Tue., Oct. 4 notes

Kinetic energy is energy of motion. Some examples (both large and microscopic scale) are mentioned and sketched above. This is a relatively easy to visualize and understand form of energy.

Radiant energy is a very important form of energy that was somehow left off the original list in the ClassNotes . Electromagnetic radiation is another name for radiant energy. Sunlight is an example of radiant energy. It's something that we can see and feel (you feel warm when you stand in sunlight). Something that is not quite so obvious is that everyone in the classroom is emitting radiant energy. This is infrared light, an invisible form of radiant energy. And actually it's not just the people; the walls, ceiling, floor and even the air in the classroom are also emitting infrared light. We can't see it and, because it's there all the time, I'm not sure whether we can feel it or not.

Latent heat energy is an, important, under-appreciated, and rather confusing type of energy. The word latent refers to energy that is hidden. That's part of the problem. Another part of what makes latent heat energy hard to visualize and appreciate is that the energy is hidden or stored in water vapor or water - that seems an unlikely place to find energy.

2. We'll get the topic of energy units out of the way

Joules are the units of energy that you would probably encounter in a physics class. Your electric bill shows the amount of energy that you have used in a month's time, the units are kilowatt-hours. We'll usually be using calories as units of energy. 1 calorie is the energy need to warm 1 gram of water 1 C (there are about 5 grams of water in a teaspoon).

3. Temperature provides a measure of the average kinetic energy of the atoms or molecules in a material.

The atoms or molecules inside the warmer object will be moving more rapidly (they'll be moving freely in a gas, just "jiggling" around while still bonded to each other in a solid). Since kinetic energy is energy of motion, temperature gives you an idea of the average speed of the moving atoms or molecules in a material.

You need to be careful what temperature scale you use when using temperature as a measure of average kinetic energy. You must use the Kelvin temperature scale because it does not go below zero (0 K is known as absolute zero). The smallest kinetic energy you can have is zero kinetic energy. There is no such thing as negative kinetic energy.

There are three temperature scales that we might have occasion to use in this class. They're shown below. There are two temperatures that you should try to remember for each scale.

The boiling and freezing points of water on both the Celsius and the Fahrenheit scales (the freezing point of water and the melting point of ice are the same). Remember that the Kelvin scale doesn't go below zero. 0 K is referred to as absolute zero, it's as cold as you can get. A nice round number of the average temperature of the earth is 300 K, that's the last temperature value to remember.

Here's some additional temperature data that I'm including just in case you're interested.

You certainly don't need to try to remember all these numbers. The world high temperature record value of 136 F above was measured in Libya at a location that was only about 35 miles from the Mediterranean coast. Water, as we have seen, moderates climate so it seemed odd that such a high temperature would have been recorded there. The World Meteorological Organization recently decided the 136 F reading was invalid and the new world record is the 134 F measurement made in Death Valley.

The continental US cold temperature record of -70 F was set in Montana and the -80 F value in Alaska. The world record -129 F was measured at Vostok station in Antarctica. This unusually cold reading was the result of three factors: high latitude, high altitude, and location in the middle of land rather than being near or surrounded by ocean (again water moderates climate, both hot and cold).

Liquid nitrogen is very cold but it is still quite a bit warmer than absolute zero. Liquid helium gets within a few degrees of absolute zero, but it's expensive and there's only a limited amount of helium available. So I would feel guilty bringing some to class and I don't think it would look any different than liquid nitrogen.

4. Energy, temperature, and specific heat
(p. 45 in the ClassNotes)

When you add energy to an object, the object will usually warm up (or if you take energy from an object the object will cool). It is relatively easy to come up with an equation that allows you to figure out what the temperature change will be (this is another equation I'll try to remember to write on the board before the next quiz - try to understand it, you don't have to memorize it).

The temperature change, ΔT, will first depend on how much energy was added, ΔE. This is a direct proportionality, so ΔE is in the numerator of the equation (ΔE and ΔT are both positive when energy is added, negative when energy is removed)

When you add equal amounts of energy to large and small pans of water, the water in the small pan will get hotter. The temperature change, ΔT, will depend on the amount of water, the mass. A small mass will mean a large ΔT, so mass should go in the denominator of the equation.

