Friday Feb. 4, 2011
click here to download today's notes in a more printer friendly format

Three songs from Xavier Rudd before class today ("Guku", "Messages", and "Better People"). 

The Practice Quiz has been graded and was returned in class today.  The average was 61 pts missed out of a total of 160 pts.  That is 62% which is pretty low but fairly normal for a practice quiz.

You should have a look at the Practice Quiz if you didn't take it in class so that you can become familiar with the quiz format.  Answers to all the questions are available online.

Here are the two versions of the Ideal Gas Law that we covered before the Practice Quiz on Wednesday.


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 (this figure wasn't shown in class)

If you warm a parcel of air the volume will increase and the density will decrease.  Pressure inside the parcel remains 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:
1. Gravity pulls downward.  The strength of the gravity force depends on the mass of the air inside the parcel.  This force is just the weight of the parcel
2. 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 doesn't rise or sink.

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 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 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.

Something like this happens in the atmosphere.

At (1) sunlight reaching the ground is absorbed and warms the ground.  This in turns warms air in contact with the ground (2)  Once this air becomes warm and its 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).  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.

In the last few minutes of class we learned a little bit about the Piccard family.
Auguste Piccard (1884-1962) together with Paul Kipfer (see p. 32 in the photocopied ClassNotes) was the lead member of a two-man team that made the first trip into the stratosphere in a balloon.  They did that on May 27, 1931.  We watched a short segment from a PBS program called "The Adventurers" that documented that trip.

Jacques Piccard (Auguste's son) was part of a two-man team that traveled to the deepest point in the ocean (35,800 feet) in a bathyscaph.  In the next week or so I will show you a short segment from an earlier test of the bathyscaph where Auguste and Jacques descended to 10,000 feet.

Finally Bertrand Piccard (Jacques son, Auguste's grandson) was part of the two man team that first circled the globe nonstop in a balloon.  That occurred much more recently, March 20, 1999, I believe.  I also plan to show you some of that trip.