Tuesday Sept. 7, 2010
click here to download today's notes in a more printer friendly format

The first day after a long 3-day weekend seemed like a good place for a couple of songs from the Flobots ("Handlebars" and "By the Time You Get This Message").

All of the names on the Report Signup sheets should now be on the Online Lists.  If you name isn't there and you think it should be, let me know.  Sorry about any misspelled names.

The Practice Quiz is Thursday this week (during the 2nd half or so of the class period)  There'll be a Practice Quiz review this afternoon from 4-5 pm in Haury 129 (aka Anthropology 129) and Wednesday afternoon at the same time in Soc. Sci. 22.


Now that we have finished the section on air pollutants, here's a list of the key points for each of the pollutants that we covered.

carbon monoxide (CO)
colorless, odorless
primary pollutant
incomplete combustion
winter, morning pollutant
temperature inversion layer
tropospheric ozone (O3)
secondary pollutant
summer, afternoon pollutant
Los Angeles - type (photochemical smog)
sulfur dioxide (SO2)
1st pollutant
London - type smog
acid rain
particulate matter (PM)
health hazard
affects visibility



An iron bar was passed around at the beginning of class.  You were supposed to guess how much it weighed.




We came back to this later in the period.



Bottles containing approximately equal volumes of water and mercury were passed around in class (thanks for being careful with the mercury).  There is a lot more mass in the bottle of mercury than in the bottle of water.  Because it has more mass the bottle of mercury also weighs more than the bottle of water (that's something you can feel).  Mercury is much denser than water.

Before we can learn about atmospheric pressure, we need to review the terms mass and weight.  In some textbooks you'll find mass defined as "amount of stuff" or "amount of a particular material."  Other books will define mass as inertia or as resistance to change in motion (this comes from Newton's 2nd law of motion, we'll cover that later in the semester).  The next picture illustrates both these definitions.



A Cadillac and a volkswagen have both stalled in an intersection.  Both cars are made of steel.  The Cadillac is larger and has more steel, more stuff, more mass.  The Cadillac is also much harder to get moving than the VW, it has a larger inertia (it would also be harder to slow down than the Volkswagen once it is moving).



Weight is a force and depends on both the mass of an object and the strength of gravity.  We tend to use weight and mass interchangeably because we spend all our lives on earth where gravity never changes.



On the earth where the pull of gravity never changes, any three objects that all have the same mass (even if they had different volumes and were made of different materials) would always have the same weight. Conversely:


When gravity is always the same, three objects with the same weight would also have the same mass.

The difference between mass and weight is clearer (perhaps) if you compare the situation on the earth and on the moon.


On the earth a brick with a mass of about 2 kg weighs about 5 pounds.  If you carried the brick to the moon it would have the same mass.  But gravity on the moon is weaker than on the earth.  Objects on the moon weigh less than on the earth. 


In the first example there is more mass (more dots) in the right box than in the left box.  Since the two volumes are equal the box at right has higher density.  Equal masses are squeezed into different volumes in the bottom example.  The box with smaller volume has higher density.




The air that surrounds the earth has mass.  Gravity pulls downward on the atmosphere giving it weight.  Galileo conducted (in the 1600s) a simple experiment to prove that air has weight.  The experiment wasn't mentioned in class.

Pressure is defined as force divided by area.  Air pressure is the weight of the atmosphere overhead divided by the area the air is resting on.  Atmospheric pressure is determined by and tells you something about the weight of the air overhead.  This is one way, a sort of large scale representation, of understanding air pressure.

Under normal conditions a 1 inch by 1 inch column of air stretching from sea level to the top of the atmosphere will weigh 14.7 pounds.  Normal atmospheric pressure at sea level is 14.7 pounds per square inch (psi, the units you use when you fill up your car or bike tires with air).


Now here's where the steel bar comes in.  The steel bar also weighs exactly 14.7 pounds.  Steel is a lot denser than air, so a steel bar only needs to be 52 inches tall to have the same weight as an air column that is 100 miles or more tall.  If a mercury bar had been used it would only have to be about 30 inches long.

14.7 psi is one weigh of expressing average sea level pressure.  Here are average sea level pressure values in different units.