Specific heat is what we use to account for the fact that different materials react differently when energy is added to them. A material with a large specific heat will warm more slowly than a material with a small specific heat. Specific heat has the same kind of effect on ΔT as mass. Specific heat is sometimes called "thermal mass" or "thermal capacity." It might be useful to think of specific heat as being thermal inertia - a substance with high specific heat, lots of thermal inertia, will be reluctant to change temperature.

Here's an important example that will show the effect of specific heat (middle of p. 45).

Equal amounts of energy (500 calories) are added to equal masses (100 grams) of water and soil. We use water and soil in the example because most of the earth's surface is either ocean or land. Before we do the calculation, try to guess which material will warm up the most. Everything is the same except for the specific heats. Will water with its 4 times larger specific heat warm up more or less than the soil?

The details of the calculation are shown below.

With its higher specific heat, the water doesn't heat up nearly as much as the soil. If we had been removing energy the wouldn't cool off as much as the soil would.

5. Water moderates climate
These different rates of warming of water and soil have important effects on regional climate.

Oceans moderate the climate. Cities near a large body of water won't warm as much in the summer and won't cool as much during the winter compared to a city that is surrounded by land. Water's ΔT is smaller than land's because water has a higher specific heat.

The yearly high and low monthly average temperatures are shown at two locations above. The city on the coast has a 30^o F annual range of temperature (range is the difference between the summer and winter temperatures). The city further inland (assumed to be at the same latitude and altitude) has an annual range of 60^o F. Note that both cities have the same 60^o F annual average temperature.

Water moderates climates - it reduces the difference between summertime high and wintertime low temperatures.

Growing tomatoes in the desert - practical application
We didn't cover this in class. Here's another situation where you can take advantage of water's high specific heat to moderate climate on a smaller scale.

You need to start tomatoes early in Tucson (mid February) before it gets too hot, so that they can produce fruit before it gets to hot. In you need to protect the plants from frost.

Here's one way of doing that. You moderate the climate and surround each plant with a "wall o water" - a teepee like arrangement that surrounds each plant. The cylinders are filled with water and they take advantage of the high specific heat of water and won't cool as much as the air or soil would during a cold night. The walls of water produce a warm moist micro climate that the tomato seedlings love. The plastic is transparent so plenty of sunlight can get through.

6. Energy transport processes

By far the most important process is at the bottom of the list above. Energy transport in the form of electromagnetic radiation (sunlight for example) is the only process that can carry energy through empty space. Electromagnetic radiation travels both to the earth (from the sun) and away from the earth back into space. Electromagnetic radiation is also responsible for about 80% of the energy transported between the ground and atmosphere.

You might be surprised to learn that latent heat is the second most important transport process. The term latent heat can refer to both a type of energy and an energy transport process (the energy is hidden in the water vapor, the water vapor can move around and carry that energy with it).

Rising parcels of warm air and sinking parcels of cold air are examples of free convection. Because of convection you feel colder or a cold windy day than on a cold calm day (the wind chill effect). Ocean currents are also an example of convection.

Convection is also one of the ways of rising air motions in the atmosphere (convergence into centers of low pressure and fronts are two other ways we've encountered so far)

Conduction is the least important energy transport at least in the atmosphere. Air is such a poor conductor of energy that it makes a very good insulator.

7. Energy transport by conduction

Conduction is the first of four energy transport processes that we will cover (and the least important transport process in the atmosphere). The figure below illustrates this process. Imagine heating the end of a piece of something just so you can visualize a hot object. If you held the object in air it would slowly lose energy by conduction and cool off.

How does that happen? 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 orange).

In the middle picture the initial layer of energetic molecules have collided with some of their neighbors and shared energy with them (these are pink). 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 (yellow) have now gained some energy. The random motions and collisions between molecules is carrying energy from the hot object out into the colder surrounding air.

Conduction transports energy from hot to cold. The rate of energy transport depends first on the temperature gradient or temperature difference between the hot object and the cooler surroundings. If the object in the picture had been warm rather than hot, less energy would flow and energy would flow at a slower into the surrounding air. If there were no temperature difference there wouldn't be any energy transport at all.

