Tuesday Feb. 7, 2012
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The best of recent selections played in the MWF section of the class.  You heard "Marching Bands of Manhattan" from Death Cab for Cutie and "Reckoner" from Radiohead before class this morning.

Thanks to a 7 am delivery from the class TA, all of the Practice Quizzes were returned in class today.  The average score of -55 (out of 150 pts = 63%) is actually a pretty typical score for a practice quiz as the table below shows (I recomputed the average after class, the value below is a little lower than what I mentioned in class).

Semester
 MWF
class
 T Th
class
S12
 61%
 63%
S11
 62%
 ---
S10
 62%
 61%
S09
 60%
 ---
S08
 64%
 66%

I would suggest you download the Practice Quiz if you didn't take it so that you can become familiar with the quiz format.  You can check your answers against the answers that are available online.  Quiz #1 in just over a week will cover Practice Quiz material plus new material that we cover between now and then.

The Experiment #1 reports were collected today.  It generally takes a week, maybe a little more, to get them graded.  Meanwhile the Experiment #2 materials should be distributed on Thursday.  If you haven't returned your Experiment #1 materials please do so as soon as you can so that they can be cleaned up and handed out to the Expt. #2 people.  The 1S1P Assignment #1 reports were also collected today.

A take-home Optional Assignment was handed out in class; the assignment is due on or before the start of class next Tuesday (Feb. 14).  Be sure to have the assignment done before you come to class.

We started working on the three steps needed 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 finish all of that up today.

First though a couple of examples involving the ideal gas law, just to refresh your memory.



A can of spray paint is a sealed rigid container.  That means N (number of gas molecules) and V (volume) stay constant.  Heating up a can of spray paint (something you shouldn't do) will increase the temperature and increase the pressure.  If the pressure gets too high the can will explode.

In this next example we add some air to a tire.

In this case the volume, V, and the temperature of the air, T, remain constant.  But we are adding air so N will increase.  This causes pressure to increase.

A volume of air in the atmosphere will behave somewhat differently.  The volume can change.  The thing that will cause the volume to change is creating an imbalance between the two pressures (two forces) shown in the figure below.


Here the pressure of the air outside the volume that is pushing inward and trying to crush the balloon is balanced by an outward pointing pressure of equal intensity from the air inside the parcel [a parcel is just a volume of air]. 

If we change something inside the balloon and upset this balance, the balloon will expand or shrink in an effort to bring the inward and outward pointing forces back into balance.

Charles' Law is a special situation involving the ideal gas law.  We can change conditions inside the balloon but will require that the pressure of the air inside the parcel remain constant (P inside is always trying to stay equal to P outside).

We'll look specifically at what happens if we heat or cool inside a parcel.  This is a little more detailed version than was given in class.
First let's imagine warming the air inside a balloon.

We'll start with air inside the balloon that is exactly the same as the air outside the balloon (same air density, temperature, and pressure inside and outside the balloon). 

Next we'll warm the air inside the balloon but leave the air outside alone.

Increasing the temperature will momentarily increase the pressure.  This creates an imbalance, so this is a temporary situation.  Now that P inside is greater than P outside the balloon will expand.


Increasing V in the ideal gas law equation will decrease P.  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 was originally. 





The pressures inside and outside are again the same.  The pressure inside is again equal to its starting value.  The 1st form of the ideal gas law show you that you can increase the temperature and volume of a parcel together in a way that keeps pressure constant (which is what Charles' law requires).  The 2nd version of the equation shows that by increasing the temperature and decreasing the density together you can keep pressure constant.

We can go through the same kind of reasoning and see what happens if we cool the air in a parcel.



We'll start with the same picture we had above. 

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 momentarily.  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.

In the atmosphere a parcel of cold air will be high density air.

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).  The air inside the parcel is again equal to the density of the air outside.

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.

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 (it's still cooler than the surrounding air).  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 (I didn't mention this in class).


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 finished the day and the week with a little information about Archimedes Law.  We've just learned that the relative strengths of the downward gravitational force and the upward pressure difference force determine whether a parcel of air will rise or sink.  Archimedes Law is another, somewhat simpler, way of trying to understand this topic.


A gallon of water weighs about 8 pounds (lbs).

If you submerge the gallon jug of water in a swimming pool, the jug becomes, for all intents and purposes, weightless.  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 bouyant 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 bouyant 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 bouyant force will be 8 pounds, the same as the downward force.  The two forces are equal and opposite.

Archimedes law doesn't really tell you what causes the upward bouyant force.  If you're really on top of this material you will recognize that it is really just another name for the pressure difference force that we just covered.

Now we imagine pouring out all the water and filling the 1 gallon jug with air.  Air is about 1000 times less dense than water;compared to water,  the jug will weigh practically nothing.




If you submerge the jug of air in a pool it will displace 1 gallon of water and experience an 8 pound upward bouyant force again.  Since there is no downward force the jug will float.

One gallon of sand (which is about 1.5 times denser than water) jug weighs 12 pounds (I try to give you accurate information and actually checked this out).


The jug of sand will sink because the downward force is greater than the upward force.

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.

The same reasoning applies to air in the atmosphere.


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.

It all comes down to how the density of an object compares to the density of the fluid (gas or liquid) surrounding it.  Something that is less dense than water (many kinds of wood for example) will float.  Something that is denser than water, like a rock, 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 Dr. Pepper (not Pepsi as shown above) was placed in a beaker of water.  The can sank.  A can of Diet Dr. Pepper on the other hand floated.

Both cans are made of aluminum which has a density almost three times higher than water.  The drink itself is largely water.  The regular soft drink also has a lot of high-fructose corn syrup, the diet drink 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 average density of the can of regular drink (water & corn syrup + aluminum + air) ends up being slightly greater than the density of water.  The average density of the can of diet drink (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). 

Many people can fill their lungs with air and make themselves float, or they can empty their lungs and make themselves sink.  People have an average density that is about the same as water.  That makes sense because we are largely made up of water (water makes up about 60% of human males and 55% of human females according to this source)


We watched another short video segment at the end of class.  This showed a trial run of the bathyscaph Trieste developed by Auguste Piccard.  In the video Auguste and his son Jacques descended to a depth of 10,000 feet in the ocean.  Jacques would later take the Trieste down to a depth of more than 35,000 feet.