School. We started half an hour late because of the all-school
discussion of the meteor strike over Russia. So I squeezed a lot into
35 minutes before a shortened recess break. We reviewed the structure
of the Earth and then we talked about the three different ways heat
flows: conduction, convection, and radiation (which in this context is
just another word for light; it does not mean ionizing radiation,
which is what you need to protect your DNA from). I brought a torch
and a saucepan to make the discussion of conduction more concrete:
cookware designers want the bottom to conduct heat very well so that
the food is heated evenly, but they want the handle to conduct heat
poorly so that you don't burn yourself. Then I added water to segue
to convection. Because hot fluids rise, convection occurs whenever a
fluid is heated from below, which occurs in very diverse contexts:
boiling water on the stove, fluid rock in Earth's mantle, and the
movement of air in the atmosphere.
Next, I drew a Sun far from our diagram of Earth, and I asked how heat
gets from the Sun to the Earth. It can't be conduction or convection,
because empty space can't do either of these. It's radiation (light).
So we observed thermal radiation (the light emitted by an object by
virtue of its temperature), noting the brightness and color of a light
bulb at different temperatures (achieved by changing the voltage). We
analyzed the color in detail by looking through diffraction gratings
to make rainbows from the white light, and noting which color in the
rainbow was brightest. The pattern that emerges is: raising the
temperature makes the light bluer, and makes it much brighter. We
think of red hot as being about the hottest temperature we ever
encounter, but really white hot is even hotter (the light is a mixture
of red, green, and blue), and blue hot is even hotter than that. (The
ocean and sky are blue because they scatter the blue light from the
Sun, not because they are emitting light.) Even objects at room
temperature emit thermal radiation, but that light is "redder than
red" or infrared. These kids had played with an infrared camera
before, so I didn't bring one, but we discussed their IR camera
experience in this new light. (Read this post to get the basics of
the IR camera experience.)
The last point I made before recess break: Earth's temperature is a
balance between the energy it gets from the Sun and the energy
(infrared light) it emits into space. To maintain a roughly stable
temperature, it must emit as much as it gets. We would examine that
balance in more detail after the break. During the break, I had a
trick to keep them thinking about this subject: I brought a parabolic
mirror, pointed it at the Sun, and we entertained ourselves setting
things on fire.
After the break, before moving on, I felt they needed more practice with
conduction, convection, and radiation, so I had them work in groups to design
thermoses. We put together ideas from the different groups to arrive at a
consensus design which minimizes conduction, convection, and radiation.
Back to the main thread: I noted how the parabolic mirror gathered energy from
the Sun over a largish area and concentrated it on a small area. If we
measured the power (energy per second) falling over one square meter
(about twice the area of the mirror), we would find that it's about
one kilowatt, or 1 kW. I brought a 1 kW hair dryer to make that more
concrete. We then talked about night vs day, and how the Sun is
fairly low in the sky during part of the day, and concluded that the
average power from the Sun on 1 square meter of Earth would be more
like 300 W. So each square meter of Earth should emit about 300 W of
infrared light in order to maintain a stable temperature.
Recall that power emitted ("brightness") increases strongly as the
temperature of an object increases. So if the temperature of that
square meter of Earth is low, it will emit less than it absorbs, and
that will raise its temperature. But if the temperature goes up very
high, it will emit more than it absorbs, and the temp will come down.
We ought to be able to calculate the temp which is just right so that
it emits exactly 300 W. This is where we returned to the computer
programming that the kids are loving so much. Most of these kids are
not familiar with algebra, but they can (with lots of guidance from
me) write a loop over a range of plausible temperatures and print out
the power emitted at each temperature.
To do this, I had to give them the equation for power (in watts)
emitted as a function of temperature: 0.0000000567 T4, where T is in
Kelvins. That led to a discussion of Fahrenheit vs Celsius vs Kelvin.
Fahrenheit is defined so that water freezes at 32 degrees and boils at
212, a 180-degree difference; Celsius is defined so that water freezes
at 0 degrees and boils at 100. Therefore, each Celsius degree is
"bigger" by 180/100 or 9/5. Therefore Fahrenheit = 9/5 Celsius + 32.
Kelvin = Celsius + 273 (I explained about absolute zero), so
Fahrenheit = 9/5 (Kelvin-273) + 32. Admittedly, most students didn't
follow all these steps, but at least one did, and I told the others to
just use this to convert while focusing on the logical steps needed to
carry out their program.
So each group wrote a Python script to check from 1 to 1000 Kelvins,
at each step printing out the power emitted and the Fahrenheit
temperature. It turns out that 26 F is the right temperature for 300
W. Is this a reasonable answer? We discussed the approximations
involved (primarily albedo, using snow as an example). Then we tried
representing this information graphically. Instead of scanning a list
of numbers to find the right temperature, I taught them how to make a
graph of power emitted vs temperature. We then added a horizontal
line at 300 W, and the temp at which the line intersects the curve is
the "right" temp. I really want to work on graph-making and
-interpreting skills, so we discussed the labels we should put on each
axis, and how to summarize the plot in words.
As a teaser for next week, a slightly more rigorous calculation shows
that Earth's global average temperature should be even colder than 26
F. The reason we are not in fact that cold is that our atmosphere
intercepts some of the outgoing infrared light and turns it back to
the surface: the greenhouse effect. There is a natural greenhouse
effect which makes our planet livable. The kids had of course heard
of the greenhouse effect and global warming, so they were able to see
right away that the problem is not the greenhouse effect per se; it is
that we are adding to the natural greenhouse effect, resulting in too
much of a good thing. More on that next week.
The original plot we made:
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