The rate of energy transport also depends on the material transporting energy (air in the example above). Thermal conductivities of some common materials are listed. Air is a very poor conductor of energy and 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 (apparently the highest of all known solids). 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.

Here's another neater sketch of conduction that was shown in class.

I brought a propane torch (2 of them actually, one to serve as a backup) to class to demonstrate the behavior of materials with different thermal conductivities. Here's what I wanted to illustrate


Copper is a good conductor. You must move your fingers several inches away from the end to keep from getting burned.	Glass has much lower thermal conductivity. You can hold onto the glass just a couple of inches from the flame and not feel any heat. Because energy is not being carried away from the end of the piece of glass, the glass can get hot enough to begin to glow red.	You can put your finger alongside the flame with just 1/2 inch or so of separation. Air is a very poor conductor. Don't put your finger above the flame though.

Because air has such a low thermal conductivity it is often used as an insulator. We didn't really discuss these examples in class.
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 momentarily). Here are some examples of insulators that use air:

Foam is often used as an insulator. Foam is filled with lots of small air bubbles, that's what provides the insulation.
You can safely hold onto a foam cup filled with liquid nitrogen (-320 F) because the foam does such a good job insulating your fingers from the cold liquid inside.

Thin insulating layer of air in a double pane window. I don't have double pane windows in my house. As a matter of fact I leave a window open so my cats can get in and out of the house (that's not particularly energy efficient). It also means there are lots of mosquitoes in the house in the summer.

We really haven't needed winter coats yet in Tucson this semester (rain coats yes but not winter coats).


Down feathers are often used in coats and sleeping bags. Packing together a bunch of the "clusters" produces very good insulation provided the feathers stay "fluffed up" and trap air. source of this image	Synthetic fibers (Primaloft - Synergy are shown above in a microphotograph) have some advantages over down. There is still some insulation when wet and the material is hypoallergenic. source of this image

A photograph of aerogel (image source), sometimes known as solid air. It's an excellent insulator because it is mostly air. The small particles in the aerogel are scattering light in the same way air molecules do. That's why it has this sky blue color.	A scanning electron microscope photograph of asbestos which was once widely used as insulation. Asbestos fibers can cause lung cancer and other damage to your lungs when inhaled. The white bar at the top left edge of the image is 50 um across. You can find this image and read more about asbestos here.

8. Energy transport by convection

I used the torch to heat up the broken glass graduated cylinder again. The glass gets so hot that you can see it starting to glow red.

How would you cool off a hot object like this? You could just hold onto it and it would eventually cool by conduction. If you were in a little bit more of a hurry you could blow on it. That's forced convection, the energy transport process we will be covering next. Or you could stick the hot end of the cylinder into some water (you'd hear a short hissing sound and the glass would probably shatter). The hissing would mean the hot piece of glass had evaporated some water. That would be an example of latent heat energy transport which we'll be discussing later in the period.

Rather than moving about randomly, the atoms or molecules move together as a group (organized motion). Convection works in liquids and gases but not solids (the atoms or molecules in a solid can't move freely).

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 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 repeats itself.

And actually you don't need to force convection, it will often happen on its own.

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. 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.

I could put my finger alongside the flame from the propane torch without any problem. There's very little energy transported sideways through air by conduction.

Be careful if you put your finger or hand above the torch. That's because there's a lot of very hot air rising from the torch. This is energy transport by free convection and its something you can sometimes see.

Up at the front of the classroom you might have been able to see (barely) the shimmering of hot rising air when I held the torch in front of the projector screen. There is a technique, called Schlieren photography, that can better catch these barely visible air motions (it is able to see and photograph the differences in air density). The photo at right is an example and shows the hot rising air above a candle. The photo was taken by Gary Settles from Penn State University and can be found at this site.

9. Real world examples of energy transport by conduction and convection
Now some surprisingly practical applications, I think, 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 room temperature (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. A piece of aluminum and a piece of wood (oak) were passed around class so that you could check this out for yourself.

Something that feels cold may not be as cold as it seems.

Our perception of cold
is more an indication of how quickly our body or hand is losing energy
than a reliable measurement of temperature.

