Monday Jan. 31, 2011
click here to download today's notes in a more printer friendly format

Three songs from Brandi Carlile this morning before class ("My Song", "I Will", and "The Story").

The Practice Quiz is Wednesday this week.  You'll have about half the period to work on the quiz. 




Here are the first two questions on an In-class Optional Assignment (you answer the questions on a blank sheet of paper, turn them in at the end of class, and if you make an honest attempt to answer all the questions you'll earn a little extra credit).  If you weren't in class but are reading through today's class notes and want to turn in the assignment at the beginning of class on Wednesday you can earn at least partial credit.  There are a total of 5 questions on the assignment.




The next bunch of material tries to explain how a mercury barometer works.  A mercury barometer is used to measure atmospheric pressure and is  really just a balance that can be used to weigh the atmosphere.  You'll find a somewhat messier version of of what follows on p. 29 in the photocopied Class Notes. 



The instrument in the left figure above ( a u-shaped glass tube filled with a liquid of some kind) is actually called a manometer and can be used to measure pressure difference.  The two ends of the tube are open so that air can get inside and air pressure can press on the liquid.  Given that the liquid levels on the two sides of  the manometer are equal, what could you about PL and PR?

The liquid can slosh back and forth just like the pans on a balance can move up and down.  A manometer really behaves just like a pan balance (pictured at right) or a teeter totter (seesaw).  Because the two pans are in balance, the two columns of air have the same weight.   PL and PR are equal (but note that you don't really know what either pressure is, just that they are equal).


Now the situation is a little different, the liquid levels are no longer equal.  You probably realize that the air pressure on the left, PL, is a little higher than the air pressure on the right, PR.  PL is now being balanced by PR + P acting together.  P is the pressure produced by the weight of the extra fluid on the right hand side of the manometer (the fluid that lies above the dotted line).  The height of the column of extra liquid provides a measure of the difference between PL and PR.

Next we will just go and close off the right hand side of the manometer.




Air pressure can't get into the right tube any more.  Now at the level of the dotted line the balance is between Pair and P (pressure by the extra liquid on the right).  If Pair changes, the height of the right column, h,  will change.  You now have a barometer, an instrument that can measure and monitor the atmospheric pressure. (some of the writing in the upper right portion of the left figure was cut off, it should read "no air pressure")

Barometers like this are usually filled with mercury.  Mercury is a liquid.  You need a liquid that can slosh back and forth in response to changes in air pressure.  Mercury is also very dense which means the barometer won't need to be as tall as if you used something like water.  A water barometer would need to be over 30 feet tall.  With mercury you will need only a 30 inch tall column to balance the weight of the atmosphere at sea level under normal conditions (remember the 30 inches of mercury pressure units mentioned earlier).  Mercury also has a low rate of evaporation so you don't have much mercury gas at the top of the right tube (it is the mercury vapor that would make a mercury spill in the classroom dangerous).



Here is a more conventional barometer design.  The bowl of mercury is usually covered in such a way that it can sense changes in pressure but is sealed to keep poisonous mercury vapor from filling a room.

In an earlier class we saw that a 52 inch long 1"x1" steel bar weighs the same as a 1" x 1" column of air stretching from sea level to the top of the atmosphere.  Now we can add a 30 inch tall 1" x 1" column of mercury (frozen so that it would be rigid) to the list.  All three columns above would weigh 14.7 pounds.  They would all be pushing against the ground with a pressure of 14.7 psi.
Here's Optional Assignment question #3






The figure above (p. 30 in the photocopied Class Notes) first shows average sea level pressure values. 1000 mb or 30 inches of mercury are close enough in this class.

Sea level pressures usually fall between 950 mb and 1050 mb. 

Record high sea level pressure values occur during cold weather.  The TV weather forecast will often associated hot weather with high pressure.  They are generally referring to upper level high pressure (high pressure at some level above the ground) rather than surface pressure.

Record low pressure values have all been set by intense hurricanes (the record setting low pressure is the reason these storms were so intense).  Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic.  Hurricane Katrina had a pressure of 902 mb.  The following table lists some of the information on hurricane strength from p. 146a in the photocopied ClassNotes.  3 of the 10 strongest N. Atlantic hurricanes occurred in 2005.

Most Intense North Atlantic Hurricanes
 Most Intense Hurricanes
to hit the US Mainland
Wilma (2005) 882 mb
Gilbert (1988) 888 mb
1935 Labor Day 892 mb
Rita (2005) 895 mb
Allen (1980) 899
Katrina (2005) 902
 1935 Labor Day 892 mb
Camille (1969) 909 mb
Katrina (2005) 920 mb
Andrew (1992) 922 mb
1886 Indianola (Tx) 925 mb

Here are the last two Optional Assignment questions

Question #4


and Question #5



I'm sticking p. 33 from the ClassNotes back in at this point even though we covered this material last Friday.


Pressure pushes upward, downward, and sideways.

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.



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 force (1 unit of upward force shown at the top of the right figure, you might have heard this called a bouyant force).  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.  You can then turn the glass upside down without the water falling 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, this is shown at the right side of the figure above).  Gravity still pulls downward on the water but the upward pressure force is able to overcome the downward pull of gravity.  The upward pointing pressure force is used to overcome gravity not to cancel out the downward pointing pressure force.

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).

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 might 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.

I'll put answers to the In Class Optional Assignment online sometime Tuesday.