Wednesday Sept. 13, 2006

The Quiz #1 Study Guide (in preliminary form) is now available online.

A new reading section has been assigned.
Here's a reminder of what we will be covering today in an effort to understand why warm air rises and cold air sinks.



An  explanation or discussion of these figures has been purposely left off.  By the end of the class today (and after some review of your notes), you should understand and be able to explain what is being depicted.


Collisions between the air atoms or molecules and the sides of the balloon keep the balloon inflated.

The ideal gas law equations tell you how variables like
the number of gas molecules,
the volume of the balloon, and
the density and temperature of the air
affect the pressure of the air in the balloon.


The pressure produced by the air molecules inside a balloon will first depend on how many air molecules are there.
As you add more and more add to something like a bicycle tire, the pressure increases.

Air pressure inside a balloon also depends on the size of the balloon.  Pressure is inversely proportional to volume, V (increasing V decreases P and vice versa).

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 of you are working on.  Water is able to move into the inverted cylinder and will do so to keep the air sample pressure equal to the pressure outside the cylinder.  As oxygen is removed from an air sample, water moves into the cylinder, the air sample volume decreases and the pressure of the air sample stays constant.



You shouldn't throw a can of spray paint into a fire.  The pressure of the gas inside a container depends on the gas temperature.  If the can gets hot enough, the buildup in pressure could cause the can to rupture.


Surprisingly 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.



Here are the two ideal gas law equations.  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.

(1) Pressure  = (Number of air molecules) multiplied by temperature divided by volume
or
(2) Pressure = (density) multiplied by (temperature)


Air in the atmosphere behaves like air in a balloon.  A balloon can grow or shrink in size depending on the pressure of the air inside. 

We start in the upper left hand corner with air inside a balloon that is exactly the same as the air outside.  The air inside and outside have been colored green.  The arrows show that the pressure of the air  inside pushing outward and the pressure of the air surrounding the balloon pushing inward are all the same.

Next week warm the air in the balloon (Fig. 2).  The ideal gas law equation tells us that the pressure of the air in the balloon will increase.  The increase is momentary though. 

Because the pressure inside is now greater than the pressure outside, the balloon will expand.  An increase in volume will reduce the pressure of the air inside.  Eventually the balloon will expand just enough that the pressures inside and outside are again in balance.  You end up with a balloon of warm low density air that has the same pressure as the air surrounding it (Fig. 3)

You can use the same reasoning to understand that cooling a balloon will cause its volume to decrease.  You will end up with a balloon filled with cold high density air.  The pressures inside and outside the balloon will be the same.

These associations: warm air = low density air and cold air = high density air are important and will come up a lot during the remainder of the semester.
In the atmosphere air temperature and air density change together in a way that keeps pressure constant.  This is Charles's Law and was demonstrated in class.  The demonstration is illlustrated and described at the top of p. 54 in the photocopied notes.


We will now look at the forces acting on a parcel or balloon of air. 

Air has mass and weight   When an air parcel has the same temperature, pressure, and density as the air around it, the parcel will remain stationary.  With gravity pulling downward on the air, there must be another force pointing upward of equal strength.  The upward force is caused by pressure differences between the bottom (higher pressure pushing up) and top of the balloon (slightly lower pressure pushing down on the balloon).

If the balloon is filled with warm, low density air the gravity force will weaken (there is less air in the balloon so it weighs less). The upward pressure difference force (which depends on the surrounding air) will not change.  The upward force will be stronger than the downward force and the balloon will rise. 

Conversely if a balloon is filled with cold low density air, gravity will strengthen and the balloon will sink.

We modified the demonstration somewhat (see bottom of p. 54 in the photocopied class notes).  We used a balloon filled with helium instead of air.  Helium is less dense than air even when the helium 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 can't rise, the gas inside is denser than the surrounding air.  As the balloon warms and expands its density decreases.  Eventually the balloon becomes less dense than the surrounding air and lifts off from the table.

Incidentally, the balloons were gone by 8am the next morning at the start of the T Th class.
A balloon pilot can adjust the temperature (and thereby the density) of the air inside a balloon and make the balloon rise or sink.
The upward pressure difference force is really just the bouyant force in Archimedes Law.  Archimedes Law is another attempt to understand and explain why objects float or sink.  Archimedes Law is discussed on pps 53a and 53b in the photocopied class notes.  This wasn't discussed in class.