Here's another example

It's pleasant standing outside on a nice day in 70 F air, it doesn't feel warm or cold. 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 extremities and skin to try to reduce energy loss).

Air is a poor conductor. If you go out in 40 F weather you will feel cold 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, it will feel very cold (your hand will actually soon begin to hurt). Keep some warm water nearby to warm up your hand.

Water is a much better conductor than air. Energy flows much more rapidly from your hand into the cold water. I mentioned in class that I thought this might be good for you. The reason is that successive application of hot and then cold is sometimes used to treat arthritis joint pain (it used to work wonders on my Dad's knee).

You can safely stick your hand into liquid nitrogen for a fraction of a second. There is an enormous temperature difference between your hand and the liquid nitrogen which would ordinarily cause energy to leave your hand at a dangerously high rate (which could cause your hand to freeze solid). It doesn't feel particularly cold though and doesn't feel wet. The reason is that some of the liquid nitrogen evaporates and quickly surrounds your hand with a layer of nitrogen gas. Just like air, nitrogen is a poor conductor (air is mostly nitrogen). The nitrogen gas insulates your hand from the cold for a very short time (the gas is a poor conductor but a conductor nonetheless) If you leave your hand in the liquid nitrogen for even a few seconds it would freeze. That would cause irreparable damage.

A question came up in class a few semesters ago about sticking you hand (or maybe just the tip of one finger) into molten lead. I've never seen it done and certainly haven't tried it myself. But I suspected that you would first need to wet your hand. Then once you stick it into the lead the water would vaporize and surround your hand with a thin layer of gas, water vapor. The water vapor is a poor conductor just like the nitrogen and oxygen in air, and that protects your hand, for a short time, from the intense heat. Here's a video (and water does play a critical role)

Wind chill
Wind chill is a really good example of energy transport by convection. As a matter of fact I'm hoping that if I mention energy transport by convection that you'll first think of wind chill. Wind chill is also a reminder that our perception of cold is an indication of how quickly our body is losing energy rather than an accurate measurement of 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 (perhaps indefinitely, I don't know). The 5 arrows represent the rate at which your body is losing energy.

A thermometer behaves differently, it is supposed to cool to the temperature of the surroundings. Once it reaches 40 F and has the same temperature as the air around it the energy loss will stop. If your body cools to 40 F you will 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 (9 arrows in both cases). The combination 40 F and 30 MPH winds results in a wind chill temperature of 28 F.

You would feel colder on a 40 F day with 30 MPH winds but the actual temperature is still 40 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 or further cooling. 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, you'd last about 30 minutes (though you might lose consciousness before that and die by drowning).

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 is a serious outdoors risk in S. Arizona in the summer.

Talk of how long you would last in 40 F water reminds me of a page from National Geographic Magazine that lists some of the limits of human survival. I can't just scan the original and add it to the notes without violating copyright laws. But if you click on the link above you'll find all of the same information online in the form of a quiz.

I was hoping to be able to cover latent heat energy transport in class today also. But, as I suspected there wasn't enough time. But I'll include the notes anyways. We'll cover this at the start of class on Thursday.

10. Latent heat energy transport

This is the 3rd and the next-to-most important energy transport process (probably also the hardest to understand).

If you had an object that you wanted to cool off quickly the best thing might be to stick it into some water. That would work first because water will conduct energy more rapidly than air. Also, and this is the most important part, when a really hot object is 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. The cooling in this case takes only a few seconds. It's a very potent energy transport process.

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 involves changes in phase or state. You need to be able to add two types of information to this picture (this is p. 55 in the ClassNotes): (i) You should be able to name each of the phase changes shown above and (ii) You should also be able to indicate whether energy must be added to or removed from the material in order for each phase change to take place. And actually there is a third thing, (iii), that we'll get to in a minute.

A solid to liquid phase change is melting, liquid to gas is evaporation, and sublimation is a solid to gas phase change.

Dry ice is the best example of sublimation that I can think of. When placed in a warm room, dry ice turns directly from solid carbon dioxide to gaseous carbon dioxide without melting first. If you wash clothes and stick them outside on a dry cold (below freezing) day they will eventually dry. The clothes would first freeze but then the ice would slowly sublime away.

