Tuesday, Jan. 31, 2012
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I did warn you last Thursday that I would be attending the Forever Tango performance at Centennial Hall (last year about this time it was Flamenco dancing).  As a result I played a couple of songs from the Forever Tango CD: "El Marne" and "Evaristo Carriego".  Here's a video with Javier Castello and Sylvia Gerbi dancing to El Marne.    And a second video with Maria Plazaola and Carlos Gavito in a dance dedicated to Evaristo Carriego (who I just learned was an Argentinian Poet).  We had time for part of a 3rd song "Negracha."

The Practice Quiz is Thursday this week.  The Study Guide has been finalized and reviews are scheduled for Tuesday and Wednesday afternoon (see the Study Guide for times and locations).

The In-class Optional Assignment that I forgot to return last Thursday was handed out today.  Answers to the questions are online.

On my way back to my office after class last Wednesday I got to wondering what the pressure was underneath the pile of bricks that I had in class.

It's less than 1 psi.  You'd need 94 bricks, 470 pounds of bricks to produce 14.7 psi.




14.7 psi might not sound like much.  But when you start to multiply 14.7 by all the square inches on your body it turns into 1000s of pounds of weight (force).

Bricks help you to understand why pressure decreases with increasing altitude.  What about density.  How does air density change with increasing altitude?  You get out of breathe more easily at high altitude than at sea level.  Air gets thinner (less dense) at higher altitude. 

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 contain the same amount (mass) of air.  This is a fairly subtle point.  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 last Thursday.

Pressure at any level in the atmosphere depends on (is determined by) the weight of the air overhead.  You might get the idea that pressure just pushes downward.


 Air pressure is a force that pushes downward, upward, and sideways.  If you fill a balloon with air and then push downward on it, you can feel the air in the balloon pushing back (pushing upward).  You'd see the air in the balloon pushing sideways as well.

Another helpful representation of air in the atmosphere might be a people pyramid.



If the bottom person in the stack above were standing on a scale, the scale would measure the total weight of all the people in the pile.  The person on the bottom of the pile is pushind downward against the ground.  But that person is also pushing upward and must be strong enough to support the weight of all the people above.  The people in this figure are analogous to layers of air in the atmosphere.




The air pressure in the four tires on your automobile pushes pushes upward with enough force to keep this 1000 or 2000 pound vehicle (my own personal vehicle) off the ground.  The air pressure also pushes downward, you'd feel it if the car ran over your foot.

This was a logical point to do a demonstration.  A demo that tries to prove that air pressure really does push upward as well as downward.  Not only that but that the upward force is fairly strong.  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 is 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 bit more detailed and more complete explanation of what is going on.  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 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 (much of the weight of the water is pushing against the sides of the flask which the instructor was supporting with his arms).

What difference does it make if pressure decreases with increasing altitude or if pressure pushes upward, downward, and sideways?
Here's one answer to that question.


Hot air balloons can go up and come back down.  I'm pretty sure you know what would cause the balloon to sink.  I suspect you don't know what causes it to float upward.

Gravity pulls downward on the balloon.  The strength of this force will depend on whether the air is hot low density air (light weight) or cold higher density air (heavier air).

Pressure from the air surrounding the balloon is pushing against the top, bottom, and sides of the balloon (the blue arrows shown above at right).  Pressure decreases with increasing altitude.  The pressure at the bottom pushing up is a little higher than at the top pushing down (the pressures at the sides cancel each other out).  Decreasing pressure with increasing altitude creates an upward pointing pressure difference force that opposes gravity.

Air pressure and air density both decrease with increasing altitude.  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 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 in the next section.

Pages 31 and 32 in the ClassNotes list some of the significant events in the early study and exploration of the atmosphere.  A few of them are included below.  We only discussed part of this in class.


Galileo's experiment that proved that air had weight was mentioned earlier in the online notes.  The mercury barometer was invented in 1643.


The earliest balloon trips into the upper atmosphere were in unheated and unpressurized gondolas.  Climbers have made it to the summit of Mt. Everest without carrying supplementary oxygen but it is difficult and requires acclimation.  Read "Into Thin Air" by Jon Krakauer if you'd like to get some idea of what it's like trying to climb Mt. Everest.



Measurements of air temperature at high altitude in unmanned balloons lead to the discovery of the stratosphere in about 1900.



Capt. Grey above will be mentioned early in a video segment that will be shown in class.  Note the types and amount of clothing he had to wear to try to stay warm.  All of his trips were in an unpressurized open gondola. 


This flight lead by Auguste Piccard is the subject of the video segment that will be shown (from a PBS program called The Adventurers).

Jacques Piccard, Auguste's son, will appear in the video and also in another segment that will be shown.  He would later travel with Lt. Don Walsh of the US Navy to a depth of about 35,800 feet in the ocean in the Mariana Trench. 

Bertrand Piccard, Jacques son was part of the first two man team to circle the globe non-stop in a balloon.  We'll also watch a portion of a video documenting the record-setting flight.