Tuesday Oct. 2, 2007

The 2nd Optional Assignment was collected in class today.

I forgot to hand out the 3rd Optional Assignment (some people picked it up at the end of the period).  It isn't due until next Tuesday so you can pick up a copy in class on Thursday.  Copies are also available in PAS 588.

The Experiment #2 reports and the revised Expt. #1 reports are due next Tuesday.  Expt. #2 doesn't take long to perform.  Collect your data, return your materials this week, and pick up the supplementary information sheet.

We are making pretty good progress on grading the 1S1P reports.  Some of the reports were returned in class today
We quickly reviewed the discussion of electromagnetic radiation found at the end of last Thursday's notes.

EM radiation is created when you cause a charge to move 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 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.

The characteristics long wavelength - low frequency - low energy go together. So do short wavelength - high frequency - high energy.  Note that the two different types of radiation both propagate at the same speed.

The figure above starts to give you an idea of how energy is transported from one place to another by electromagnetic radiation.


You add energy when you cause an electrical charge to move up and down and create the EM radiation (top).
In the middle figure, the EM radiation then travels out to the right (it could be through empty space or through something like the atmosphere). 

Once the EM radiation encounters an electrical charge at another location (bottom right), the energy reappears as the radiation causes the charge to move.  Energy has been transported 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 mixed together, you see white light.

1.
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.

2.
 The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit.  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.  This is illustrated in the following figure:




3.
The third rule tells you something about the kind of radiation emitted by an object.  We will see that objects usually emit radiation at many different wavelengths.  There is one wavelength however at which the object emits more energy than at any other wavelength.  This is called lambda max (lambda is the greek character used to represent wavelength) and is called the wavelength of maximum emission.  The third rule allows you to calculate "lambda max."  This is illustrated below:



The following graphs (at the bottom of p. 65 in the photocopied Class Notes) also help to illustrate the Stefan-Boltzmann law and Wien's law.


Notice first that both and warm and the cold objects emit radiation over a range of wavelengths.

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 the warmer object emits a lot more radiant energy than the colder object.

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.  We'll be interested in and looking at the EM radiation emitted by the tungsten filament in the bulb.


We start with the bulb turned off (Point 3 near the bottom right part of the figure above).  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.  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 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 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.  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 (a 200 Watt bulb was used so it was pretty bright).  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.  Small diffraction gratings were handed out in class.  A diffraction grating will spread out all of the colors in the white light emitted by the bulb.  You could see the vivid violets, blue, green, yellow, orange, and red light that make up white 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 something I forgot to mention in class.  This is invisible light.  A tungsten bulb like this is not especially efficient, at least not as a source of visible light.
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.

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 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 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)


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 (without the earth getting really hot like 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 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.


Next we are going to see that the atmosphere behaves somewhat differently, when it comes to emitting and absorbing electromagnetic radiation, than the earth or the sun.  We will need to understand, in particular, how the atmosphere filters incoming sunlight and outgoing IR radiation emitted by the ground.  Then we will be able to study energy balance on the earth with an atmosphere (and one that contains greenhouse gases).

In some respects the earth and the sun behave just like the tungsten filament in the light bulb used in the class demonstration.  Both the earth and the sun emit continuous spectra.  Part of the light emitted by the sun falls in the visible part of the spectrum.  If you were to look at the sun (something you shouldn't do of course) with one of the diffraction gratings handed out in class you would see all the colors of visible light.  There wouldn't be any gaps or colors missing.  This is shown again at the top of the figure below.

Gases behave differently.  We looked at the visible light emitted by helium (a high-voltage power supply was need to heat the helium so that it would be hot enough to emit visible light).  Rather than a continuous spectrum, the helium emitted only certain wavelengths.  This is called a line spectrum.  Helium contains only two electrons and is a relatively simple atom and its line spectrum was also fairly simple.

Neon (Ne) also emitted a line spectrum, thought there were more lines at different wavelengths.

Finally we looked at the visible light emitted by molecular nitrogen.  In this case the spectrum was somewhere in between a continous spectrum and a line spectrum.  You were able to see bands of colored light rather than clear line emitted by the nitrogen (the bands are probably very closely spaced lines). 


This is closer to being a continous spectrum but there were still gaps, wavelengths without any emissions.
In the same kind of way, air absorbs some wavelengths and transmits others.  We will need to worry about the filtering effect of the atmosphere on ultraviolet, visible, and infrared light because all three types of light are found in sunlight.