In each case above 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 and cause it to boil).

That much is pretty clear. The confusing part of this topic is when phase changes occur without you playing any role. Energy is still required to melt ice; in this case the needed energy will be taken from the surroundings. It is not always obvious what the "surroundings" are.

Here is the third thing to understand, (iii). When energy is taken from the surroundings, what effect will that have on the surroundings? When you take energy from the surroundings, the surroundings will cool.

Here's an example where you play the role of the surroundings. You'll be able to feel what happens when energy is taken from your body and used to evaporate some water.

When you step out of the shower in the morning you're covered with water. Some of the water evaporates. It doesn't ask permission, it just evaporates whether you want it to or not. The energy needed for evaporation is taken from the surroundings, from your body. Because your body is losing energy you feel 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 (I have been using Tedy Bruschi as an example for several years but he's now retired so I have switched to Scooby Wright). It would take 8 people running at 20 MPH to evaporate the resulting ice water.

Latent heat energy is energy that is hidden in water or water vapor. We can now start to visualize what that means and how that works.


Energy added to melt the ice is hidden in the water that results	Energy added to evaporate the water is added to the energy already in the water and is hidden in the water vapor

Phase changes can go in the other direction

Again (i) try to name each phase change and (ii) show the direction of energy flow (into or out of the material) when the phase change occurs

You might not have heard of deposition before when a gas changes directly to a solid. The formation of frost is an example of deposition.

You can consciously remove energy from water vapor to make it condense. You take energy out of water to cause it to freeze (you could put water in a freezer; energy would flow from the relatively warm water to the colder surroundings). If one of these phase changes occurs, without you playing a role, energy will be released into the surroundings (causing the surroundings to warm).

Note the direction of the energy arrows - energy is being released into the surroundings (warming the surroundings). It's kind of like a genie coming out of a magic lamp. One Scooby Wright worth of kinetic energy is released when enough water freezes to make an ice cube. Many Scooby Wrights are released when water vapor condenses.

This release of energy into the surroundings and the warming of the surroundings is a little harder for us to appreciate because it never really happens to us in a way that we can feel. Have you ever stepped out of an air conditioned building into warm moist air outdoors and had your glasses or sunglasses "steam up"? Water vapor never condenses onto your body (your body is too warm). However if it did you would feel warm. It would be just the opposite of the cold feeling when you step out of the shower or a pool and the water on your body evaporates. You know how cold the evaporation can make you feel, the same amount of condensation would produce a lot of warming. I suspect we'd be surprised at how much warming it produces.

Alternate view showing the latent heat energy in water vapor and water coming out of hiding during a phase change and being released into the surroundings.

Here's a practical application of what we have been learning.

Cans of a cold drink are taken out of the refrigerator and placed on the kitchen table on a warm dry day and a warm humid day. Except for the differences in the amount of moisture in the air everything else is the same. Moisture has condensed onto the can above at right. Do the two cans warm up at the same rate or does one warm up more quickly than the other. In the latter case which can warms up most rapidly.

The can on the right will warm more quickly. Equal amounts of 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. I suspect that the condensation may actually be the dominant process.

The foam "cozy", "koozie", or whatever you want to call it, that you can put around a can of soda or beer is designed to insulate the can from the warmer surroundings but also, and probably more importantly, to keep water vapor in the air from condensing onto the can (source of the image above)

We're beating this concept to death but we're almost done. Two more figures to illustrate how latent heat energy transport can carry energy from location to another. This first one is my favorite, it ties everything together.

1. You've just stepped out of the shower and are covered with water. The water is evaporating and energy is being taken from your body.

2. The water vapor (containing the energy taken from your body), drifts into the kitchen where it finds a cold can sitting on a table.

3. Water vapor comes into contact with the cold can and condenses. The hidden latent heat energy in the water vapor is released into the can and warms the drink inside.

Without you even leaving the bathroom,
energy has effectively been transported from your warm body to the cold can in the kitchen.

Here's what happens on a much grander scale in the atmosphere.

We start in this picture in the tropics where there is often a 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. This would warm the air.

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

Here are scanned images of the lecture outline or summary sheet with some of the main details filled in.