Tuesday Feb. 26, 2008

Quiz #1 has been graded and was returned in class.  Be sure to carefully check your quiz for errors.

The 1S1P Topic #2 reports were returned in class.  The Topic #3 reports should be graded and returned on Thursday.  That will complete 1S1P Assignment #1.  Assignment #2 will probably appear sometime this week.

The Optional Assignment #2 papers were returned today.
Chapter 2 is concerned with energy, temperature, heat, energy transport, energy balance between the earth, atmosphere, and space. 

It is easy to lose sight of the main concepts because there are so many details.  The following (found on pps 43&44 in the photocopied Class Notes) is meant to introduce some of what we will be covering in class from Chapter 2.

We will learn the names of several different types or forms of energy. Kinetic energy is energy of motion. Some examples are mentioned and sketched above.  It is a relatively easy to visualize and understand form of energy.

Latent heat energy is perhaps the most underappreciated and most confusing type of energy. The word latent refers to energy that is hidden in water and water vapor.  The hidden energy emerges when water vapor condenses or water freezes.

Radiant energy is a very important form of energy that was for some reason left off the original list.  Sunlight is an example of radiant energy that we can see and feel (you feel warm when you stand in and absorb sunlight).  There are many types of radiant energy that are invisible.



The four energy transport processes are listed below.
 

By far the most important process is electromagnetic radiation (light is a common form of electromagnetic radiation).  This is the only process that can transport energy through empty 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.

Rising parcels of warm air and sinking parcels of cold air are examples of convection.  Because of convection you feel colder or a cold windy day than on a cold calm day.  Note that convection is a 3rd way of causing rising air motions in the atmosphere (convergence into centers of low pressure, and fronts were the other two ways).  This is a topic we are really going to beat to death.  Archimedes law will make an appearance when we cover convection.

Ocean currents are also an example of convection.  Ocean currents transport energy from the warm tropics to colder polar regions.


Water vapor is a particularly important form of invisible energy.  When water vapor condenses to produce the water droplets (or ice crystals) in a cloud, an enormous amount of latent heat energy is released into the atmosphere. 

It is hard to visualize or appreciate the amount of energy released into the atmosphere during condensation.  You can imagine the work that you would do carrying a gallon of water (8 pounds) from Tucson to the top of Mt. Lemmon.  To accomplish the same thing Mother Nature must first evaporate the water and (if my calculations are correct) that requires about 100 times the energy that you would use to carry the 8 pounds of water to the summit of Mt. Lemmon.  And Mother Nature transports a lot more than just a single gallon.

The next picture shows energy being transported from the sun to the earth in the form of electromagnetic radiation.

We are aware of this energy because we can see it (sunlight also contains invisible forms of light) and feel it.  With all of this energy arriving at and being absorbed by the earth, what keeps the earth from getting hotter and hotter?  The answer is that the earth also sends energy back into space (the orange and pink arrows in the figure below)






This infrared light is an invisible form of energy (it is weak enough that we don't usually feel it either).  A balance between incoming and outgoing energy is achieved and the earth's annual average temperature remains constant.

We will also look closely at energy transport between the earth's surface and the atmosphere. This is where latent heat energy transport and convection and conduction operate (they can't outside the atmosphere into outer space).


That is also where the atmospheric greenhouse operates.  That will be a important goal in Chapter 2 - to better understand how the atmospheric greenhouse effect works.


Remember that without the greenhouse effect, the global annual average surface temperature on the earth would be about 0o F rather than 60o F.
Now we're ready to start covering some of the material in Chapter 2.  We'll start on p. 45 in the photocopied Classnotes.

When you add energy to an object, the object will usually warm up (conversely when 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.


The temperature change will first depend on how much energy was added.  This is a direct proportionality, so delta E is in the numerator of the equation.

When you add equal amounts of energy to a small pan of water and to a large pan of water, the small pan will heat up more quickly.  The temperature change, delta T, will depend on the mass.  A small mass will mean a large delta T, so mass should go in the denominator of the equation.  

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 behaves in the same kind of way as mass.  Specific heat is sometimes called "thermal mass" or "thermal capacity."

Here's an important example that will show the effect of specific heat.


Equal amounts of energy (note that calories are units of energy) are added to equal masses of water and dirt.  We use water and dirt in the example because most of the earth's surface is either water or dirt. Water has a higher specific heat than soil, it only warms up 5o C.  The soil has a lower specific heat and warms up 20o C, 4 times more than the water.

These different rates of warming of water and soil have important climate implications.


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.

The city above on the coast has a 30o F annual range of temperature.  The city further inland (assumed to be at the same latitude and altitude) has an annual range of 60o F.  Note that both cities have the same 60o F annual mean temperature.

One more thing from near the bottom of p. 45 in the photocopied Classnotes.

The equation at the bottom of the figure above allows you to calculate how much energy is required to melt ice or evaporate water or sublimate dry ice.  You multiply the mass by the latent heat, a variable that depends on the particular material that is changing phase.  We'll need this equation in an experiment conducted at the end of class.
When you add energy to an object and the object warms, what exactly is happening inside the object?

The figure above is on p. 46 in the photocopied Class Notes.  Temperature provides a measure of the average kinetic of the atoms or molecules in a material.  The atoms or molecules in a cold material will be moving more slowly than the atoms or molecules in a warmer object.

