Wed., Mar. 5 notes

Wednesday Mar. 5, 2008

The Quiz #2 Study Guide is now available.

The Experiment #3 materials were distributed today. You will have another opportunity to check out materials on Friday.
The Experiment #4 materials should become available next week.

Note: By the end of next week you should either already have completed an experiment, should be working on an experiment, or should be working on or have plans to start working on one of the other options (book report, scientific paper report).

Class began with a quick review of the two rules governing the amount of radiation (the Stefan-Boltzmann law) and the kind of EM radiation (Wien's Law).

A couple of new figures that illustrate these two laws were added at the end of the notes from Monday, Mar. 3. The graph below also helps to illustrate the Stefan-Boltzmann law and Wien's law, particularly the meaning of lambda max.

Notice first that both and warm and the cold objects emit radiation over a range of wavelengths. In some respects this is like quiz grades. Not everyone in the room gets the same score; there's usually a very wide range of scores. Objects do emit more of one particular wavelength than any other wavelength. This is lambda max.

The area under the warm object curve is much bigger than the area under the cold object curve. The area under the curve is a measure of the total radiant energy emitted by the object. This illustrates the fact that warmer objects emit a lot more radiant energy than colder objects.

Lambda max has shifted toward shorter wavelengths for the warmer object. This is Wien's law in action. The warmer object is emitting a lot of short wavelength radiation that the colder object doesn't emit.

A bulb connected to a dimmer switch can be used to demonstrate the rules above (see p. 66 in the photocopied Classnotes). We'll be interested in and looking at the EM radiation emitted by the tungsten filament in the bulb.

The bottom of p. 66 has been redrawn below for clarity:

We start with the bulb turned off (Setting 0). The filament will be at room temperature which we will assume is around 300 K (remember that is a reasonable and easy to remember value for the average temperature of the earth's surface). The bulb will be emitting radiation, it's shown on the top graph above. The radiation is very weak so we can't feel it. It is also long wavelength far IR radiation so we can't see it. The wavelength of peak emission is 10 micrometers.

Next we use the dimmer switch to just barely turn the bulb on (the temperature of the filament is now about 900 K). The bulb just barely became visible and and had an orange color. This is curve 1, the middle figure. Note the far left end of the emission curve has moved to the left of the 0.7 micrometer mark - into the visible portion of the spectrum. That is what you are able to see, the small fraction 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 if you put your hand next to the bulb).

Finally we turn on the bulb completely (it was a 200 Watt bulb so it got pretty bright). 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 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. It is interesting that most of the radiation emitted by the bulb is still in the IR portion of the spectrum (lambda max is 1 micrometer). This is invisible light. A tungsten bulb like this is not especially efficient, at least not as a source of visible light.

You were able to use one of the diffraction gratings to view all the colors that make up visible light.
When you looked at the bright white bulb filament through one of the diffraction gratings the colors were smeared out to the right and left as shown below:

Some of the gratings behaved a little differently as shown below:

The sun emits electromagnetic radiation. That shouldn't come as a surprise since you can see it and feel it. The earth also emits electromagnetic radiation. It is much weaker and invisible. The kind and amount of EM radiation emitted by the earth and sun depend on their respective temperatures.

The curve on the left is for the sun. We first used Wien's law and a temperature of 6000 K to calculate lambda max and got 0.5 micrometers. This is green light; the sun emits more green light than any other kind of light. The sun doesn't appear green because it is also emitting lesser amounts 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 (37% near IR + 12% far IR), and 7% is ultraviolet light. More than half of the light emitted by the sun is invisible. We can't see it, but we can feel it.

100% of the light emitted by the earth (temperature = 300 K) is invisible IR light. The wavelength of peak emission for the earth is 10 micrometers.

Because the sun (surface of the sun) is 20 times hotter than the earth a square foot of the sun's surface emits energy at a rate that is 160,000 (20x20x20x20) times higher than a square foot on the earth. Note the vertical scale on the earth curve is different than on the sun graph. If both the earth and sun were plotted with the same vertical scale, the earth curve would be too small to be seen.

We saw earlier that tungsten bulbs produce a lot of wasted infrared light (wasted in terms of not lighting up a room). They also produce a warm white color. Energy efficient compact fluorescent lamps (CFLs) are designed to mimic the visible light output of a tungsten bulb without producing a lot of wasted infrared light. CFLs come with different color temperature ratings.

The bulbs with the hottest temperature rating (5500 K ) in the figure above emits more purples, blues, and greens and produces a cooler, bluish white. This is much closer to the light emitted by the sun.

The tungsten bulb (3000 K) and the CFLs with temperature ratings of 3500 K and 2700 K produce a warmer white.

Three CFLs with the temperature ratings above were set up in class so that you could see the difference between warm and cool white light.

You can see a clear difference between the cool white bulb on the left in the figure below and the warm white light produced by a tungsten bulb (2nd from the left) and 2 CFCs with low temperature ratings (3rd and 4th from the left). This figure is from an article on compact fluorescent lamps in Wikipedia.

We now have most of the tools we will need to begin to study energy balance on the earth. It will be a balance between incoming sunlight energy and outgoing energy emitted by the earth. We will look at the simplest case, first, the earth without an atmosphere (or at least an atmosphere without greenhouse gases) found on p. 68 in the photocopied Classnotes.

You might first wonder how, with the sun emitting so much more energy than the earth, it is possible for the earth to be in energy balance with the sun. The earth is located about 90 million miles from the sun and therefore only absorbs a very small fraction of the energy emitted by the sun.

To understand how energy balance occurs we start, in Step #1, by imagining that the earth starts out very cold and is not emitting any EM radiation at all. It is absorbing sunlight however so it will begin to warm.

Once the earth starts to warm it will also begin to emit EM radiation, though not as much as it is getting from the sun (the slightly warmer earth in the middle picture is now colored blue). Because the earth is still gaining more energy than it is losing the earth will warm some more.

Eventually it will warm enough that the earth (now shaded green) will emit the same amount of energy (though not the same wavelength energy) as it absorbs from the sun. This is radiative equilibrium, energy balance. The temperature at which this occurs is about 0 F. That is called the temperature of radiative equilibrium. You might remember this is the figure for global annual average surface temperature on the earth without the greenhouse effect.

The section on the filtering effect of the atmosphere on light has been moved to the Friday, Mar. 7 notes. We will start class on Friday by quickly reviewing that material.