Thu., Mar. 1 notes

Thursday, Mar. 1, 2018

Haim "When We Were Young" (3:32), "If I Could Change Your Mind" (3:59), "Forever" (4:05), "I'll Try Anything Once" (3:32), "Right Now" (4:30), "Hazy Shade of Winter" (3:02), "Better Off" (3:30)

Rules governing the emission of EM radiation

We'll spend a big part of the class learning about some rules governing the emission of electromagnetic radiation. Here they are:

Everything warmer than 0 K will emit EM radiation. Everything in the classroom: the people, the furniture, the walls and the floor, 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 (or perhaps because it is always there we've grown accustomed to it and ignore it). Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature. In the classroom most everything has a temperature of around 300 K and we will see that means everything is emitting far-infrared (FIR) radiation with a wavelength of about 10µm.

The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit. Don't worry about the units (though they're given in the figure below), you can think of this as amount, or rate, or intensity. Don't worry about σ (the Greek character rho) 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 (found on p. 64 in the ClassNotes):

The cool object is emitting 2 arrows worth of energy. This could be the earth at 300 K. The warmer object is 2 times warmer, the earth heated to 600 K. The earth then would emit 32 arrows (16 times more energy).

The earth has a temperature of 300 K. The sun is 20 times hotter (6000 K). Every square foot of the sun's surface will emit 20⁴ (160,000) times more energy per second than a square foot of the earth's surface.

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 but not in equal amounts. Objects emit more of one particular wavelength than any of the others. This is called λ_max ("lambda max", lambda is the Greek character used to represent wavelength) and is the wavelength of maximum emission. The third rule allows you to calculate λ_max. The tendency for warm objects to emit radiation at shorter wavelengths is shown below.

The cool object could be emitting infrared light (that would be the case for the earth at 300 K). It might be emitting a little bit of red light that we could see. That's the 2 arrows of energy that are colored red. The warmer object will also emit IR light but also shorter wavelengths such as yellow, green, blue, and violet (maybe even some UV if it's hot enough). Remember though when you start mixing different colors of visible light you get something that starts to look white. The cool object might appear to glow red, the hotter object would be much brighter and would appear white.

Here's another way of understanding Stefan Boltzmann's law and Wien's Law (the graph below is on the bottom of p. 63 in the ClassNotes).

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). The warm object emits all the wavelengths the cooler object does plus lots of additional shorter wavelengths.

The peak of each curve is λ_maxthe wavelength of peak emission (the object emits more of that particular wavelength than any other wavelength). Note that λ_max has shifted toward shorter wavelengths for the warmer object. That 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.

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

It is relatively easy to see Stefan-Boltzmann's law and Wien's Law in action. The class demonstration consisted of an "ordinary" 200 W tungsten bulb is connected to a dimmer switch (see p. 65 in the photocopied ClassNotes and note that setting 0 is not included in the figure in the ClassNotes). We'll be looking at the EM radiation emitted by the bulb filament.

The graph at the bottom of p. 65 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. We can use Wien's Law to calculate the wavelength of peak emission, λ_max. The wavelength of peak emission is 10 micrometers which is long wavelength, far IR radiation so we can't see it.

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. Note 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 were 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 is 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.

Light emitted by the earth and sun; warm and cool white; tungsten bulbs, compact fluorescent bulbs, and LED bulbs

The figure compares the light emitted by the sun and the earth.

The curve on the left is for the sun. The surface of the sun has a temperature of 6000 K so we can use Wien's law to calculate λ_max . It turns out to be 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 (it's a cooler white than emitted by a tungsten bulb). 44% of the radiation emitted by the sun is visible light, Very nearly half of sunlight (49%) is IR light (37% near IR + 12% far IR). 7% of sunlight is ultraviolet light. More than half of the light emitted by the sun (the IR and UV light) is invisible.

100% of the light emitted by the earth (temperature = 300 K) is invisible far 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 the sun's surface emits energy at a much higher rate than the earth (160,000 times higher). 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 much too small to be seen.

Ordinary tungsten bulbs (incandescent bulbs) produce a lot of wasted energy. This is because they emit a lot of invisible infrared light that doesn't light up a room (it will warm 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 much blue, green or violet).

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 (daylight). The temperature of the sun is 6000 K and lambda max is 0.5 micrometers. The spectrum of the 5500 K bulb is similar. Even though the color temperature is high this is referred to as cool white because it contains more blue, green, and violet light.

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 actually 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 and depressing (a student in class once said the light resembles Tucson at night). The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in a hospital corridor. I prefer the 3500 K bulb in the middle.

The photograph below (from this source) showing the difference between warm white and cooler white is one of the best I've seen. It's better than the demonstration shown in class because there are more bulbs (guess what I'll be doing this weekend).

