Thursday Sept. 8, 2011
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Three songs from a new artist that I just stumbled upon, Eilen Jewell.  You heard "Mess Around" (seeing her live in a little bar or cafe in Brussels would be fun),  "Everywhere I Go", "Hooked", and "Too Hot to Sleep." 

Today was most likely the last call for Expt. #1.  Unless noted otherwise experiment reports are due Sept. 20, one week from next Tuesday.  Try to wrap up the experiment early next week so that you can return the materials and pick up the supplementary information handout.

Also the 1st 1S1P assignment is now available.  What that means is this is your first opportunity to start on your semester long quest of earning 45 1S1P pts.  In this current assignment you have a choice of three topics.  Two of these will count as part of the 4 report total you are allowed to submit during the semester, the 3rd is a Bonus Assignment.  You can write as many Bonus Assignment reports as you'd like.  I would encourage you to turn in at least one report so that you can begin to get an feeling for how the reports will be graded.

We spent part of the beginning of the class period covering a little new material.  If this were a real quiz (the first real quiz is two weeks from today) you would have been given the entire period.

I went out into my vegetable garden early this morning and picked up 5 bricks to bring into school for today's class.  You can learn a lot about pressure from bricks. 

For example the photo below (taken in my messy office) shows two of the bricks.  One is sitting flat, the other is sitting on its end.  Each brick weighs about 5 pounds.  Would the pressure at the base of each brick be the same in this kind of situation? 



Pressure is determined by (depends on) weight so you might be tempted to say the pressures would be equal.  But pressure is weight divided by area.  In this case the weights are the same but the areas are different.  In the situation at left the 5 pounds must be divided by an area of about 4 inches by 8 inches = 32 inches.  That works out to be about 0.15 psi.  In the other case the 5 pounds should be divided by a smaller area, 4 inches by 2 inches = 8 inches.  That's a pressure of 0.6 psi, 4 times higher.  Notice also these pressures are much less the 14.7 psi sea level atmospheric pressure.

The real reason I brought the bricks was so that you could understand what happens to pressure with increasing altitude.  Here's a drawing of the 5 bricks stacked on top of each other.

At the bottom of the pile you would measure a weight of 25 pounds (if you wanted to find the pressure you'd divide 25 lbs by the 32 square inch area on the bottom of the brick).  If you moved up a brick you would measure a weight of 20 pounds, the weight of the four bricks that are still above.  The pressure would be less.  Weight and pressure will decrease as you move up the pile.

The atmosphere is really no different.  Pressure at any level is determined by the weight of the air still overhead.  Pressure decreases with increasing altitude because there is less and less air remaining overhead.  The figure below is a more carefully drawn version of what was done in class.



At sea level altitude, at Point 1, the pressure is normally about 1000 mb.  That is determined by the weight of all (100%) of the air in the atmosphere.

Some parts of Tucson, at Point 2, are 3000 feet above sea level (most of the valley is a little lower than that around 2500 feet).  At 3000 ft. about 10% of the air is below, 90% is still overhead.  It is the weight of the 90% that is still above that determines the atmospheric pressure in Tucson.  If 100% of the atmosphere produces a pressure of 1000 mb, then 90% will produce a pressure of 900 mb. 

Pressure is typically about 700 mb at the summit of Mt. Lemmon (9000 ft. altitude at Point 3) and 70% of the atmosphere is overhead..

Pressure decreases rapidly with increasing altitude.  We will find that pressure changes more slowly if you move horizontally.  Pressure changes about 1 mb for every 10 meters of elevation change.  Pressure changes much more slowly normally if you move horizontally: about 1 mb in 100 km.  Still the small horizontal changes are what cause the wind to blow and what cause storms to form.

Point 4 shows a submarine at a depth of about 30 ft. or so.  The pressure there is determined by the weight of the air and the weight of the water overhead.  Water is much denser and much heavier than air.  At 30 ft., the pressure is already twice what it would be at the surface of the ocean (2000 mb instead of 1000 mb).

What difference does it make if pressure decreases with increasing altitude?
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.

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.

2a.  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). 

2. The densest air is found in the bottom layer.  The bottom layer is compressed the most, 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).

3.  Finally something that I didn't mention in class.  The rate of pressure change with altitude depends on air density.  Pressure is decreasing most rapidly with increasing altitude in the densest air at the bottom of the picture.