Tue., Oct. 3 notes

Tuesday Oct. 3, 2006

Optional Assignment #2 was collected in class today.
Optional Assignment #3 questions will be asked during class on Tuesday and Thursday this week. This assignment will be due at the beginning of class next Tuesday (Oct. 10).

The Experiment #2 reports and the Expt. #1 report revisions are also due next Tuesday (Oct. 10). Return your Expt. #2 materials this week so that you can pick up the supplementary information sheet.

All of the 1S1P Assignment #1 papers have now been graded.

Have a quick look at the classnotes from last Thursday's class. A few things were slipped in after class. A figure explaining the difference between temperature (a measure of the average kinetic energy) and heat (the total kinetic energy of the atoms or molecules in an object) was added. You should also know the boiling points and freezing points of water on the Fahrenheit, Celsius, and Kelvin temperature scales (the freezing point of water is equal to the melting point of ice). 300 K is a good easy to remember value for the average temperature of the surface of the earth.

There are four energy transport processes: conduction, convection, latent heat and electromagnetic radiation. We'll look at conduction first; in the atmosphere it is the least important of the four.

The figure above illustrates energy transport by conduction. A hot object is stuck in the middle of some air. In the first picture the random motions of the atoms or molecules near the object have caused them to collide with and pick up energy from the object. This is reflected by the increased speed of motion or increased kinetic energy of these molecules or atoms (these guys are colored red). In the middle picture the energetic molecules have collided with some of their neighbors and shared energy with them (these are orange). The neighbor molecules have gained energy though they don't have as much energy as the molecules next to the hot object. In the third picture molecules further from the object now have gained some energy (the yellow ones). The random motions and collisions between molecules is carrying energy from the hot object out into the material.

The rate of energy transport depends on the material. Thermal conductivities of some materials are listed above. Air is a very poor conductor of energy. Air is generally regarded as an insulator. Water is a little bit better conductor. Metals are generally very good conductors. Diamond has a very high thermal conductivity. Diamonds are sometimes called "ice." They feel cold when you touch them. The cold feeling is due to the fact that they conduct energy very quickly away from your warm fingers when you touch them.

The rate of energy transport also depends on temperature difference. If the object in the picture had been warm rather than hot, less energy would flow or energy would flow at a slower into the surrounding material.

Here's a demonstration that we won't be able to do in class. The demonstration would involve opening a of glacial acetic acid (acetic acid gives vinegar its characteristic smell) in the front of the classroom. The acetic acid would begin to evaporate into the air. Collisions with air molecules would begin to move the acetic acid molecules toward the back of the room.

The strong irritating odor of the acetic acid would make it difficult to breath at the front of the room.

The odor would eventually spread throughout the class room. This is an example of diffusion. Because it involves random molecular motions it is, in many respects, like the conduction of heat.

Convection is a second way of transporting energy. Convection involves more organized motion of atoms or molecules in a liquid or gas (but not in a solid, the atoms or molecules aren't able to move freely enough).

In the top picture above the air surrounding a hot object has been heated by conduction. Then a person (yes that is a drawing of a person's head) is blowing the blob of warm air off to the right. Cooler air moves in and surrounds the hot object and the cycle can repeat itself. This is forced convection. If you have a hot object in your hand you could just hold onto it and let it cool by conduction. That might take a while because air is a poor conductor. Or you could blow on the hot object and force it to cool more quickly.

Note, in the bottom left figure, that the hot air is also low density air. It actually isn't necessary to blow on the hot object, the warm air will rise by itself. Energy is being transported away from the hot object. This is called free convection and represents another way of causing rising air motions in the atmosphere (rising air motions are important because rising air expands (as it moves into lower pressure surroundings) and cools. If the air is moist, clouds can form.

Note the example at right is also free convection. The sinking air motions that would be found around a cold object have the effect of transporting energy from the warm surroundings to the colder object.

Next are some real world applications of heat transport by conduction and convection

Metals are better conductors than wood. If you touch a piece of 70 F metal it will feel colder than a piece of 70 F wood. A piece of 70 F diamond would feel even colder because it is a better conductor than metal. Our perception of cold is more an indication of how quickly our hand is losing energy than a reliable measurement of temperature.

Touching a piece of ice also feels colder even though ice is not an especially good conductor. The cold feeling tells us that our hand is losing a lot of energy. I this case the high rate of energy loss is due to the large temperature differrence between our hand and the ice rather than just the thermal conductivity of the ice.

If you go outside on a 40 F day (calm winds) you will feel cold; your body is losing energy to the colder surroundings. A thermometer behaves differently. It actually cools to the temperature of the surroundings. Once there it won't lose any additional energy.

