Tue., Feb. 10 notes

Songs this morning selected from Dave McGraw and Mandy Fer: "Slumbering Rose" (5:25), "Grow" (4:18), "Serotiny" (4:53), "Comin' Down" (5:13).

The Practice Quiz has been graded and was returned in class today.

The Practice Quiz has been graded and was returned in class today. You'll find the number of points missed (out of 150 points total) written in the upper left hand corner on the front side of your quiz. The average grade was -58 which works out to be 61%, which as you can see below, is very typical for the Practice Quiz for the spring semester.

Semester	8 am class	9:30 am class	10 am class	2 pm class	Semester	8 am class	9:30 am class	2 pm class
S15	61	59
S14			63	62	F14	66	64
S13	---			72	F13	63	67
S12	63			61	F12	66		66
S11	---			62	F11	65		65
S10	61			62	F10	67		60
S09	---			60	F09	68		66
S08	66			64	F08	65		65

You should download the Practice Quiz if you didn't take it just to become familiar with the format. Some similar questions, maybe even the same questions, will be on Quiz #1 scheduled for Feb. 19. Answers to the questions on the Practice Quiz can be found here.

The Experiment #1 reports were collected today. It takes some time to get those graded. You can expect them back sometime next week. I plan to have as many Expt. #2 sets of materials as I can prepare in class on Thursday. Checkout will be first come first served. If you haven't yet returned your Expt. #1 materials please do so as soon as you can, we need the graduated cylinders for Expt. #2. We're starting to work on the 1S1P reports. The radon reports should be graded by Thursday this week.

A take home Optional Assignment was handed out in class today. It is due one week from today (Feb. 17). To earn full extra credit on the assignment it must be done before you come to class.

We were trying to understand why warm air rises and cold air sinks before the Practice Quiz last Thursday. The first step was learning about the ideal gas law:

We'll be working on the two remaining steps today.
Step #2 Charles' Law

Charles Law requires that the pressure of a parcel of air remain constant (parcel is just another word for volume). Changing the temperature of a volume of air will cause a change in density and volume; pressure will stay constant. This is an important situation because this is how volumes of air in the atmosphere behave.

This is probably the most difficult part of today's class and is worked out in lots of detail.

We start with a balloon of air. The air inside and outside the balloon (or parcel) are exactly the same.

Note the pressure pushing inward is balanced by the pressure of the air inside the balloon that is pushing outward. If we change something inside the balloon that upsets this pressure balance, the balloon would expand or shrink until the pressures were again in balance.

Volumes of air in the atmosphere will always try to keep the pressure of the air inside the parcel constant (P inside is always trying to stay equal to P outside). That's why we say air in the atmosphere obeys Charles' Law.

First let's imagine warming the air inside a balloon. We'll won't change the temperature of the air outside the balloon.

Increasing the temperature will BRIEFLY and MOMENTARILY increase the pressure. This creates an imbalance. Now that P inside is greater than P outside the balloon will expand.

Increasing the volume causes the pressure to start to decrease. The balloon will keep expanding until P inside is back in balance with P outside.

We're left with a balloon that is larger, warmer, and filled with lower density air than it had originally.

The pressures inside and outside are again the same. The pressure inside is back to what it was before we warmed the air in the balloon. You can increase the temperature and volume of a parcel together in a way that keeps pressure constant (which is what Charles' law requires). Or you can increase the temperature and decrease the density together and keep the pressure constant.

In nature the change in temperature and volume occur simultaneously. It's like jumping from the first to the last step above.

We can go through the same kind of reasoning and see what happens if we cool the air in a parcel. I've included all the steps below; that wasn't done in class.

We'll start with a parcel of air that has the same temperature and density as the air around it.

We'll cool the air inside the parcel. The air outside stays the same.

Reducing the air temperature causes the pressure of the air inside the balloon to decrease. Because the outside air pressure is greater than the pressure inside the balloon the parcel is compressed.

The balloon will get smaller and smaller (and the pressure inside will get bigger and bigger) until the pressures inside and outside the balloon are again equal. The pressure inside is back to the value it had before you cooled the air in the parcel.

The first and last steps, without all the intermediate and momentary details, are shown below.

Cooling some air will cause volume to decrease and density to increase while pressure stays constant.

If you want to skip all the details and just remember one thing, here's what I'd recommend

Parcels of atmospheric air and air in balloons behave the same way, they both obey Charles' Law. 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 shrinks down to practically nothing when dunked in the liquid nitrogen. It is filled with very cold, very high density air. When the balloon is pulled from the liquid nitrogen and starts to warm up it expands. Density in the balloon decreases. The volume and temperature keep changing in a way that kept pressure constant (pressure inside the balloon is staying equal to the air pressure outside the balloon). Eventually the balloon ends up back at room temperature (unless it pops while warming up).

Step #3 Vertical forces acting on parcels of air

We dunk the helium filled balloon in liquid nitrogen to cool it off and make it denser than air. When you pull the balloon out of the liquid nitrogen the helium is cold and denser than the surrounding air. I set it on the table (dark blue above).

As the balloon of helium warms and expands its density decreases (light blue). For a brief moment it has the same density as the surrounding air (green). It's neutrally buoyant at this point. Then it warms back to near room temperature where it is again less dense than the air and lifts off the table (yellow).

Free convection

Something like this happens in the atmosphere. I didn't show the following picture in class. I have another demonstration that I'll bring on Thursday and will mention free convection then.

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 density of the warm air 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 convection; many of our summer thunderstorms start this way.