Typical sea level pressure is 14.7 psi or about 1000 millibars (the units used by meterologists and the units that we will use in this class most of the time) or about 30 inches of mercury (refers to the reading on a mercury barometer).  If you ever find yourself in France needing to fill your automobile tires with air (I lived in France for a while and owned a  Peugeot 404) remember that the air compressor scale is probably calibrated in bars.  2 bars of pressure would be equivalent to 30 psi.


Pressure at sea level is determined by the weight of the air overhead.  What happens to pressure as you move upward in the atmosphere.  We can use a pile of bricks to help answer this question.  I use bricks because you can see them.  You can think of the bricks representing layers of air in the atmosphere.

Each brick weighs 5 pounds.  At the bottom of the 5 brick tall pile you would measure a weight of 25 pounds (if you wanted to find the pressure you'd divide 25 lbs by the 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 still above.  To get the pressure you would need to divide by the area.  It should be clear that 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 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 33 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 33 ft., the pressure is already twice what it would be at the surface of the ocean (2000 mb instead of 1000 mb).

The person in the picture below (not shown in class) is 20 feet underwater.  At that depth there is a pretty large pressure pushing against his body from the surrounding water.  The top of the snorkel is exposed to the much lower air pressure at the top of the pool.  If the swimmer puts his mouth on the snorkel the pressure at the bottom of the pull would collapse his lungs.




We took a bit of a detour at this point.


Hot air balloons can rise or can sink.  Most everyone in the classroom knew that gravity is what causes a balloon (or another object) to fall.  Not very many people know that an upward pressure force is what can cause a balloon to float upward. 

Pressure decreases with increasing altitude.  That means that the air pressure pushing against the bottom of a balloon is a little bit stronger than the force pushing against the top of the balloon.  There isn't much of a difference in the strength of the two forces but there is a difference.  And this force points upward from high toward lower pressure. 

The two forces are always opposing each other.  When the air in the balloon is cold and dense the balloon sinks.  When the air is hot and has low density the balloon rises. 

We'll come back to this topic in a week or so, don't worry if you aren't understanding it fully right now.


Air is compressible, so a pile of mattresses (clean mattresses not the disgusting things you sometimes see at the curb in front of someone's house) might be a more realistic representation of layers of air in the atmosphere.  We can use mattresses to understand how air density changes with increasing altitude.






Four mattresses are stacked on top of each other.  Mattresses are reasonably heavy, the mattress at the bottom of the pile is compressed the most by the weight of all the 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.

Here's a slightly clearer version of the figure drawn in class



There's a lot of information in this figure.  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.

Each layer of air contain the same amount (mass) of air.  This is a fairly subtle point.  You can tell because the pressure decrease as you move upward through each layer is the same (100 mb).  Pressure depends on weight.  So if the pressure change is the same everytime you move up one layer, the weights of each of the layers must be equal.  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.  Each layer has the same amount of air (same mass).  The bottom layer is compressed the most so it has the smallest volume.  Mass/( small volume) gives a high density.  The top layer has the same amount of air but about twice the volume.  It therefore has a lower density.

3.  The rate of pressure change with altitude depends on air density.  The most rapid rate of pressure decrease with increasing altitude is in the densest air at the bottom of the picture. 

This is where class ended today.  But I have added one more figure that explains why the rate of pressure change as you move or down in the atmosphere depends on air density.  The following figure wasn't shown in class.


There is a lot going on here. 

Point 1 - Notice there is a 100 mb drop in pressure in both air layers.  In order for this to be true both layers must weigh the same.  In order for both layers to have the same weight they must contain the same amount of air, they have the same mass.

Point 2a - The pressure decreases 100 mb in a relatively short distance.  This produces a relatively rapid rate of pressure decrease with increasing altitude.
Point 2b - The pressure also decreases 100 mb but in a longer distance.  Pressure is decreasing at a slower rate in this layer.

Point 3 - The air in the left layer is denser than the air in the right layer.  The same amount (mass) of air is squeezed into a thinner layer, a smaller volume, in the left layer.  This results in relatively high density air.

The fact that the rate of pressure decrease with increasing altitude depends on air density is a fairly subtle but important concept.  This concept will come up 2 or 3 more times later in the semester.  For example, we will use this concept to explain why hurricanes can intensify and get as strong as they do. 

Try to reproduce this figure in your mind (together with the written discussion and explanation) the next time you are lying in bed at night trying to fall asleep.  It'll put you right to sleep without any of the side effects that medications might have.