Thu., Oct. 5 notes

Thursday Oct. 5, 2006

The Optional Assignment #2 papers have been graded and were returned in class. Answers to those questions are now available online.
Several more questions were added to Optional Assignment #3. There are now a total of 15 questions. The assignment is now complete and is due at the beginning of class next Tuesday.

The Quiz #2 Study Guide is now available (in preliminary form) online.

The Experiment #2 reports (and the revised Expt. #1 reports) are due next Tuesday. If you haven't returned your Expt. #2 materials yet, you will need to come by my office (PAS 588) to leave the materials and pick up the supplementary information sheet. You can do that Friday or next Monday.

The next 1S1P assignment should appear on the class web page sometime later today.

Today:
Types of electromagnetic radiation

Everything emits radiation

rules governing the emission of radiation
demonstration
emission by the sun and earth

Radiative equilibrium simple case (earth without an atmosphere)

Filtering effect of the atmosphere

Radiative equilibrium more complex case (earth with an atmosphere containing greenhouse gases)

Write these down on a small card or piece of paper and carry it around on campus today. Periodically you can take the paper out of your pocket and see how much you remember of what we covered.

Before reading through today's notes, have a look back at the end of Tuesday's notes. The last figure shows how EM radiation emitted at one location can travel through space and later cause a positive charge at another location to bob up and down.

One of the ways of producing EM radiation is to move a charge up and down. If you move a charge up and down slowly (upper left in the figure above) you would produce long wavelength radiation that would propagate out to the right at the speed of light. If you move the charge up and down more rapidly you produce short wavelength radiation that also propagates at the same speed.

Once the EM radiation encounters the charges at the right side of the figure above, the EM radiation causes those charges to oscillate up and down. In the case of the long wavelength radiation the charge at right oscillates slowly. This is low frequency and low energy motion. The short wavelength causes the charge at right to oscillate more rapidly - high frequency and high energy motion.

The characteristics long wavelength & low frequency & low energy go together. So do short wavelength & high frequency & high energy.

The figure above also shows how EM radiation can transport energy from one place to another. You add energy when you cause the charges at left to oscillate. The EM radiation then travels out to the right (through empty space if necessary). Once the EM radiation encounters an electrical charge, the charge start to oscillate and the energy added at left reappears at right. Energy has been carried from left to right.

This is really just a partial list of some of the different types of EM radiation. In the top list, shortwave length and high energy forms of EM radiation are on the left (gamma rays and X-rays for example). Microwaves and radiowaves are longer wavelength, lower energy forms of EM radiation.

We will mostly be concerned with just ultraviolet light (UV), visible light (VIS), and infrared light (IR). Note the micrometer (millionths of a meter) units used for wavelength. The visible portion of the spectrum falls between 0.4 and 0.7 micrometers (UV and IR light are both invisible). All of the vivid colors shown above are just EM radiation with slightly different wavelengths. WHen you see all of these colors together, you see white light.

The figure above and the next one below were redrawn after class to make them a little clearer.
Unless an object is very cold (0 K) it will emit EM radiation. All the people, the furniture, the walls and the floor in the classroom are emitting EM radiation. Often this radiation will be invisible so that we can't see it and weak enough that we can't feel it. Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.

The Stefan Boltzmann law allows you to determine the amount of energy emitted per unit area per time (calories emitted per square centimeter per second for example). Don't worry about the units, you can think of this as amount, or rate, or intensity. Don't worry about σ either, it is just a constant. The amount depends on temperature to the fourth power. If the temperature of an object doubles the amount of energy emitted will increase by a factor of 2 to the 4th power (that's 2 x 2 x 2 x 2 = 16). A hot object just doesn't emit a little more energy than a cold object it emits a lot more energy than a cold object.

The third rule tells you something about the kind of radiation emitted by an object. We will see that objects usually emit radiation over a range of wavelengths. The third rule, Wien's law, allows you to calculate "lambda max" the wavelength of peak emission. An object will emit more radiation at this wavelength than at any other wavelength.

The next picture (a little different from the one drawn in class, it was redrawn to make it clearer) might make these rules a little clearer. This graph compares the radiation emitted by a cold and a hot object.

We'll start with the cold object (the blue shaded curve). It is emitting radiation over a range of wavelengths. All the wavelengths aren't being emitted in equal amounts. You can see that lambda max is the peak of the emission curve. The blue shaded area under the curve is the total energy emitted by the cold object.

The hot object also emits radiation over a wide range of wavelengths (including those emitted by the cold object). Lambda max for the hot object has shifted to shorter wavelength as predicted by Wien's Law (as T gets larger, the ratio 3000/T gets smaller). The area under the hot object curve is much larger than the area under the cold object curve. This is the Stefan Boltzmann law in action. The hot object will emit a lot more radiation than the cold object.

You can see these rules in action with a simple light bulb demonstration.

The object that will be emitting the radiation is the tungsten filament in a 200 W bulb. We start with the bulb turned off. The filament will be at room temperature which we will assume is around 300 K. The bulb will be emitting radiation (note the small curve above labelled room temp). The radiation is very weak so we can't feel it. It is also long wavelength far IR radiation (lambda max about 10 micrometers) so we can't see it. But, believe me, it is there.

Next we use the dimmer switch to just barely turn the bulb on. The bulb wasn't very bright at all and had an orange color. This is curve 1 in the figure. Note the far left end of the curve has moved left of the 0.7 micrometer mark - into the visible portion of the spectrum. That is what you are able to see the small, the portion of the radiation emitted by the bulb that is visible light (but just long wavelength red and orange light). Most of the radiation emitted by the bulb is to the right of the 0.7 micrometer mark and is invisible IR radiation (it is strong enough now that you could feel it).

