The atmosphere and the weather

Why do rising parcels of air cool?

Remember that an air parcel is a bubble of air enclosed within an imaginary, elastic boundary keeping it separated from the rest of the air. No gas leaves or enters the parcel, but the shape of the parcel is allowed to change. The air pressure inside the parcel will always adjust itself to be the same as the air pressure in the surrounding environment. So when a parcel is lifted in the atmosphere, its air pressure decreases to match that of the surrounding air. Since the air pressure outside the parcel decreases as the parcel is lifted, the parcel will expand as it is lifted. This means that the number density of air in the parcel decreases (same number of gas molecules but in a larger or expanded volume). Energy is used to expand the parcel (increase its size), so the temperature of the parcel also decreases. Mathematically, the pressure, number density, and temperature of a gas are related in an equation called the gas law:

pressure

=

temperature

x

number density

x

constant

Pressure decreases when a parcel is lifted. From the gas law, the (number density x temperature) must also decrease. Both number density and temperature decrease when a parcel expands. Conversely, when an air parcel is lowered in the atmosphere, it is compressed because the air pressure outside the parcel increases. When parcels are lowered the air pressure, number density, and temperature of the gas in the parcel increase. In this case energy from the surrounding atmosphere is used to compress the parcel (decrease its size). This transfer of energy from surrounding environment to parcel acts to increase the parcel temperature.

A couple of everyday examples may help you to keep this straight. When air under high pressure, like that contained in an spray can or a bicycle tire, is released it feels cold. The spray nozzle or tire valve get cold because the air that is coming out is expanding and cooling. When air is compressed, like when operating a bicycle pump, it feels warm. The pump gets warm because air is getting compressed and warmed.

Key points:

1. When an air parcel moves upward, the air temperature in the parcel decreases because it is expanding.
2. When an air parcel moves down, the air temperature in the parcel increases because it is being compressed.
3. Because we do not allow air inside a parcel to mix with air outside the parcel, the atmospheric temperature outside of the air parcel has no effect on the air temperature inside the parcel. In other words, changes in the air temperature within a rising (or sinking) parcel result from changes in the outside air pressure alone. The air temperature within a rising (or sinking) parcel does not have to be the same as the temperature of the air surrounding the parcel.

An in-class demonstration "Cloud in a bottle" will be done to illustrate some of the aspects of cloud formation.

Rules for moving air parcels up and down in the atmosphere

1. The starting temperature and water vapor content (use the dew point) of the parcel is taken to be the measured conditions at ground level. You will always be given this information.

2. As long as the parcel is unsaturated (relative humidity < 100% or whenever the dew point temperature of the parcel less than the temperature of the parcel), the rate of cooling is 10°C for every 1000 meters the parcel is lifted.

3. As a rising parcel cools, its relative humidity increases. Once the relative humidity reaches 100% (determined when the parcel temperature cools down to its original dew point temperature), further lifting (and cooling) results in net condensation, forming a cloud. Remember that an air parcel will never contain more water vapor than its capacity or saturation mixing ratio.

   Since condensation releases latent heat within the parcel, the rate of cooling is slower. Parcels which are saturated cool at a rate of 6°C for every 1000 meters the parcel is lifted. Also keep in mind that once a cloud begins to develop in a parcel, just enough water vapor will condense into liquid water so that the air in the parcel remains saturated (relative humidity = 100% and the dew point temperature equals the air temperature inside the parcel).

4. When lowering an air parcel in the atmosphere, the temperature changes are reversed. If there is no cloud (liquid water) in the parcel, the air temperature in the parcel increases at a rate of 10°C for every 1000 meters the parcel is lowered.

   If there is a cloud in the parcel, it will evaporate because as the parcel warms its capacity for water vapor increases. As long as there is still a cloud (liquid water) in the parcel, just enough water will evaporate to keep the relative humidity at 100% and the dew point temperature equals the air temperature. Since it takes energy to evaporate water, the rate of heating is slower. Parcels which contain an evaporating cloud warm at a rate of 6°C for every 1000 meters the parcel is lowered until the entire cloud has evaporated.

Numerical example for raising and lowering an air parcel

Now lets look at a numerical example. Below is a link to two tables. The first table shows you what you would know about the atmosphere before performing lifting a surface parcel upward. You would have to determine at what altitude a cloud would form by filling in the blanks. The second table shows the solution. NOTE: dont worry about the columns labeled environmental temperature and stability, we have not covered that material yet. We will go over the solution in detail during class. Click Here to view the example.