Thursday Sept. 15, 2011
click here to download today's notes in a more printer friendly format

A few songs from a local group, Calexico (joined in some of the songs by Mariachi Luz de Luna, also from Tucson, and Francois Breut a French singer), in honor of Mexican Independence Day tomorrow Sept. 16.  You heard "Quattro (World Drifts In)", "Ballad of Cable Hogue" and "Si Tu Disais".  Here's another that I didn't have time to play in class"Alone Again Or".

The Quiz #1 Study Guide is now online.  There are 4 reviews scheduled for early next week.  See the study guide for times and locations.

I'll return the In-class Optional Assignment next Tuesday.  Answers to the questions might appear online before then.


Today we'll be learning why warm air rises and cold air sinks (the figure below can be found on p. 49 in the ClassNotes)


Hot air balloons rise (they also sink), so does the relatively warm air in a thunderstorm (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 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 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 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.  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 that wasn't shown in class.



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.

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.



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).




Charles' Law is a special case involving the ideal gas law.  Charles Law is a situation where the pressure in a volume of air remains constant.  T, V, and density can change but they must do so in a way that keeps P constant.  This is what happens in the atmosphere.  A volume of air is free to expand or shrink.  It does so to keep the pressure inside the air volume constant (the pressure inside the volume is staying equal to the pressure of the air outside the volume).

Read through the explanation on p. 52 in the photocopied Classnotes.  In the atmosphere a parcel (balloon) of air will always try to keep its pressure the same as the pressure of the surrounding air.  If they aren't equal the parcel will either expand or shrink until they are again equal.

If you warm air it will expand and density will decrease until the pressure inside and outside the parcel are equal.
If you cool air the parcel will shrink and the density will increase until the pressures balance.

These two associations:
(i)   warm air = low density air
(ii)  cold air = high density air
are important and will come up a lot during the remainder of the semester.

Click here if you would like a little more detailed, more step-by-step, explanation of Charles Law.
Here's a visual summary of Charles' Law

As you warm a parcel of air the volume will increase and the density will decrease.  Pressure inside the parcel will remain constant.  If you cool the parcel of air it's volume decreases and its density increases.  Pressure inside the parcel remains constant.

Charles Law can be demonstrated by dipping a balloon in liquid nitrogen.  You'll find an explanation on the top of p. 54 in the photocopied ClassNotes.


The balloon had shrunk down to practically zero volume when pulled from the liquid nitrogen.  It was filled with cold high density air.  As the balloon warmed the balloon expanded and the density of the air inside the balloon decreased.  The volume and temperature kept changing in a way that kept pressure constant.  Eventually the balloon ends up back at room temperature (unless it pops while warming up).

And finally the last step toward understanding why warm air rises and cold air sinks.  We'll have a look at the forces that act on parcels of air in the atmosphere.  This information is found on p. 53 in the photocopied ClassNotes.



Basically it comes down to this - there are two forces acting on a parcel* of air in the atmosphere:

First is gravity, it pulls downward.  The strength of the gravity force (the weight of the air in the parcel) depends on the mass of the air inside the parcel. 

Second there is an upward pointing pressure difference force.  This force is caused by the air outside (surrounding) the parcel.  Pressure decreases with increasing altitude.  The pressure of the air at the bottom of a parcel pushing upward is slightly stronger than the pressure of the air at the top of the balloon that is pushing downward.  The overall effect is an upward pointing force.

When the air inside a parcel is exactly the same as the air outside, the two forces are equal in strength and cancel out.  The parcel is neutrally bouyant and it wouldn't rise or sink, it would just sit in place.

If you replace the air inside the balloon with warm low density air, it won't weigh as much.  The gravity force is weaker.  The upward pressure difference force doesn't change (because it is determined by the air outside the balloon which hasn't changed) and ends up stronger than the gravity force.  The balloon will rise.

Conversely if the air inside is cold high density air, it weighs more.  Gravity is stronger than the upward pressure difference force and the balloon sinks.

* the word parcel just means a small volume of air.

We did a short demonstration to show how density can determine whether an object or a parcel of air will rise or sink.  We used balloons filled with helium (see bottom of p. 54 in the photocopied Class Notes).  Helium is less dense than air even when it has the same temperature as the surrounding air.  A helium-filled balloon doesn't need to warmed up in order to rise.