Archimedes' principle
Here's another way of trying to understand why warm air rises and cold air sinks - Archimedes Law or Principle. It's a perhaps simpler way of understanding the topics. A bottle of water can help you to visualize the law.

A gallon of water weighs about 8 pounds (lbs). I wouldn't want to carry that much water on a hike unless I really thought I would need it.

If you submerge the gallon jug of water in a swimming pool, the jug becomes, for all intents and purposes, weightless. That seems kind of amazing. Archimedes' Law (see figure below, from p. 53a in the photocopied ClassNotes) explains why this is true.

Archimedes first of all tells you that the surrounding fluid will exert an upward pointing buoyant force on the submerged water bottle. That's why the submerged jug can become weightless.

Archimedes law also tells you how to figure out how strong the buoyant force will be. In this case the 1 gallon bottle will displace 1 gallon of pool water. One gallon of pool water weighs 8 pounds. The upward buoyant force will be 8 pounds, the same as the downward force. The two forces are equal and opposite.

What Archimedes law doesn't really tell you is what causes the upward buoyant force. You should know what the force is - it's the upward pressure difference force.

I wish I could get my hands on a gallon of mercury but I can't (and am not sure I'd be able to carry it to class even if I could)


Sand is about 50% denser than water. The weight of a gallon of sand is more than a gallon of water. The downward force is greater than the upward force and the bottle of sand sinks.	A gallon of water immersed in water is weightless.

You can sum all of this up by saying anything that is less dense than water will float in water,
anything that is more dense than water will sink in water.

Most types of wood will float (ebony and ironwood will sink). Most rocks sink (pumice is an exception).

The same reasoning applies to air in the atmosphere though it's harder to appreciate because air is invisible. When we say immersed in a fluid the fluid can be a liquid like water or a gas like air.

Air that is less dense (warmer) than the air around it will rise. Air that is more dense (colder) than the air around it will sink.

Here's a little more information about Archimedes that I didn't mention in class.

There's a colorful demonstration that shows how small differences in density can determine whether an object floats or sinks.

A can of regular Pepsi was placed in a beaker of water. The can should sink (it didn't in class). A can of Diet Pepsi on the other hand floated.

Both cans are made of aluminum which has a density almost three times higher than water; aluminum by itself would sink. The drink itself is largely water. The regular soda also has a lot of high-fructose corn syrup, the diet soda doesn't. The mixture of water and corn syrup has a density greater than plain water. There is also a little air (or perhaps carbon dioxide gas) in each can (the diet soda probably wouldn't float if it weren't for the gas in the can.

The average density of the can of regular soda (water & corn syrup + aluminum + air) should end up being slightly greater than the density of water. The average density of the can of diet soda (water + aluminum + air) is slightly less than the density of water.

In some respects people in swimming pools are like cans of regular and diet soda. Some people float (they're a little less dense than water), other people sink (slightly more dense than water).

Here's another demonstration of what we have been learning - a Galileo thermometer. It's a little fragile and I already had too much stuff with me today so I'll bring it (and explain how it works) on Thursday.

Source of the image below

I believe this is the gondola flown into the stratosphere by Auguste Piccard and Paul Kipfer is shown above (source). The figure caption is in German so I am not sure that is the case.

Auguste Piccard is shown in the figure at left. The gondola he took into the stratosphere is shown at right. Note how one side is black and the other white. By turning the gondola they could control the temperature inside (pointing the black side toward the sun would warm the gondola, turning the white side would allow the gondola to cool off).

We watched about 10 minutes of video describing Piccard's first trip into the stratosphere (they very nearly didn't make it back down alive).

That was about all the time we had in class today. I have several more videos that I would like to show at some point.

You might have heard about Felix Baumgartner and the Red Bull Stratos balloon (or seen the GoPro commercial during a recent Super Bowl). On Oct. 14, 2012 he reached an altitude of nearly 128,000 feet (39 km or 24 miles) and then jumped. He reached a speed of 843 MPH on the way down (Mach 1.25 or 1.25 times the speed of sound).

Here's a short video (1:25) that I'll show in class on Thursday. It shows portions of his jump. If you have time you should really watch the longer version (9:32). Baumgartner began to spin during the descent but was able get out of it. He came very close to blacking out.

Jacques Piccard, Auguste's son, would later travel with Lt. Don Walsh of the US Navy to a depth of about 35,800 feet in the ocean in the Mariana Trench (Auguste participated in some of the test descents to 10,000 ft). They did that in the Bathyscaph Trieste (shown below) on Jan. 23, 1960 (source of the image). I'll try to show a short video of one of their test dives (to 10,000 ft.)

Here's a National Geographic video describing film director James Cameron's much more recent dive to the Challenger Deep in the Mariana Trench on Mar. 12, 2012 (2:16). (note mention of the 16,000 psi pressure on the submersible at the bottom of the ocean)

Bertrand Piccard, Jacques' son (Auguste's grandson) was part of the first two man team to circle the globe non-stop in the Breitling Orbiter 3 balloon (Mar. 20, 1999). Brian Jones was the second team member (source of the left image above, source of the right image). I've got a pretty good video summary of their trip. Here are three online videos of the event: short summary (1:40), longer summary (6:15 with music only, no commentary) and a full documentary (54:06).


We've poured out the water and filled the 1 gallon jug with air. Air is much less dense than water; compared to water, the jug will weigh practically nothing. But it still displaces a gallon of water and experiences the 8 lb. upward buoyant force. The bottle of air would rise (actually it shoots up to the top of the pool).	A bottle filled with water is weightless. The density of the material inside and outside the bottle are the same.