Tuesday Oct. 13, 2009
click here to download today's notes in a more printer friendly format.

 Some what I guess might be called Rockabilly music before class today: "Hot Rod Lincoln" (part 1 and part 2) and "I Gotta Get Drunk" from the Twangbangers.

The Experiment #2 reports were collected in class today.  If you weren't able to turn in your report (or haven't yet returned your materials) please do so as soon as you can.  It takes about a week to get those graded.  I'm guessing you should expect to get them back next Thursday Oct. 22.  You will then have a chance to revise your reports if you want to.

I am planning to distribute the Expt. #3 materials in class on Thursday before the quiz.

The most recent Optional Assignment was returned in class today.  If you don't see a grade marked, you received full credit (0.5 extra credit points).  Be sure to check the online answers because not all of the problems on the assignment were graded.

We started with the bottom half of p. 61 in the photocopied ClassNotes - the electromagnetic spectrum (part of it anyway)


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 for these kinds of light.  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 all the colors are mixed together you see white light.

Here are some rules governing the emission of electromagnetic radiation:


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, even the air, 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 (it might just be that because it is there all the time we just aren't aware of 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.  Technically it's energy per unit area per unit time, but 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.
1.
Notice first that both and warm and the cold objects emit radiation over a range of wavelengths (the curves above are like quiz scores, not everyone gets the same score, there is a distribution of grades)

2.
You can now see better what Lambda max represents.  Lambda max has shifted toward shorter wavelengths for the warmer object.  This is Wien's law in action.  The warmer object is emitting lots of types of short wavelength radiation that the colder object doesn't emit.

3.
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.

An ordinary 200 W tungsten bulb connected to a dimmer switch can be used to demonstrate these rules (see p. 66 in the photocopied ClassNotes).  We'll be seeing the EM radiation emitted by the bulb filament.


The graph at the bottom of p. 66 has been split up into 3 parts and redrawn for improved 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 wasn't very bright at all and had an orange color.  This is curve 1, the middle figure.  The curve is bigger and has shifted left.  The far left end of the emission 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, just 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 very efficient, at least not as a source of visible light.

You were able to use one of the diffraction gratings to separate the white light produced by the bulb into its separate colors.
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 grating handed out in class behaved a little differently and spread out the colors horizontally, vertically, and diagonally.
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 (UV + IR) 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) 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 (with a temperature of around 300 K) to be in energy balance with the sun (6000 K).  At the top right of the figure you can see that the earth is located about 90 million miles from the sun and therefore only absorbs a very small fraction of the total 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 (0 K) and is not emitting any EM radiation at all.  It is absorbing sunlight however so it will begin to warm.  This is like opening a bank account, the balance will be zero.  But then you start making deposits and the balance starts to grow.

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).  Once you find money in your bank account you start to spend it.  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.

Before we start to look at radiant energy balance on the earth with an atmosphere we need to learn about filters.  The atmosphere will filter sunlight as it passes through the atmosphere toward the ground.  The atmosphere will also filter IR radiation emitted by the earth as it tries to travel into space.

We will first look at the effects simple blue, green, and red glass filters have on visible light.  This is just to become familiar with filter absorption graphs.



If you try to shine white light (a mixture of all the colors) through a blue filter, only the blue light passes through.  The filter absorption curve shows 100% absorption at all but a narrow range of wavelengths that correspond to blue light.  Similarly the green and red filters only let through green and red light.

The following figure is a simplified, easier to remember, representation of the filtering effect of the atmosphere on UV, VIS, and IR light (found on p. 69 in the photocopied notes).  The figure was borrowed from a previous semester because it was drawn more neatly.


You can use your own eyes to tell you what the filtering effect of the atmosphere is on visible light.  Air is clear, it is transparent.  The atmosphere transmits visible light.

In our simplified representation oxygen and ozone make the atmosphere pretty nearly completely opaque to UV light .  Don't let the word opague bother you - we assume that the atmosphere absorbs all incoming UV light, none of it makes it to the ground.  This is of course not entirely realistic.

Greenhouse gases make the atmosphere a selective absorber of IR light - the air absorbs certain IR wavelengths and transmits others.  It is the atmosphere's ability to absorb (and also emit) certain wavelengths of infrared light that produces the greenhouse effect and warms the surface of the earth.

Note "the atmospheric window" centered at 10 micrometers.  Light emitted by the earth at this wavelength will pass through the atmosphere.  Another transparent region, another window, is found in the visible part of the spectrum.

You'll find a more realistic picture of the atmospheric absorption curve on p. 70 in the photocopied Classnotes, but the simplified version above will work fine for us.

