Tuesday, Sep. 11, 2012
click here to download a more printer friendly version of today's notes

Three songs from one of my favorite local groups: Calexico.  I played "Alone Again Or", "Quattro (World Drifts In)",  and the "Ballad of Cable Hogue".  There's a good chance Calexico will be back on Thursday together with Mariachi Luz de Luna (another local group that often plays with Calexico) to celebrate the upcoming "El Grito de la Independencia" holiday on Sept. 16 (Mexican independence from Spain).

The first set of 1S1P reports was collected today.  It usually takes some time to get all of these graded.  I will try not to make a new assignment until you get at least one of your reports back.

The first Optional Assignment is due at the start of class on Thursday.  There's a good chance that there will be an In-class Optional Assignment on Thursday also.

Today was the "last call" for Expt. #1.  If you didn't pick up materials you'll need to try to do Expt. #2 or Expt #3.

The Practice Quiz has been graded and was returned in class today.  The average was 66% which, as you can seen from the table below, is pretty typical.


MWF class
 T Th class
F12
 66%
 66%
F11
 65%
 65%
F10
 60%
 67%
F09
 66%
 68%
F08
 64%
 65%

If you didn't take the Practice Quiz you can download a copy.  I would suggest you do that so that you can become familiar with the quiz format.  Here are answers to the questions on the Practice Quiz.

We've spent the last couple of classes looking at air pressure and how it changes with altitude.  Today we'll consider air density and air temperature.

How does air density change with increasing altitude?  You should know the answer to that question.  You get out of breath more easily at high altitude than at sea level.  Air gets thinner (less dense) at higher altitude.  A lungful of air at high altitude just doesn't contain as much oxygen as at lower altitude or at sea level. 

Because air is compressible, a stack of mattresses might be a more realistic representation of layers of air than a pile of bricks.


Four mattresses are stacked on top of each other.  Mattresses are reasonably heavy, the mattress at the bottom of the pile is compressed by the weight of the three mattresses above.  This is shown at right.  The mattresses higher up aren't squished as much because their is less weight remaining above.  The same is true with layers of air in the atmosphere.


The statement above is at the top of p. 34 in the photocopied ClassNotes.  I've redrawn the figure found at the bottom of p. 34 below.

There's a lot of information in this figure and it is worth spending a minute or two looking at it and thinking about it.

1. You can first notice and remember that pressure decreases with increasing altitude.  1000 mb at the bottom decreases to 700 mb at the top of the picture.  You should be able to explain why this happens.

2.  Each layer of air contains the same amount (mass) of air.  This is a little more subtle.  You can tell because the pressure drops by 100 mb as you move upward through each layer.   Pressure depends on weight.  So if all the pressure changes are equal, the weights of each of the layers must be the same.  Each of the layers must contain the same amount (mass) of air (each layer contains 10% of the air in the atmosphere). 

3. The densest air is found at the bottom of the picture.  The bottom layer is compressed the most because it is supporting the weight of all of the rest of the atmosphere.  It is the thinnest layer in the picture and the layer with the smallest volume.  Since each layer has the same amount of air (same mass) and the bottom layer has the smallest volume it must have the highest density.  The top layer has the same amount of air but about twice the volume.  It therefore has a lower density (half the density of the air at sea level).  Density is decreasing with increasing altitude.

4.  Finally pressure is decreasing most rapidly with increasing altitude in the densest air in the bottom layer.  This is something we covered at the end of class a week ago.

What happens to air temperature with increasing altitude.  Again, our personal experience is that it decrreases with increasing altitude.  It is colder at the top of Mt. Lemmon than it is here in the Tucson valley.

That is true up to an altitude of about 10 km (about 30,000 ft.).  People were very surprised in the early 1900s when they used balloons to carry instruments above 10 km and found that temperature stopped decreased and even began to increase 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 in this class.

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 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.  The next time you're in an airplane try to look up at the sky above.  There's less air and less scattering of light.  As a result the sky is a darker blue.  If you got high enough the sky would eventually become black.

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.    The ozone layer is found in the stratosphere.  Peak ozone concentrations occur near 25 km altitude.