Finally we turn on the bulb completely. The filament temperature is now about 3000K. The bulb is emitting a lot more visible light, all the colors, though not all in equal amounts. The bulb was also much brighter. The mixture of the colors produces a warm white light. It is warm because it is a mixture that contains a lot more red, orange, and yellow than blue, green, and violet light.

This figures compares the EM radiation emitted by the earth and the sun (a redrawn version of what was drawn in class). First because the sun (surface of the sun) is 20 times hotter than the earth a square meter of the sun's surface emits energy at a rate that is 160,000 times higher than the earth. Lambda max for the sun is 0.5 micrometers, green light. The sun doesn't appear green because it is also emitting a lot of violet, blue, yellow, orange, and red - together this mix of colors appears white. 44% of the radiation emitted by the sun is visible light, 49% is IR light, and 7% is ultraviolet light.

100% of the light emitted by the earth is invisible IR light. The wavelength of peak emission for the earth is 10 micrometers.

Now we're almost ready to learn about radiative equilibrium. That's just another word for energy balance. Before doing so here's an analogous situation.

Radiative equilibrium is like:
adding water to a leaky bucket

Water is being added to the bucket. No water is being lost so the water level rises.

The water level has reached a hole in the side of the bucket. Water is being lost though not as quickly as water is being added. The water level slowly rises some more.

Now the water is being added and lost at equal rates. The water level won't change. This is a condition of equilibrium.

Energy balance on the earth without an atmosphere. The earth (shaded blue) starts out very cold and is not emitting any EM radiation at all. It is absorbing sunlight however so it will warm. Once the earth starts to warm it will begin to emit EM radiation, though not as much as it is getting from the sun (the slightly warmer earth is now colored green). Eventually it will warm enough that the earth (now shaded brown) will emit the same amount of energy (though not the same wavelength energy) as it absorbs from the sun. This is radiative equilibrium. The temperature at which this occurs is 0 F (on the earth without any atmosphere). That is called the temperature of radiative equilibrium.

Before we move to the more complex situation of radiative equilibrium on the earth with an atmosphere, we need to learn something about how gases in the atmosphere affect different kinds of light that passes through the atmosphere.

This is a slightly simplified representation of the filtering effect of the atmosphere on UV, VIS, and IR light (found on p. 69 in the photocopied notes, a more realistic version is reproduced on p. 70). 0% absorption means the atmosphere behaves like a window made of clear glass, the air is transparent to light. The light can pass freely through the atmosphere. 100% absorption on the other hand means the atmosphere is opaque to light, it blocks the light by absorbing it.

In our simplified representation oxygen and ozone make the atmosphere a pretty good absorber of UV light The atmosphere is pretty nearly perfectly transparent to VIS light (we can check this out with our eyes, we can see through the air, it is clear). Greenhouse gases make the atmosphere a selective absorber of IR light - it absorbs certain IR wavelengths and transmits others.. Note "the atmospheric window" centered at 10 micrometers. Light emitted by the earth at this wavelength will pass through the atmosphere. IR light emitted by the earth at slightly different wavelengths will be absorbed by greenhouse gases. It is this ability of H₂0, CO₂, etc to selectively absorb certain wavelengths of IR light that is responsible for the greenhouse effect.

Here's another look at radiative equilibrium on the earth without an atmosphere. Here we're looking at the situation from a vantage point on the ground. In the previous case we were looking at the earth from a point in outer space.

Two units of sunlight arriving at the earth and being absorbed at the ground are balanced by 2 units of IR radiation emitted by the earth. It is the fact that there are equal amounts of energy being absorbed and emitted that tells you this is radiative equilibrium. Balance occurs when the earth's temperature is 0 F.

Now the figure we have all been waiting for, energy balance on the earth with an atmosphere. (this figure was redrawn to make it clearer) THe greenhouse effect is hidden somewhere in the figure.

1. First there are 2 units (2 arrows) of sunlight energy arriving at the top of the atmosphere. We assume that all of this is transmitted by the atmosphere and gets absorbed at the ground. We'll see how realistic this is next Tuesday.

2. The ground is emitting 1 unit of IR radiation at a wavelength that is transmitted by the atmosphere. Radiation that falls in the atmospheric window region centered at 10 micrometers perhaps.

3. The ground emits an additional 2 units of radiation at slightly different wavelengths that are absorbed by greenhouse gases in the atmosphere. IF it weren't for these greenhouse gases this energy would have gone into space.

At this point you might wonder how can the ground emit 3 units of energy when it is only getting 2 from the sun. The energy balance diagram isn't finished yet, when it is finished we'll see that there isn't a problem.

4. The atmosphere is absorbing two units of IR radiation (radiation that was emitted by the earth). To be in energy balance the atmosphere must also emit 2 units of IR light. ONe is emitted upwards into space, the other downward toward the ground.

Down at the ground now we see that we are now in energy balance. The ground gets 2 units of energy from the sun + 1 unit from the atmosphere. This balances the 3 units that are being emitted by the ground.

Now an important observation. The ground is emitting 3 units. If you look back at the picture of energy balance on the earth without an atmosphere you would see that the ground was only emitting 2 units. The ground in that example had a temperature of 0 F. In this example, the ground must be warmer in order to be able to emit 3 units of radiation. The ground temperature in this case is nearer to 60 F.

In both pictures of radiative equilibrium (with and without the atmosphere) there were 2 units of incoming sunlight. In the case of the earth without an atmosphere the earth emitted 2 units of energy back into space. In case with an atmosphere the ground is warmer and emits 3 units. It can get away with this because some of what it emits is absorbed by the atmosphere. The atmosphere in turn emits radiation and some of this heads back to the ground. This is the greenhouse effect. Greenhouse gases absorb some of the energy emitted by the earth (that would otherwise be lost) and return some that energy back to the ground.