Here's the outer space view of radiative equilibrium on the earth without an atmosphere.  The important thing to note is that the earth is absorbing and emitting the same amount of energy (4 arrows absorbed balanced by 4 arrows emitted).



We will be moving from an outer space vantage point of radiative equilibrium (figure above) to the earth's surface (figure below).

Don't let the fact that there are
4 arrows are being absorbed and emitted in the top figure and
2 arrows absorbed and emitted in the bottom figure
bother you.  The important thing is that there are equal numbers of arrows coming in and going out.  That is what indicates energy balance.  Balance occurs then the earth has warmed to 0 F.

The next step is to add the atmosphere.
We will study a simplified version of radiative equilibrium just so you can identify and understand the various parts of the picture.  Keep an eye out for the greenhouse effect.  Here's the figure that we ended up with in class


It would be hard to sort through all of this if you weren't in class (and maybe even if you were) to see how it developed.  So below we will go through it again step by step (which you are free to skip over if you wish). 


1.   The figure shows two rays of incoming sunlight that pass through the atmosphere, reach the ground, and are absorbed.  100% of the incoming sunlight is transmitted by the atmosphere.  This wouldn't be too bad of an assumption if sunlight were just visible light.  But it is not it is about half IR light and some of that is going to be absorbed.

The ground is emitting 3 rays of IR radiation.

2.   One of these is emitted by the ground at a wavelength that is NOT absorbed by greenhouse gases in the atmosphere.  This radiation passes through the atmosphere and goes out into space.

3.  The other 2 units of IR radiation emitted by the ground are absorbed by greenhouse gases is the atmosphere.

4.   The atmosphere is absorbing 2 units of radiation.   In order to be in radiative equilibrium,the atmosphere must also emit 2 units of radiation.  1 unit of IR radiation is sent upward into space, 1 unit is sent downward to the ground where it is absorbed.

The greenhouse effect is found in this absorption and emission of IR radiation by the atmosphere.  Here's how you might put it into words:

Before we go any further we will check to be sure that every part of this picture is in energy balance.

The ground is absorbing 3 units of energy (2 green arrows and one purple arrow above) and emitting 3 units of energy (one pink and two red arrows)

The atmosphere is absorbing 2 units of energy and emitting 2 units of energy

2 units of energy arrive at the earth from outer space, 2 units of energy leave the earth and head back out into space.


The greenhouse effect makes the earth's surface warmer than it would be otherwise (global annual average of 60 F instead of 0 F). 

Energy balance with (right) and without (left) the greenhouse effect.  At left the ground is emitting 2 units of energy, at right the ground is emitting 3 units.  Remember that the amount of energy emitted by something depends on temperature.  The ground must be warmer to be able to emit 3 arrows of energy rather than 2 arrows.

Here's another explanation (that wasn't mentioned in class).  At left the ground is getting 2 units of energy.  At right it is getting three, the extra one is coming from the atmosphere.  Doesn't it seem reasonable that ground that absorbs 3 units of energy will be warmer than ground that is only absorbing 2?
Class ended with a demonstration, one that might save students (that live off campus and pay electric bills) some money. 

Earlier today we learned that ordinary tungsten bulbs (incandescent bulbs) produce a lot of wasted energy.  They emit a lot of infrared light that is wasted because it doesn't light up a room (it will heat up a room but there are better ways of doing that).  The light that they do produce is a warm white color (tungsten bulbs emit lots of orange, red, and yellow light and not as much blues, greens and violets).  Energy efficient compact fluorescent lamps (CFLs) are being touted as an ecological alternative to tungsten bulbs because they use substantially less electricity, don't emit a  lot of wasted infrared light, and also last longer.  CFLs come with different color temperature ratings.

The bulb with the hottest temperature rating (5500 K ) in the figure above is meant to mimic or simulate sunlight.  The temperature of the sun is 6000 K and lambda max is 0.5 micrometers.  The spectrum of the 5500 K bulb is similar.

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.  Personally I find the 2700 K bulb "too warm," it makes a room seem gloomy at night.  The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in the hallways in a hospital.  I prefer the 3500 K bulb in the middle.

This figure below is from an article on compact fluorescent lamps in Wikipedia for those of you that weren't in class and didn't see the bulb display..  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).


There is one downside to these energy efficient CFLs.  The bulbs shouldn't just be discarded in your ordinary household trash because they contain mercury.  They should be disposed of properly.

Good job today in class.  From where I stand it looked like you were awake, thinking, participating, and I hope understanding the material.