Tue., Sep. 12 notes

Tue., Sep. 12, 2006

"Storm Clouds" on the horizon (i.e. various things that are due or coming due in the not too distant future)

The 1S1P reports were collected today. It will take some time to grade all these reports. You should expect to start seeing some of the reports being returned next week.
The Optional Assignment is due Thursday (extra copies still available)
The Experiment #1 reports are due next Tuesday. You should complete the experiment and return

your materials this week.

Quiz #1 is Thursday next week (Sept. 21). A preliminary version of the Quiz #1 Study Guide is now available.

There is a new reading assignment

Now don't get discouraged and think that there are only black clouds headed our way. There are some good things coming this week also. Here is one of them, here is another.

The practice quizzes have been graded. Answers to the questions are online. The average grade (60%) was quite a bit lower than average grades in past NATS 101 courses. The instructor made two suggestions: (1) that you get your notes organized, keep everything (hand written notes and photocopied class notes) together in one place and (2) that you briefly look over your notes after each class (if they don't make sense then they won't make any more sense in a week or two when it comes time to study for the next quiz). If there is a part of one class that you don't understand ask questions now, don't wait until just a day or two before the next quiz.

Today we will try to understand why warm air rises and cold air sinks. This will be a three step process.

When you fill a balloon with air you really aren't filling it with air. You put some air molecules into the balloon but the inside of the balloon is still mostly empty space. So what keeps the balloon inflated? It is the rapid motions (they're moving around at 100s of MPH) of the air atoms and molecules. When they collide with and bounce off the inside walls of the balloon they push outward. This outward force (divided by the area on which it is exerted) is pressure. The ideal gas law equations tell you what determines how strong or weak the pressure will be.

When you warm or cool a parcel (a volume) of air in the atmosphere, the parcel will expand or shrink. It does this in an attempt to keep the pressure inside the parcel constant. The pressure of the air inside the parcel that is pushing out stays the same as the pressure of the air outside the parcel pushing in. This is a special situation involving the ideal gas law. This is called Charles' Law. We will find that a parcel of air that is warmer than the surrounding air will have lower density than the surrounding air. Air that is colder than the surrounding air will have higher density than the surrounding air.

Once we understand how air parcels behave when warmed or cooled we can look at the forces that act on air parcels. Small changes in one or the other of these forces will determine whether a parcel of air rises or sinks (or just remains stationary).

The pressure produced by the air molecules inside a balloon will first depend on how many air molecules are there.
As you add air to a bicycle tire the tire pressure increases.

Air pressure inside a balloon also depends on the size of the balloon. Pressure is inversely proportional to volume, V (increasing V decreases P and vice versa).

Note it is possible to keep pressure constant by changing N and V together in just the right kind of way. This is what happens in the experiment that some of you are working on. As oxygen is removed from an air sample, the air sample volume decreases and pressure of the air sample stays constant.

You shouldn't throw a can of spray paint into a fire. The pressure of the gas inside a container depends on the gas temperature.

The volume of the can doesn't change. Heating the gas inside the can increases the pressure. If the pressure gets high enough the can explodes.

Surprisingly the pressure does not depend on the mass of the molecules. Pressure doesn't depend on the composition of the gas. Gas molecules with a lot of mass will move slowly, the less massive molecules will move more quickly. They both will collide with the walls of the container with the same force.

Here are the two ideal gas law equations. You can ignore the constants k and R if you are just trying to understand how a change in one of the variables would affect the pressure. You only need the constants when you are doing a calculation involving numbers.

(1) Pressure = (Number of air molecules) multiplied by temperature divided by volume
or
(2) Pressure = (density) multiplied by (temperature)

Air in the atmosphere behaves like air in a balloon. A balloon can grow or shrink in size depending on the pressure of the air inside.

We start in the upper left hand corner with air inside a balloon that is exactly the same as the air outside. The air inside and outside have been colored green. The arrows show that the pressure of the air inside pushing outward and the pressure of the air surrounding the balloon pushing inward are all the same.

Next week warm the air in the balloon. The ideal gas law equation tells us that the pressure of the air in the balloon will increase. The increase is momentary though. Because the pressure inside is now greater than the pressure outside the balloon will expand. An increase in volume will reduce the pressure of the air inside. Eventually the balloon will expand just enough that the pressures inside and outside are again in balance. You end up with a balloon of warm low density air that has the same pressure as the air surrounding it.

You can use the same reasoning to understand that cooling a balloon will cause its volume to decrease. You will end up with a balloon filled with cold high density air. The pressures inside and outside the balloon will be the same.

These associations: warm air = low density air and cold air = high density air are important and will come up a lot during the remainder of the semester.

In the atmosphere air temperature and air density change together in a way that keeps pressure constant. This is Charles's Law and was demonstrated in class. The demonstration is illlustrated and described at the top of p. 54 in the photocopied notes.

As temperature changes, the volume and density also change in a way that keeps pressure inside the balloon constant (the pressure inside is always staying equal to and in balance with the air pressure outside the balloon).

Air in the atmosphere behaves like a balloon. A change in temperature causes air density to change in order to keep pressure inside and outside the balloon equal. We will now look at the forces acting on a parcel or balloon of air.

Air has mass and weight (Galileo may have been the first person to prove that air had weight, here is a description of the experiment that he may have performed). When an air parcel has the same temperature, pressure, and density as the air around it, the parcel will remain stationary. With gravity pulling downward on the air, there must be another force pointing upward of equal strength. The upward force is caused by pressure differences between the bottom (higher pressure pushing up) and top of the balloon (slightly lower pressure pushing down on the balloon).

If the balloon is filled with warm, low density air the gravity force will weaken (there is less air in the balloon so it weighs less). The upward pressure difference force (which depends on the surrounding air) will not change. The upward force will be stronger than the downward force and the balloon will rise.

Conversely if a balloon is filled with cold low density air, gravity will strengthen and the balloon will sink.

We modified the demonstration somewhat (see bottom of p. 54 in the photocopied class notes). We used a balloon filled with helium instead of air. Helium is less dense than air even when the helium has the same temperature as the surrounding air. A helium filled balloon doesn't need to warmed up in order to rise.

We dunked the helium filled balloon in some liquid nitrogen to cool it and to cause the density of the helium to increase. When removed from the liquid nitrogen the balloon can't rise, the gas inside is denser than the surrounding air. As the balloon warms and expands its density decreases. Eventually the balloon becomes less dense than the surrounding air and lifts off from the table.

A balloon pilot can adjust the temperature (and thereby the density) of the air inside a balloon and make the balloon rise or sink.

The upward pressure difference force is really just the bouyant force in Archimedes Law. Archimedes Law is another attempt to understand and explain why objects float or sink. Archimedes Law is discussed on pps 53a and 53b in the photocopied class notes. This wasn't discussed in class. I did mention a hidden optional assignment, however.

In the last 10 or 15 minutes of class we watched a couple more video segments. The first showed Auguste and Jacques Piccard's descent to 10,000 ft. depth in the ocean in a bathyscaph. The second discussed the first successful flight around the globe non-stop in a balloon. Bertrand Piccard was a member of the two -man team.