Tuesday Sept. 14, 2010
click here to download today's notes in a more printer friendly format

A couple of songs from the Playing for Change/Song Around the World DVD.  The first was War/No More Trouble (I think - it might have been Don't Worry) the second was about the best version of Stand By Me that I've ever heard.

The Practice Quiz has been graded and was returned in class today.  Practice Quiz scores are usually pretty low.  The average for this class was above average.  The 1st, real, quiz will cover material that was on the Practice Quiz and new material that we cover between now and the end of class on Tuesday, Sep. 21.
Semester
 MWF class
T Th class
F10
 60%
 67%
S10
 62%
 61%
F09
 66%
 68%
S09
 60 %
 ---
F08
 64%
 65%
S08
 64%
 66%

Here are some questions from an In class Optional Assignment that I gave the other section last Friday (I owe you an In-class assignment like this one - maybe Thursday).  We'll be covering material today that relates to questions 1 and 2,





Here are answers to the questions.

We spent the first 3/4 of the class trying to really understand why warm air rises and cold air sinks.

Hot air balloons rise (they also sink), so does the relatively warm air in a thunderstorm (its warmer than the air around it).   Conversely cold air sinks.  The surface winds caused by a thunderstorm downdraft (as shown above) can reach speeds of 100 MPH and are a serious weather hazard.

A full understanding of these rising and sinking motions is a 3-step process (the following is from the bottom part of p. 49 in the photocopied ClassNotes)
We will first learn about the ideal gas law.  That is an equation that tells you which/how properties of the air inside a balloon work to determine the air's pressure.  Then we will look at Charles' Law, a special situation involving the ideal gas law (air temperature and density change together in a way that keeps the pressure inside a balloon constant).  Then we'll learn about the vertical forces that act on air (an upward and a downward force).

Students working on Experiment #1 will need to understand the ideal gas law to be able to explain why/how their experiment works.

The figure above makes an important point: the air molecules in a balloon "filled with air" really take up very little space.  A balloon filled with air is really mostly empty space.  It is the collisions of the air molecules with the inside walls of the balloon that keep it inflated.


Up to this point in the semester we have been thinking of pressure as being determined by the weight of the air overhead.  Air pressure pushes down against the ground at sea level with 14.7 pounds of force per square inch.  If you imagine the weight of the atmosphere pushing down on a balloon sitting on the ground you realize that the air in the balloon pushes back with the same force.  Air everywhere in the atmosphere pushes upwards, downwards, and sideways. 

The ideal gas law equation is another way of thinking about air pressure, sort of a microscopic scale version.  We ignore the atmosphere and concentrate on just the air inside the balloon.  We are going to "derive" an equation.  Pressure (P) will be on the left hand side.  Relevant properties of the air inside the balloon will be found on the right side of the equation.
In A
the pressure produced by the air molecules inside a balloon will first depend on how many air molecules are there, N.  If there weren't any air molecules at all there wouldn't be any pressure.  As you add more and more add to something like a bicycle tire, the pressure increases.  Pressure is directly proportional to N; an increase in N causes an increase in P.  If N doubles, P also doubles (as long as the other variables in the equation don't change).

In B
air pressure inside a balloon also depends on the size of the balloon.  Pressure is inversely proportional to volume, V .  If V were to double, P would drop to 1/2 its original value.

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 Experiment #1 that some students are working on.  Oxygen in a graduated cylinder reacts with steel wool to form rust.  Oxygen is removed from the air sample which is a decrease in N.  As oxygen is removed, water rises up into the cylinder decreasing the air sample volume.  N and V both decrease in the same relative amounts and the air sample pressure remains constant.  If you were to remove 20% of the air molecules, V would decrease to 20% of its original value and pressure would stay constant.

Part C: Increasing the temperature of the gas in a balloon will cause the gas molecules to move more quickly.  They'll collide with the walls of the balloon more frequently and rebound with greater force.  Both will increase the pressure.  You shouldn't throw a can of spray paint into a fire because the temperature will cause the pressure inside the can to increase and the can could explode. 

Surprisingly, as explained in Part D, 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.

The figure below (which replaces the bottom of p. 51 in the photocopied ClassNotes) shows two forms of the ideal gas law.  The top equation is the one we just derived and the bottom is a second slightly different version.  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 (which we won't be doing).



Charles' Law is a special case involving the ideal gas law.  Charles Law requires that the pressure in a volume of air remain constant.  T, V, and density can change but they must do so in a way that keeps P constant.  This is what happens in the atmosphere.  A volume of air is free to expand or shrink.  It does so to keep the pressure inside the air volume constant (the pressure inside the volume is staying equal to the pressure of the air outside the volume).

Read through the explanation on p. 52 in the photocopied Classnotes.  In the atmosphere a parcel (balloon) of air will always try to keep its pressure the same as the pressure of the surrounding air.  If they aren't equal the parcel will either expand or shrink until they are again equal.

If you warm air it will expand and density will decrease until the pressure inside and outside the parcel are equal.
If you cool air the parcel will shrink and the density will increase until the pressures balance.

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

Click here if you would like a little more detailed, more step-by-step, explanation of Charles Law.  Here's a visual summary of Charles' Law (this figure wasn't shown in class)


If you warm a parcel of air the volume will increase and the density will decrease.  Pressure inside the parcel remains constant.  If you cool the parcel of air it's volume decreases and its density increases.  Pressure inside the parcel remains constant.