Here's the same picture drawn again (for clarity) with some additional information.  We need to explain why when temperature decreases all the way up to the top of the troposphere, it can start increasing again in the stratosphere.


6.   Sunlight is a mixture of ultraviolet (7%), visible (44%, colored green in the picture above) and infrared light (49%, colored red).  We can see the visible light.

6a. 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? 

     Absorption of ultraviolet light by ozone warms the air in the stratosphere and explains why the air can warm (oxygen also absorbs UV light).  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.

7.  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).  It really was quite a daring trip at the time at the time, and they very nearly didn't survive it.  More about this on Thursday and a short (10 min) video.

Next it was time for a demonstration that I didn't have time to do before the Practice Quiz last Thursday.  On Thursday I was trying to convince you that air pressure not only pushes downward but also upward and sideways.


One way to see this is to put a brick on top of a balloon.  The balloon gets squished but not flattened.  It eventually pushes back with enough force to support the brick. 

The demonstration is summarized on p. 35 a in the ClassNotes.


Don't worry too much about the details above because there's a more detailed explanation below.  At this point you should wonder why is it that the water in a balloon will fall while the water in the wine glass does not.

Here's a little more detailed examination.  First the case of a water balloon.



The figure at left shows air pressure (red arrows) pushing on all the sides of the balloon.  Because pressure decreases with increasing altitude, the pressure from the air at the top of the balloon pushing downward (strength=14) is a little weaker than the pressure from the air at the bottom of the balloon that is pushing upward (strength=15).  The two sideways forces cancel each other out.  The total effect of the pressure is a weak upward pressure difference force (1 unit of upward force shown at the top of the right figure). 

Gravity exerts a downward force on the water balloon.  In the figure at right you can see that the gravity force (strength=10) is stronger than the upward pressure difference force (strength=1).  The balloon falls as a result.  This is what you know would happen if you let go of a water balloon, it would fall.

In the demonstration a wine glass is filled with water.  A small plastic lid is used to cover the wine glass.  The wine glass is then turned upside and the water does not fall out.



All the same forces are shown again in the left most figure.  In the right two figures we separate this into two parts.  First the water inside the glass isn't feeling the downward and sideways pressure forces (because they're pushing on the glass, they're included on the right figure ).  Gravity still pulls downward on the water but the upward pressure force is able to overcome the downward pull of gravity.  It can do this because all 15 units are used to overcome gravity and not to cancel out the downward pointing pressure force.  The net upward force ( 5 units) is strong enough to keep the water in the glass.

The demonstration was repeated using a 4 Liter flash (more than a gallon of water, more than 8 pounds of water).  The upward pressure force was still able to keep the water in the flask.  Actually it's not quite as impressive as it might seem - much of the weight of the water is pushing against the sides of the flask which the instructor was supporting with his arms.

We weren't done yet.  We had a little time to get started on a new topic, the ideal gas law.  This is a first step in really understanding why warm air rises and cold air sinks. 


Hot air balloons rise (they also sink), so does the relatively warm air in a thunderstorm updraft (it's 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 (stronger than many tornadoes) 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 only had time to look at the first step today.
We will first learn about the ideal gas law.  That is an equation that tells you which 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 fully 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 mostly empty space.  It is the collisions of air molecules traveling at 100s of miles per hour 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'll end up with an equation.  Pressure (P) will be on the left hand side of the equation.  Relevant properties of the air inside the balloon will be found on the right hand side.





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.  Here's a little more detailed look at that experiment.




An air sample is trapped together with some steel wool inside a graduated cylinder.  The cylinder is turned upside down and the open end is stuck into a glass of water.  This is shown at left above.  Water will move into or out of the cylinder to keep Pout equal to Pin.  We assume that neither of these pressures changes during the experiment.  In this experiment pressure is constant.

Oxygen in the cylinder reacts with steel wool to form rust.  Oxygen is removed from the air sample which causes N (the total number of air molecules) to decrease.  Removal of oxygen would ordinarily cause a drop in Pin.  But, 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.  It is the change in V that you can measure and use to determine the oxygen percentage concentration in air.



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).



We'll come back to this topic and make use of these equation in class on Thursday.  I also mentioned that if someone reminds me, I'll put both equations on the board for you to use during the next quiz.