Fri., Feb. 7 notes

Friday Feb. 7, 2014

A live version of Okkervil River's "Lost Coastlines" before class.

The Practice Quiz has been graded and was returned in class today. You'll find the number of points missed (out of 160 points total) written in the upper left hand corner on the front side of your quiz. The average grade was -61 which works out to be 62%, which as you can see below, is very typical for the Practice Quiz.

Semester	8 am class	10 am class	2 pm class	Semester	8 am class	9:30 am class	2 pm class
S14		63	62	F14
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 last of the 1S1P Assignment #1 reports was due today. I've added a link on the class home page so that you can keep track of how the grading of the reports is progressing.

Could you fill in the blanks in a statement like this?

___________________ law or principle states that an object immersed in a fluid experiences a(n) ____________________ equal to the ____________________ of the fluid that is _____________________.

The answers are at the end of today's notes.

We've spent a lot of time looking at air pressure and how it changes with altitude. Today we'll consider air density and air temperature.

How does air density change with increasing altitude? You should know the answer to that question. You get out of breath more easily at high altitude than at sea level. Air gets thinner (less dense) at higher altitude. A lungful of air at high altitude just doesn't contain as much oxygen as at lower altitude or at sea level.

It would be nice to understand why air density decreases with increasing altitude.

The people pyramid reminds you that there is more weight, more pressure at the bottom of the atmosphere than there is higher up.

Let's image layers of air in the atmosphere as being like mattresses stacked on top of each other. This is better than the piles of bricks representation we have used. Mattresses are compressible, bricks (and people) aren't. Mattresses are also reasonably heavy, the mattress at the bottom of the pile would be squished by the weight of the three mattresses above. This is shown at right. The mattresses higher up aren't compressed as much because there is less weight remaining above. The same is true with layers of air in the atmosphere.

The statement above is at the top of p. 34 in the photocopied ClassNotes. I've redrawn the figure found at the bottom of p. 34 below.

There's a surprising amount of information in this figure and it is worth spending a minute or two looking for it and thinking about it.

1. You can first notice and remember that pressure decreases with increasing altitude. 1000 mb at the bottom decreases to 700 mb at the top of the picture. You should be able to explain why this happens.

2. Each layer of air contains the same amount (mass) of air. This is a fairly subtle point. You can tell because the pressure drops by 100 mb as you move upward through each layer. Pressure depends on weight. So if all the pressure changes are equal, the weights of each of the layers must be the same. Each of the layers must contain the same amount (mass) of air (each layer contains 10% of the air in the atmosphere).

3. The densest air is found at the bottom of the picture. The bottom layer is compressed the most because it is supporting the weight of all of the rest of the atmosphere. It is the thinnest layer in the picture and the layer with the smallest volume. Since each layer has the same amount of air (same mass) and the bottom layer has the smallest volume it must have the highest density. The top layer has the same amount of air but about twice the volume. It therefore has a lower density (half the density of the air at sea level). Density is decreasing with increasing altitude.

4. Finally pressure is decreasing most rapidly with increasing altitude in the densest air in the bottom layer. This is something we covered a week or two ago and something we'll use again 2 or 3 times later in the semester.

What happens to air temperature with increasing altitude. Again our personal experience is that it decreases with increasing altitude. It is colder at the top of Mt. Lemmon than it is here in the Tucson valley.

That is true up to an altitude of about 10 km (about 30,000 ft.). People were very surprised in the early 1900s when they used balloons to carry instruments above 10 km and found that temperature stopped decreased and even began to increase with increasing altitude.

Measurements of air temperature at high altitude in unmanned balloons lead to the discovery of the stratosphere in about 1900 (the information above is on p. 31 in the ClassNotes).

The figures below are more clearly drawn versions of what was done in class.

The atmosphere can be split into layers depending on whether temperature is increasing or decreasing with increasing altitude. The two lowest layers are shown in the figure above. There are additional layers (the mesosphere and the thermosphere) above 50 km but we won't worry about them in this class.

1. We live in the troposphere. The troposphere is found, on average, between 0 and about 10 km altitude, and is where temperature usually decreases with increasing altitude. [the troposphere is usually a little higher in the tropics and lower at polar latitudes]

The troposphere can be stable or unstable (tropo means "to turn over" and refers to the fact that air can move up and down in the troposphere). The troposphere contains most of the water vapor in the atmosphere (the water vapor comes from evaporation of ocean water and then gets mixed throughout the troposphere by up and down air motions) and is where most of the clouds and weather occurs.

