is 5 g/kg and the SMR is 8 g/kg?
10. If the temperature in this room is 20?C (68?F) and the AMR is 8 g/kg. What is the relative humidity of the air in the room?
11. If the temperature outside is 15?C and the AMR is 5 g/kg. At what temperature would dew point occur?
12. The temperature outside is 32?C (90?F) and the RH is 25%. What is the AMR?
13. What relationship generally exists between water vapor capacity and temperature?

Adiabatic Processes
As a parcel of air rises the pressure decreases and the temperature of the parcel decreases due to expansion. The process of cooling (or warming) due to expansion (or compression) without gaining or extracting heat energy is referred to as “adiabatic”.
If a parcel of air is unsaturated (its relative humidity is less than 100%) it will cool at Dry Adiabatic Lapse Rate (DALR) – 5.5 F° per 1000 feet (10 C°/km). If the parcel of air ascends and cools to dewpoint temperature, the air becomes saturated and condensation occurs. The ascending, saturated air continues to cool adiabatically but at a lower rate. The lower rate is called Saturated Adiabatic Lapse Rate (SALR). The average saturated rate is 3.3 F° per 1000 feet (6° C/km). The 3.3 F° per 1000 feet (6° C/km) rate is an average, in reality the saturated rate can vary and be as low as 2 F°/1000 feet.

Figure 2. Air over a mountain range.

Refer to Figure 2 (above) for questions 14-22 and assume that a parcel of air on the windward side is forced to rise up and over a 6000 feet mountain.
The initial temperature at the base of the mountain at 0’ is 76.5° F.
The lifting condensation level, or the elevation where the parcel becomes saturated, is 3000 feet.
The DALR is 5.5 F° /1000 feet
The SALR is 3.3 F°/1000 feet

Determine the temperature of the parcel of air at the following elevations as it rises up the windward side of the mountain (Figure 2).
14. 1000’
15. 3000’
16. 6000’

Once the parcel of air crests the summit, the air descends on the leeward side of the mountain. As the air descends, the air immediately becomes less than saturated as it descends and warms by compression at the dry rate.
Determine the temperature for each of the elevations (below) as the dry parcel of air descends on the leeward side of the mountain (Figure 2).
17. 2000’
18. 0’
19. Is the temperature at 0’ on the leeward side of the mountain warmer or cooler than the initial temperature at 0’ on the windward side?
20. Briefly explain why the temperature difference exists between 0’ on the windward side of the mountain and 0’ on the leeward side.
21. Assuming that no additional water vapor is added to the atmosphere as the air crests the mountain and begins to descend (i.e. the AMR remains constant), will the relative humidity on the leeward side of the mountain increase, decrease, or remain the same as the parcel of air descends from 6000 feet to 0 feet?
22. Provide a brief explanation for your answer (from #21 above):