Fri., Feb. 22 notes

Friday Feb. 22, 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 sometime next week. A new 1S1P assignment will be made soon, perhaps as early as next week.

The Optional Assignment #2 papers were returned today.

Chapter 2 is concerned with energy, temperature, heat, energy transport, and 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 sunlight). There are many types of radiant energy that are invisible.

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 free convection. Because of convection you feel colder or a cold windy day than on a cold calm day. Ocean currents are also an example of convection. Ocean currents transport energy from the warm tropics to colder polar regions.

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 also make an appearance when we cover convection.

Conduction is the least important energy transport at least in the atmosphere. Air is such a poor conductor of energy that it is generally considered to be an insulator.

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 0^o F rather than 60^o 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 large mass will mean a small 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 8^o C. The soil has a lower specific heat and warms up 32^o 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 30^o F annual range of temperature. 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 mean temperature.

Adding energy to an object will usually cause it to warm. But there is another possibility, the object could change phase (change from solid to liquid or gas). Adding energy to ice might cause the ice to melt. Adding energy to water could cause it to evaporate.

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 used this equation in an experiment conducted at the end of class. We'll also use the equation relating delta T and delta E that we discussed earlier.

Rather than trying to calculate delta T (top figure) we are going to measure temperature change, delta T, and use the second equation (bottom figure) to measure energy flow.

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 171.6 g. The cup itself weighed 3.7 g, so we have 167.9 g of water.

(b)
The water's temperature was 20.5o C.

(c)
35.0 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 9.5o C. That is a temperature drop of 11o C.

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 1846.9 calorie figure above. This was used to evaporate 35.0 grams of liquid nitrogen. So we divided 1846.9 calories by 35 grams to get 52.8 calories needed per gram. That is our measured value of the latent heat of vaporization of nitrogen. As trustworthy gentleman at the back of the classroom informed us that the known value is 48 cal/g, so our measurement was fairly close.

The following material wasn't covered in class on Friday. If you carefully read through this material you'll find a link to a hidden optional (extra credit) assignment that you can download, print, and turn in at the beginning of class on Monday.

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 it would be 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. This is a good spot to hide the link to the hidden optional assignment.

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. 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.