Thursday Feb. 25, 2010
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The music today was from Duffy ("Rockferry" and "Mercy" and "Distant Dreamer").  A friend just recently told me about her.  She had at least one song in the recent movie "An Education."

The Experiment #2 reports are due next Tuesday.  You can still return the materials and pick up the supplementary information sheet this week or early next week.  You'll need to come by my office in PAS 588 between about 9:30 and 5 pm.  You'll find a box just inside the door and copies of the information sheet nearby.

The revised Expt. #1 reports are due Thursday next week (please return the original report).

The first of the 1S1P Bonus Assignments is due Tuesday next week.

There was a 2-question in-class optional assignment today.  You'll find both questions at the end of today's notes.  If you weren't in class and are reading these notes you can turn in answers to the questions at the start of class next Tuesday and receive at least partial credit.


We first reviewed some material (temperature, heat, and temperature scales) that was stuck onto the end of the online notes from last Tuesday.  Material that we weren't able to cover in class because of the fire alarm.


Conduction is the first of four energy transport processes that we will cover (the least important transport process in the atmosphere).  The figure below illustrates this process.  A hot object is stuck in the middle of some air.


In the top picture some of the atoms or molecules near the hot object have collided with the object and picked 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 pink). 

In the middle picture the initial bunch of 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 out have now (the yellow ones) gained some energy.  The random motions and collisions between molecules is carrying energy from the hot object out into the colder material.

Conduction transports energy from hot to cold.  The rate of energy transport depends first on the material (air in the example above).  Thermal conductivities of some common materials are listed.  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 (cooking pans are often made of stainless steel but have aluminum or copper bottoms to evenly spread out heat when placed on a stove).  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.

Transport of energy by conduction is similar to the transport of a strong smell throughout a classroom by diffusion.  Small eddies of wind in the classroom blow in random directions and move smells throughout the room..  For our demonstration we used curry powder.



With time the smell seemed to have spread throughout about half the room.  A second pile of curry powder was placed in the back of the room so that everyone would get a chance to smell it.


Because air has such a low thermal conductivity it is often used as an insulator.  It is important, however, to keep the air trapped in small pockets or small volumes so that it isn't able to move and transport energy by convection (we'll look at convection shortly).  Here are some examples of insulators that use air:


Foam is filled with lots of small air bubbles (it is important that the bubbles be small otherwise convective air currents become establised; we'll see that convection is a more efficient energy transport process than conduction)


Thin insulating layer of air in a double pane window



Hollow fibers (Hollofil) filled with air used in sleeping bags and winter coats.  Goose down works in a similar way.


Convection was the next energy transport process we had a look at.  Rather than moving about randomly, the atoms or molecules move as a group.  Convection works in liquids and gases but not solids. 


At Point 1 in the picture above a thin layer of air surrounding a hot object has been heated by conduction. Then at Point 2 a person (yes, that is a drawing of a person's head) is blowing the blob of warm air off to the right.  The warm air molecules are moving away at Point 3 from the hot object together as a group (that's the organized part of the motion).  At Point 4 cooler air moves in and surrounds the hot object and the whole process 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.  I had wanted to put a small fan behind the curry powder to help spread the smell further out into the classroom, but I forgot to bring the fan.


A thin layer of air at Point 1 in the figure above (lower left) is heated by conduction.  Then because 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 (Point 3).  Energy is being transported away from the hot object into the cooler surrounding air.  This is called free convection and represents another way of causing rising air motions in the atmosphere.  Cooler air moves in to take the place of the rising air at Point 4 and the cycle repeats itself.

The example at upper right is also free convection.  Room temperature air in contact with a cold object loses energy and becomes cold high density air.  The sinking air motions that would be found around a cold object have the effect of transporting energy from the room temperature surroundings to the colder object.

In both examples of free convection, energy is being transported from hot toward cold.


Now some practical applications of what we have learned about conductive and convective energy transport.  Energy transport really does show up in a lot more everyday real life situations than you might expect.




Note first of all there is a temperature difference between your hand and a 70 F object.  Energy will flow from your warm hand to the colder object.  Metals are better conductors than wood.  If you touch a piece of 70 F metal it will feel much colder than a piece of 70 F wood, even though they both have the same temperature.  A piece of 70 F diamond would feel even colder because it is an even better conductor than metal. 