You can think of heat as being the total kinetic energy of all the molecules or atoms in a material.  The next figure might make the distinction between temperature (average kinetic energy) and heat (total kinetic energy) clearer.

A cup of water and a pool of water both have the same temperature.  The average kinetic energy of the water molecules in the pool and in the cup are the same.  There are a lot more molecules in the pool than in the cup.  So if you add together all the kinetic energies of all the molecules in the pool you are going to get a much bigger number than if you sum the kinetic energies of the molecules in the cup.  There is a lot more stored energy in the pool than in the cup.  It would be a lot harder to cool (or warm) all the water in the pool than the cup.

In the same way the two groups of people shown have the same average amount of money per person.  The $100 held by the larger group at the left is greater than the $20 total possessed by the smaller group of people on the right. 

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 (0o 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.
Speaking of temperature scales.

You should remember the temperatures of the boiling point and freezing point of water on the Fahrenheit, Celsius, and Kelvin scales.  300 K is a good easy-to-remember value for the global annual average surface temperature of the earth.


You certainly don't need to try to remember all these numbers (this figure wasn't shown in class).  The world high temperature record was set in Libya, the US record 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.   You'll find more record high and low temperature data on p. 58 and p. 61 in Chapter 3 of the text.  Precipitation records are shown on p. 358.  Note that even liquid nitrogen is still quite a bit warmer than absolute zero.
Conduction is the first of four energy transport processes that we will cover.  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 red). 

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 (sauce 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.

The following three figures show a demonstration that was performed in class.  Curry powder was used instead of acetic acid (concentrated acetic acid is too dangerous; contact with the vapor causes eye burns and irreversible eye damage, severe irritation of the respiratory tract, and corrosion of the digestive tract).  Curry also smells a lot better than acetic acid (which gives vinegar its distinctive smell).

As the smell of the curry gets into the air, collisions with air molecules begin to move the smell toward the back of the room.

If acetic acid had been used the instructor (and perhaps the front row of students) might have lost consciousness by this point.

later still.  I was surprised how quickly and how far the curry smell was able to travel.  ILC 150 must have a very good ventilation system.
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:


Small bubbles of air trapped in foam

Thin insulating layer of air


Hollow fibers (Hollofil) filled with air used in sleeping bags and winter coats

We didn't have time to cover the following material in class.  Read through it carefully and you should have no trouble find a hidden optional (extra credit) assignment that you can download, print, answer, and turn in at the beginning of class on Thursday.

Convection was the next energy transport process we will 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 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.

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 (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).  Cooler air moves in to take the place of the rising air at Point 4 and the process repeats itself.

The example at upper 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.
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 real life situations than you might expect.


Note first of all there is a temperature difference between your hand and a 70o 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.  A piece of 70 F diamond would feel even colder because it is a 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.

Ice fells cold even though is not a particularly good conductor.  In this case a lot of energy is flowing from your hand to the ice because there is a much larger temperature difference.  This high rate of energy loss causes ice to feel cold.

Air is a poor conductor.  If you stick your hand out in 40 F weather the air won't conduct energy away from your hand very quickly at all and the air won't feel very cold.

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).  Water is a much better conductor than air.  Energy flows much more rapidly from your hand into the cold water. 
Now we're in a perfect position to understand wind chill.

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).  A thermometer behaves differently.  It actually cools to the temperature of the surroundings.  Once it reaches 40 F 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 (because convection together with conduction are transporting energy away from your body).  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 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, 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 usually not a 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.  Don't confuse either of the links above with a link to a hidden optional assignment.
Finally we did an experiment at the end of class. The object of the experiment was to measure the latent heat of vaporization of liquid nitrogen.  That just means measuring the amount of energy needed to evaporate a gram of liquid nitrogen.  The students that are doing Experiment #2 are measuring the latent heat of fusion of ice, the energy needed to melt one gram of ice.  You'll find the following figure on p. 45a in the photocopied Classnotes.


(a)
Some room temperature water poured into a styrofoam cup weighed 174.0 grams.  The cup itself weighed 3.7 g, so we have 170.3 g of water.

(b)
The water's temperature was 21.3o C.

(c)
37.0 g of liquid nitrogen was poured into the cup of water.

It takes energy to turn liquid nitrogen into nitrogen gas.  The needed energy came from the water.  This flow of energy is shown in the middle figure above.  We assumed that because the experiment is performed in a styrofoam cup that there is no energy flowing between the water in the cup and the surounding air.

(d)
After the liquid nitrogen had evaporated we remeasured the water's temperature.  It had dropped to 10.0o C.  That is a temperature drop of 11.3o C.

Now we'll go back to our earlier equation (top figure below)


Rather than trying to calculate delta T,  we are going to measure temperature change, delta T, and use the second equation (bottom figure) to measure the amount of energy that flowed from the water into the liquid nitrogen.

Because we knew how much water we started with, its temperature drop, and water's specific heat we can calculate how much energy was taken from the water.  That is the 1924.4 calorie figure above.  This was used to evaporate 37.0 grams of liquid nitrogen.  So we divided 1924.4 calories by 37 grams to get 52.0 calories needed per gram.  That is our measured value of the latent heat of vaporization of nitrogen.  As trustworthy student in the middle of the room informed us that the known value is 48 cal/g, so our measurement was fairly close.