We dunked the helium-filled balloon in some liquid nitrogen to cool it and to cause the density of the helium to increase.  When removed from the liquid nitrogen the balloon didn't rise, the gas inside was denser than the surrounding air (the purple and blue balloons in the figure above).  As the balloon warms and expands its density decreases.  The balloon at some point has the same density as the air around it (green above) and is neutrally bouyant.  Eventually the balloon becomes less dense that the surrounding air (yellow) and floats up to the ceiling (which in ILC 150 is about 30 feet high)

Something like this happens in the atmosphere.


Sunlight shines through the atmosphere.  Once it reaches the ground at (1) it is absorbed and warms the ground.  This in turns warms air in contact with the ground (2)  As this air warms, its density starts to decrease.  When the air density is low enough, small "blobs" of air separate from the air layer at the ground and begin to rise, these are called "thermals."  (3) Rising air expands and cools (we've haven't covered this yet and it might sound a little contradictory).  If it cools enough (to the dew point) a cloud will become visible as shown at Point 4.  This whole process is called free convection; many of our summer thunderstorms start this way.

We spent the last part of today's class starting a new topic - Surface Weather Maps.  We began by learning how weather data are entered onto surface weather maps.

Much of our weather is produced by relatively large (synoptic scale) weather systems - systems that might cover several states or a significant fraction of the continental US.  To be able to identify and characterize these weather systems you must first collect weather data (temperature, pressure, wind direction and speed, dew point, cloud cover, etc) from stations across the country and plot the data on a map.  The large amount of data requires that the information be plotted in a clear and compact way.  The station model notation is what meterologists use.




A small circle is plotted on the map at the location where the weather measurements were made.  The circle can be filled in to indicate the amount of cloud cover.  Positions are reserved above and below the center circle for special symbols that represent different types of high, middle, and low altitude clouds.  The air temperature and dew point temperature are entered to the upper left and lower left of the circle respectively.  A symbol indicating the current weather (if any) is plotted to the left of the circle in between the temperature and the dew point; you can choose from close to 100 different weather symbols (on a handout distributed in class).  The pressure is plotted to the upper right of the circle and the pressure change (that has occurred in the past 3 hours) is plotted to the right of the circle. 

We worked through this material one step at a time (refer to p. 36 in the photocopied ClassNotes).  Some of the figures below were borrowed from a previous semester or were redrawn and may differ somewhat from what was drawn in class.


The center circle is filled in to indicate the portion of the sky covered with clouds (estimated to the nearest 1/8th of the sky) using the code at the top of the figure.  3/8ths of the sky is covered with clouds in the example above.



Then symbols are used to identify the actual types of high, middle, and low altitude clouds observed in the sky.  Later in the semester we will learn the names of the 10 basic cloud types.  Six of them are sketched above and symbols for them are shown.  This figure wasn't shown in class.

A complete list of cloud symbols was on a handout distributed in class (a copy can be found here ) You do not, of course, need to remember all of the cloud symbols.


A straight line extending out from the center circle shows the wind direction.  Meteorologists always give the direction the wind is coming from.  In this example the winds are blowing from the NW toward the SE at a speed of 5 knots.  A meteorologist would call these northwesterly winds. 

Small barbs at the end of the straight line give the wind speed in knots.  Each long barb is worth 10 knots, the short barb is 5 knots.  Knots are nautical miles per hour.  One nautical mile per hour is 1.15 statute miles per hour.  We won't worry about the distinction in this class, we will just consider one knot to be the same as one mile per hour.



Here are four more examples.  What is the wind direction and wind speed in each case.  Click here for the answers.

The air temperature and the dew point temperature are probably the easiest data to decode.


The air temperature in this example was 64o F (this is plotted above and to the left of the center circle).  The dew point temperature was 39o F and is plotted below and to the left of the center circle.  The box at lower left reminds you that dew points range from the mid 20s to the mid 40s during much of the year in Tucson.  Dew points rise into the upper 50s and 60s during the summer thunderstorm season (dew points are in the 70s in many parts of the country in the summer).  Dew points are in the 20s, 10s, and may even drop below 0 during dry periods in Tucson (that has been the case here recently).

And last something I forgot to cover in class.



A symbol representing the weather that is currently occurring is plotted to the left of the center circle (in between the temperature and the dew point).  Some of the common weather symbols are shown.  There are about 100 different weather symbols that you can choose from (click here if you didn't get a copy of the handout distributed in class today).  There's no way I could expect you to remember all of these weather symbols.