2a. The thunderstorm shown in the figure with its strong updrafts and downdrafts indicates unstable conditions. When the thunderstorm reaches the top of the troposphere, it runs into the bottom of the stratosphere which is a very stable layer. The air can't continue to rise into the stratosphere so the cloud flattens out and forms an anvil (anvil is the name given to the flat top of the thunderstorm). The flat anvil top is something that you can go outside and see and often marks the top of the troposphere.

ISS016-E-027426

ISS015-E_27038

ISS007-E-13020

Here are several images of thunderstorms and anvil clouds taken from above, from the International Space Station (all 3 images courtesy of the Image Science and Analysis Laboratory, NASA Johnson Space Flight Center, www.eol.jsc.nasa.gov).

This photo was selected as the Picture of the Day on Wikipedia for Dec. 22, 2007.
Photo credit: Luca Galluzi www.galluzi.it

2b. The summit of Mt. Everest is a little over 29,000 ft. tall and is close to the average height of the top of the troposphere.

2c.   Cruising altitude in a passenger jet is usually between 30,000 and 40,000, near or just above the top of the troposphere, and at the bottom of the stratosphere. The next time you're in an airplane try to look up at the sky above. There's less air and less scattering of light. As a result the sky is a darker purple color not blue. If you get high enough the sky would eventually become black.

3. Temperature remains constant between 10 and 20 km and then increases with increasing altitude between 20 and 50 km. These two sections form the stratosphere. The stratosphere is a very stable air layer. Increasing temperature with increasing altitude is called an inversion. This is what makes the stratosphere so stable.

4.   A kilometer is one thousand meters. Since 1 meter is about 3 feet, 10 km is about 30,000 feet. There are 5280 feet in a mile so this is about 6 miles (about is usually close enough in this class).

5.    The ozone layer is found in the stratosphere. Peak ozone concentrations occur near 25 km altitude.

Here's the same picture drawn again (for clarity) with some additional information. We need to explain why when temperature decreases all the way up to the top of the troposphere, it can start increasing again in the stratosphere.

6. Sunlight is a mixture of ultraviolet (7%), visible (44%, colored green in the picture above) and infrared light (49%, colored red). We can see the visible light.

6a. On average about 50% of the sunlight arriving at the top of the atmosphere passes through the atmosphere and is absorbed at the ground (20% is absorbed by gases in the air, 30% is reflected back into space). This warms the ground. The air in contact with the ground is warmer than air just above. As you get further and further from the warm ground, the air is colder and colder. This explains why air temperature decreases with increasing altitude in the troposphere.

5b. How do you explain increasing temperature with increasing altitude in the stratosphere?

Absorption of ultraviolet light by ozone warms the air in the stratosphere and explains why the air can warm (oxygen also absorbs UV light). The air in the stratosphere is much less dense (thinner) than in the troposphere. So even though there is not very much UV light in sunlight, it doesn't take as much energy to warm this thin air as it would to warm denser air closer to the ground.

7. That's a manned balloon; Auguste Piccard and Paul Kipfer are inside. They were the first men to travel into the stratosphere (see pps 31 & 32 in the photocopied Class Notes). It really was quite a daring trip at the time, and they very nearly didn't survive it.

Pages 31 and 32 in the ClassNotes list some of the significant events in the early study and exploration of the atmosphere. A few of them are included below.

Note the mercury barometer was invented in 1643.

The earliest balloon trips into the upper atmosphere were in unheated and unpressurized gondolas. Climbers have made it to the summit of Mt. Everest without carrying supplementary oxygen but it is difficult and requires acclimation. You can't acclimate to conditions above 25,000 ft and can't remain up there very long - it's referred to as the "death zone." (Read "Into Thin Air" by Jon Krakauer if you'd like to get some idea of what it's like trying to climb Mt. Everest)

Note the clothing that Capt. Grey had to wear to try to stay warm. All of his trips were in an open, unpressurized gondola.

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. This was used to control the temperature inside the gondola during the flights.

You might have heard about Felix Baumgartner and the Red Bull Stratos balloon (or seen the GoPro commercial during the 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) showing portions of his jump. If you have time you should really watch the longer version (8:17). 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).

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 below, source of the right image)

Here's a pretty good video recap of the expedition.

___Archimedes____ law or principle states that an object immersed in a fluid experiences a(n) ___upward buoyant force____ equal to the ______weight_______ of the fluid that is ______displaced_______.