Something that feels cold may not be as cold as it seems. 
Our perception of cold is more an indication of how quickly our hand is losing energy than a reliable measurement of temperature.

Here's a similar situation.


It's pleasant standing outside on a nice day in 70 F air.  But if you jump into 70 F pool water you will feel cold, at least until you "get used" to the water temperature (your body might reduce blood flow to your extremeties and skin to try to reduce energy loss).

Air is a poor conductor.  If you go out in 40 F weather you will feel colder largely because there is a larger temperature difference between you and your surroundings (and temperature difference is one of the factors that affect rate of energy transport by conduction). 

If you stick your hand into a bucket of 40 F water (I would suggest you give it a try sometime), it will feel very cold (your hand will actually soon begin to hurt).  Water is a much better conductor than air.  Energy flows much more rapidly from your hand into the cold water. 


Ice feels cold even though it is not a particularly good conductor.  This is because of the large temperature difference between your hand and the water.  The ice figure wasn't shown in class.

What about liquid nitrogen?  It has a temperature of -320F!  You can safely stick your hand in liquid nitrogen for a fraction of a second.  It doesn't feel particularly cold and doesn't feel wet.  Some of the liquid nitrogen quickly evaporates and surrounds your hand with a layer of nitrogen gas.  This gas is a poor conductor and insulates your hand from the cold for a short time.


This basic knowledge puts us in a perfect position to understand the concept of wind chill temperature.


Your body works hard to keep its core temperature around 98.6 F.  If you go outside on a 40 F day (calm winds) you will feel cool; your body is losing energy to the colder surroundings (by conduction mainly).  Your body will be able to keep you warm for a little while anyway (maybe indefinitely, I don't know).  A thermometer behaves differently, it is supposed to cool to the temperature of the surroundings.  Once it reaches 40 F it won't lose any additional energy.  If your body cools to 40 F you will probably die.


If you go outside on a 40 F day with 30 MPH winds your body will lose energy at a more rapid rate (because convection together with conduction are transporting energy away from your body).  Note the additional arrows drawn on the figures above indicating the greater heat loss.  This higher rate of energy loss will make it 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 28 F day without any wind.  Your body is losing energy at the same rate in both cases.  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, it will just cool more quickly on a windy day.  Once the thermometer reaches 40 F there won't be any additional energy flow.   The thermometer would measure 40 F on both the calm and the windy day. 


Standing outside on a 40 F day is not an immediate life threatening situation.  Falling into 40 F water is. 


Energy will be conducted away from your body more quickly than your body can replace it.  Your core body temperature will drop and bring on hypothermia. Be sure not to confuse hypothermia with hyperthermia which can bring on heatstroke and which is also a serious outdoors risk in S. Arizona.


At this point I showed a picture from the March 2005 issue of National Geographic. A Buddhist monk was standing in a frigid waterfall.  The caption for the photograph read "To focus the mind and increase awareness of self, Shingon Buddhists like Souei Sakamoto practice takigyo,chanting for hours while standing in frigid waterfalls at the Oiwasan Nissekiji Temple in Toyama, Japan."  (I can't really scan the photograph and include it in the classnotes because of copyright laws)

A second photograph from the December 2005 issue showed a monk hanging from a tree by his feet.  The caption there read "
To see life as it truly is - that's the goal of a student in China who strengthens mind and body under the rigorous tutelage of a Shaolin kung fu master."

Perhaps the most amazing example of a physical and mental task (not mentioned in class) is the 1000-day challenge undertaken by the "marathon monks" of Mount Hiei, Japan.

I hope you don't mind an occasional digression like this.  I spend a lot of time riding my bicycle uphills.  It's not really painful but can definitely be uncomfortable.  I've noticed that you can sometimes be distracted by a thought and ride a mile or so and completely blank out the discomfort.  With some "Buddhist monk like" training I wonder if maybe I couldn't ride uphill more or less indefinitely and not feel any discomfort at all.  This time of the year it is sometimes cold in the morning when I'm out riding my bike.  With some mental training I hope be to be able to block out the feeling of cold fingers and toes.  I'm not there yet but will continue to work on it.



Latent heat energy transport was the next topic of the day.
Energy transport in the form of latent heat is the second most important energy transport process (second only to electromagnetic radiation). 