If you go outside on a 40 F day with 30 MPH winds your body will lose energy at a more rapid rate. It will feel colder than a 40 F day with calm winds. Actually, in terms of the rate at which your body loses energy, the windy 40 F day would feel the same as a calm 28 F day. The combination 40 F and 30 MPH winds results in a wind chill temperature of 28 F. The thermometer will again cool to the temperature of its surroundings. ON a windy day it will cool more quickly, but once it ends up at 40 F it won't cool any further. The thermometer would measure 40 F on both the calm and the windy day.

Water is a much better conductor than air. If you fall into 40 F water your body will lose energy at a high enough rate that your metabolism might not be able to keep up with it. Falling into 40 F water is a life-threatening situation.

Energy transport in the form of latent heat is the second most important energy transport process (second only to electromagnetic radiation). It is a little tricky to see how the energy is actually transported from one place to another. Before worrying about that a little review is necessary.

A solid to liquid phase change is melting, liquid to gas is evaporation, and sublimation is a solid to gas phase change (dry ice sublimates when placed in a warm room, it turns directly from solid carbon dioxide to gaseous carbon dioxide).

In each case energy must be added to the material changing phase. You can consciously supply the energy (such as when you put water in a pan and put the pan on a hot stove) or the needed energy will be taken from the surroundings (from your body when you step out of a shower in the morning).

Here's a school kids analogy:

You need to give a kid some energy in order to get him or her up and walking around. Even more energy is needed to get the kid outside running.

A 240 pound man (or woman) running at 20 MPH has just enough energy to be able to melt an ordinary ice cube. It would take 8 people to evaporate the resulting water.

You can consciously remove energy from water vapor to make it condense or from water to cause it to free (you could put water in a freeze, a cold "box"; energy would flow from the relatively warm water to the colder surroundings). Or if one of these phase changes occurs energy will be released into the surroundings (causing the surroundings to warm).

A can of cold drink will warm more quickly in warm moist surroundings than in warm dry surroundings. Heat will flow from the warm air into the cold cans in both cases. Condensation of water vapor is an additional source of energy and will warm that can more rapidly.

Here are the school kids again. They're out on the play ground running around and you need to get them back inside the classroom and sitting at their desks.

Now we put everything together and see how energy gets carried from one place to another.

The story starts at left in the tropics where there is often an abundance or surplus of energy; sunlight evaporates ocean water. The resulting water vapor moves somewhere else and carries hidden latent heat energy. This hidden energy reappears when something (air running into a mountain and rising, expanding, and cooling) causes the water vapor to condense. The condensation releases energy into the surrounding atmosphere.

Energy arriving in sunlight in the tropics has effectively been transported to the atmosphere in Tucson.

We'll spend the next couple of class periods on electromagnetic radiation. It is the most important energy transport process because it can travel through empty space.

To really understand EM radiation you need to understand electric fields. To understand electric fields we need to quickly review static electricity.

We used a sweater and two balloons to demonstrate the rules above.

If you rub a balloon with a wool sweather the balloon and the sweater become electrically charged (static electricity is one of the reasons I don't like wearing wool sweaters).

We actually charged up two balloons. We didn't know what charge the balloons carried just that they both had the same charge.

If you bring the balloons close to each other they are pushed apart by a repulsive electrical force.

The sweater and the balloon carry opposite charges. IF they are brought together they experience an attractive electrical force.
Now the bottom figure from p. 59 in the photocopied class notes.

The balloons can help you understand the picture above. Imagine placing one of the balloons at the center of the picture and assume that it is positively charged. The second balloon is placed at various positions (1, 2, and 3) around the central balloon. The arrows in the picture are the electric field. They give the direction and strength of the force that would be exerted on the second positive charge. At Position 1, for example a positively charged balloon would be pushed (by the + charge on the center balloon) to the upper right with a strong force. At Position 2 the force points straight up but isn't as strong because the + charge at Position 2 is further from the center charge. At Position 3 the charge is pushed to the left with a weak force.

You can also use the electric field arrows to figure out what would happen to a negative charge. The direction of the force is reversed.
Here are some sample questions about static electricity and electric fields (these are not part of Optional Assignment #3).

The figures on p. 60 in the photocopied class notes have been broken into 3 parts below for clarity.

We imagine turning on a source of EM radiation and then a short time later we take a snapshot. The EM radiation is a wavy pattern of electric and magnetic field arrows. We'll ignore the magnetic field lines. The E field lines sometimes point up, sometimes down. The pattern of arrows repeats itself.

Note the + charge near the right of the picture. At the time this picture was taken the EM radiation exerts a fairly strong upward force on the + charge.

This picture was taken a short time later and the radiation has traveled a little further to the right. The EM radiation now exerts a relatively weak downward force on the + charge.

The + charge is now being pushed upward again. A movie of the + charge would show it bobbing up and down much like a swimmer in the ocean would do as waves passed by.

The wavy pattern used to depict EM radiation (the wavy line connects the heads of the electric field arrows) can be described spatially in terms of its wavelength, the distance between identical points on the pattern.

Or you can describe the radiation temporally using the frequency of oscillation (number of up and down cycles completed by an oscillating charge per second)