Charles Law can be demonstrated by dipping a balloon in liquid nitrogen.  You'll find an explanation on the top of p. 54 in the photocopied ClassNotes.


The balloon had shrunk down to practically zero volume when pulled from the liquid nitrogen.  It was filled with cold high density air.  As the balloon warmed the balloon expanded and the density of the air inside the balloon decreased.  The volume and temperature kept changing in a way that kept pressure constant.  Eventually the balloon ends up back at room temperature (unless it pops while warming up).

And finally the last step toward understanding why warm air rises and cold air sinks.  We'll have a look at the forces that act on parcels of air in the atmosphere.  This information is found on p. 53 in the photocopied ClassNotes.




Basically it comes down to this - there are two forces acting on a parcel* of air in the atmosphere:
1. Gravity pulls downward.  The strength of the gravity force depends on the mass of the air inside the parcel.  This force is just the weight of the parcel
2. There is an upward pointing pressure difference force.  This force is caused by the air outside (surrounding) the parcel.  Pressure decreases with increasing altitude.  The pressure of the air at the bottom of a parcel pushing upward is slightly stronger than the pressure of the air at the top of the balloon that is pushing downward.  The overall effect is an upward pointing force.

When the air inside a parcel is exactly the same as the air outside, the two forces are equal in strength and cancel out.  The parcel is neutrally bouyant and doesn't rise or sink.

If you replace the air inside the balloon with warm low density air, it won't weigh as much.  The gravity force is weaker.  The upward pressure difference force doesn't change (because it is determined by the air outside the balloon which hasn't changed) and ends up stronger than the gravity force.  The balloon will rise.

Conversely if the air inside is cold high density air, it weighs more.  Gravity is stronger than the upward pressure difference force and the balloon sinks.

* the word parcel just means a small volume of air.

We spent the last portion of the period looking at how temperature changes with increasing altitude in the atmosphere.  Temperature can increase, decrease, even remain constant with increasing altitude.  The figures below are more clearly drawn versions of what was done in class.


The atmosphere can be split into layers depending on whether temperature is increasing or decreasing with increasing altitude.  The two lowest layers are shown in the figure above.  There are additional layers (the mesosphere and the thermosphere) above 50 km but we won't worry about them. 

1. We live in the troposphere.  The troposphere is found, on average, between 0 and about 10 km altitude, and is where temperature usually decreases with increasing altitude.  [the troposphere is usually a little higher in the tropics and lower at polar latitudes]

The troposphere contains most of the water vapor in the atmosphere (the water vapor comes from evaporation of ocean water and then gets mixed throughout the troposphere by up and down air motions) and is where most of the clouds and weather occurs.  The troposphere can be stable or unstable (tropo means to turn over and refers to the fact that air can move up and down in the troposphere).

2a. The thunderstorm shown in the figure with its strong updrafts and downdrafts indicates unstable conditions.  When the thunderstorm reaches the top of the troposphere, it runs into the bottom edge of the stratosphere which is a very stable layer.  The air can't continue to rise into the stratosphere so the cloud flattens out and forms an anvil (anvil is the name given to the flat top of the thunderstorm).   The flat anvil top is something that you can go outside and see and often marks the top of the troposphere.

2b.  The summit of Mt. Everest is a little over 29,000 ft. tall and is close to the average height of the top of the troposphere.

2c.   Cruising altitude in a passenger jet is usually between 30,000 and 40,000, near or just above the top of the troposphere, and at the bottom of the stratosphere.

3.  Temperature remains constant between 10 and 20 km and then increases with increasing altitude between 20 and 50 km.  These two sections form the stratosphere.  The stratosphere is a very stable air layer.  Increasing temperature with increasing altitude is called an inversion.  This is what makes the stratosphere so stable.

4.   A kilometer is one thousand meters.  Since 1 meter is about 3 feet, 10 km is about 30,000 feet.  There are 5280 feet in a mile so this is about 6 miles (about is usually close enough in this class). 



5.   Sunlight is a mixture of ultraviolet (7%), visible (44%), and infrared light (49%).  We can see the visible light.

5a. On average about 50% of the sunlight arriving at the top of the atmosphere passes through the atmosphere and is absorbed at the ground (20% is absorbed by gases in the air, 30% is reflected back into space).  This warms the ground.  The air in contact with the ground is warmer than air just above.  As you get further and further from the warm ground, the air is colder and colder.  This explains why air temperature decreases with increasing altitude in the troposphere.

5b. How do you explain increasing temperature with increasing altitude in the stratosphere.  

     The ozone layer is found in the stratosphere (peak concentrations are found near 25 km altitude).  Absorption of ultraviolet light by ozone warms the air in the stratosphere and explains why the air can warm.  The air in the stratosphere is much less dense (thinner) than in the troposphere.  So even though there is not very much UV light in sunlight, it doesn't take as much energy to warm this thin air as it would to warm denser air closer to the ground.

6. I didn't mention this point in class.  That's a manned balloon; Auguste Piccard and Paul Kipfer are inside.  They were the first men to travel into the stratosphere (see pps 31 & 32 in the photocopied Class Notes)  We'll have a look at a short segment of video at some point that describes their voyage.  It really was quite a daring trip at the time at the time, and they very nearly didn't survive it.