If you had an object that you wanted to cool off quickly you could blow on it.  Or you could stick it into some water, that would cool it off pretty quickly because water will conduct energy more rapidly than air.  With a really hot object immersed in water, you'd probably hear a brief sizzling sound, the sound of boiling water.  A lot of energy would be taken quickly from the hot object and used to boil (evaporate) the water. 

Latent heat energy transport is sometimes a little hard to visualize or understand because the energy is "hidden" in water vapor or water.


Latent heat energy transport is associated with changes of phase (solid to liquid, water to water vapor, that sort of thing) 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 add or supply the energy (such as when you put water in a pan and put the pan on a hot stove) or the phase change can occur without you playing any role.  In that case the needed energy will be taken from the surroundings.  When you step out of the shower in the morning, the water takes energy from your body and evaporates.  Because your body is losing energy your body feels cold. 




The object of this figure is to give you some appreciation for the amount of energy involved in phase changes.  A 240 pound man or woman running at 20 MPH has just enough kinetic energy (if you could capture it) to be able to melt an ordinary ice cube.  It would take 8 people running at 20 MPH to evaporate the resulting water. 

When you freeze water and make an ice cube energy is released into the surroundings.  You can picture the released energy as being a 240 lb person running at full speed.




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 freezer;  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).  Note the orange energy arrows have turned around and are pointing from the material toward the surroundings.

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.  The condensation may actually be the dominant process.

You feel cold when you step out of a shower and water on your body evaporates.  The opposite situation, stepping outdoors on a humid day and actually having water vapor condense onto your body (it can happen to your sunglasses but not to you, your body is too warm).  If it did happen it would warm you up.





This figure shows how energy can be transported from one location to another in the form of latent heat.  The story starts at left in the tropics where there is often an abundance or surplus of sunlight energy.  Some of the incoming sunlight evaporates ocean water.  The resulting water vapor moves somewhere else and carries hidden latent heat energy with it. 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 probably the next couple of class periods on electromagnetic (EM) radiation.  It is the most important energy transport process because it can travel through empty space.  The notes that follow are quite a bit more detailed those written down in class.

To really understand EM radiation you need to know something about electric fields.  To understand electric fields we need to quickly review a basic rule concerning static electricity. 


These rules were demonstrated using a wool sweater and a couple of balloons.


Each balloon was rubbed with the sweater.  The balloons (and the sweater) all became electrically charged (the balloons had one polarity of charge, the sweater had the other).  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.

Our next step in understanding EM is to learn something about electric field arrows.  Imagine placing a + charge at the three positions shown in the figure below.

Then choose one of the three arrows at the bottom of the picture to show both the direction and the force that would be exerted on each charge.


Here's the answer.  The closer the charge is to the center, the greater the strength of the outward force.  With just a little thought you can see that if you were to place + charges at other positions you would quickly end up with a figure that looks like the pattern at the bottom of p. 59 in the photocopied ClassNotes.

The electric field arrows in this picture show the direction and give an idea of the strength that would be exerted on a positive placed at any position in the figure. 


You'll find the following on p. 60 in the photocopied ClassNotes.  I just hinted that this was the direction we would be going once we come back to this topic next Tuesday.  I'll put in some of the details just in case you are reading ahead.

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 electric field arrows repeats itself. 

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


Textbooks often represent EM radiation with a wavy line like shown above. But what does that represent?

The wavy line just connects the tips of a bunch of electric field arrows.

This picture was taken a short time after the first snapshot when the radiation had traveled a little further to the right.  The EM radiation now exerts a somewhat weaker downward force on the + charge.


The + charge is now being pushed upward again.  A movie of the + charge, rather than just a series of snapshots, would show the charge 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 can be described spatially in terms of its wavelength, the distance between identical points on the pattern.  By spatially we mean you look at different parts of the radiation at one particular instant frozen in time.



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).  By temporally we mean you at one particular point for a certain period of time.



In-class Optional Assignment

Question #1
The _______ is the amount of energy that you must add
to 1 gram of a material to raise its temperature 1 C.
a. density    b. kinetic energy    c. latent heat    d. specific heat    e. thermal conductivity


Question #2


Try to identify the energy transport process shown at each of the numbered points in the picture above.