The bulb on the left has a tungsten filament and a color temperature of 3000K. Then moving from left to right are CFL bulbs with color temperatures of 2700 K, 3500 K, 4100 K, 5500 K, and 6500 K.

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 (at a hazardous materials collection site or perhaps at the store where they were purchased). I suspect a lot of people don't do that.

It probably won't be long before LED bulbs begin to replace tungsten and CFL bulbs. The price has been dropping in the last year or two.

LED stands for light emitting diode. We won't be looking at them in detail except to say that a single LED can produce only a single color, it can't produce white light. What is done instead is to put three small LEDS, producing red green and blue light, in close proximity. When they are illuminated the three colors mix together to produce white light.

CFLs sometimes take 30 seconds or a minute to come to full brightness. LED bulbs turn on instantaneously.

Radiative equilibrium on the earth without an atmosphere
We will first look at the simplest kind of situation, the earth without an atmosphere (or at least an atmosphere without greenhouse gases). The next figure is on p. 67 in the ClassNotes. Radiative equilibrium is really just balance between incoming and outgoing radiant energy.

You might first wonder how it is possible for the relatively small and cool earth (with a temperature of around 300 K) to be in energy balance with the much larger and hotter sun (6000 K). Every square foot of the sun emits 160,000 times as much energy as a square foot on the earth. At the top right of the figure, however, you can see that because the earth is located about 90 million miles from the sun and only absorbs a very tiny fraction of the total energy emitted by the sun. The earth only needs to balance the energy it absorbs from 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 (4 of the 5 arrows of incoming sunlight in the first picture are absorbed, 1 of the arrows is being reflected) so it will begin to warm This is like opening a bank account, the balance will start at 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). Only the four arrows of incoming sunlight that are absorbed are shown in the middle figure. The arrow of reflected sunlight has been left off because it doesn't really play a role in energy balance (reflected sunlight is like a check that bounces - it really doesn't affect your bank account balance). The earth is emitting 3 arrows of IR light (in red). Because the earth is still gaining more energy (4 arrows) than it is losing (3 arrows) the earth will warm some more. Once you find money in your bank account you start to spend it. But as long as deposits are greater than the withdrawals the balance will grow.

Eventually the earth will warm enough that it (now shaded brown & blue) will emit the same amount of energy as it absorbs from the sun. This is radiative equilibrium, energy balance (4 arrows of absorbed energy are balanced by 4 arrows of emitted energy). That is called the temperature of radiative equilibrium (it's about 0 F for the earth).

Note that it is the amounts of energy, not the kinds of energy that are important. Emitted radiation may have a different wavelength than the absorbed energy. That doesn't matter. As long as the amounts are the same the earth will be in energy balance. Someone might deposit money into your bank account in Euros while you spend dollars.

The world viewed in near IR light.
The world would not look the same if we were able to see near IR light instead of visible light.


visible light reflected by the tree and photographed with normal film	near IR light reflected by the tree and photographed using near IR film

The picture at left was taken using normal film, film that is sensitive to visible light. The picture at right used near infrared film. In both pictures we are looking at sunlight that strikes the tree or the ground and is reflected toward the camera where it can be photographed (i.e. these aren't photographs of light being emitted by the tree or the ground).

The tree at left is green and relatively dark (it reflects green light but absorbs the other colors of visible light). The tree at right and the ground are white, almost like they were covered with snow. The tree and grass on the ground are very good reflectors of near infrared light. Here are many more images taken with infrared film.

Photographs of the ground taken from an air plane using ordinary film at left (responds to visible light) and near infrared film at right. Notice how much clearer the river is in the picture at right. The IR photograph is able to "see through" the haze. The haze is light being scattered predominantly by air molecules. You may remember from the 1S1P topic on scattering that air molecules scatter shorter wavelengths in much greater amounts that longer wavelengths. Near IR light is not scattered nearly as much as visible light.

You wouldn't have seen the tree or the river if the photos above had been taken at night. That is because they are photographs of reflected sunlight.

This is a picture of the far IR light that is emitted by a house (source of this image). You'd see this during the day or night, sunlight doesn't need to be present.

Remember that the amount of energy emitted by an object depends strongly on temperature (temperature to the 4th power in the Stefan-Boltzmann law). Thus it is possible to see hot spots that emit a lot of energy and appear "bright" and colds spots. Photographs like these are often used to perform an "energy audit" on a home, i.e. to find spots where energy is being lost. Once you locate one of these hot spots you can add insulation and reduce the energy loss. This photograph has been color coded. Reds and orange mean more intense emission of IR radiation (warmer temperature) than the blues and greens. The reds show you were energy is being lost (often through poorly insulating windows). Many of the roof tops are blue, they are cool. There is probably a lot of insulation in the attic and little energy is being lost out the roof.

Later in the semester we will looking at satellite photographs of clouds. Satellites take pictures of both the visible light reflected by clouds and also the IR radiation emitted by clouds.