In recognition of your ability
to hum and whistle at the same time, your fellow students have awarded you a
room on the lawn. But only over winter break. After canceling your ski vacation
in Aspen and Vail, you settle in to your new abode and discover that it's
awfully cold. They've turned off all the heat! It's too late to go shopping for
an electric heater tonight, so you prepare for a difficult night's sleep.
Fortunately, the room comes with a fireplace. Unfortunately, the room's previous occupants already burned all the available firewood. That doesn't really present a big problem because you have no homework to do on the room's wooden desk. After throwing the desk onto the sidewalk a couple of times to "soften it up," you take out a match and soon have a nice fire going in the fireplace.
1. You sit in front of the fire, trying to keep warm, and soon find yourself poking at the burning desk with various ordinary objects. You have two old, broken umbrellas--one made entirely of plastic and the other made mostly of metal. While the ends of both umbrellas heat up quickly when you put them in the fire, the handle of the plastic umbrella remains much cooler than that of the metal umbrella. What characteristic of the materials accounts for this difference in behavior, and why does this characteristic differ between plastic and metal?
Answer: The characteristic that matters here is
thermal conductivity and metals have much higher thermal conductivities than
plastics because metals have mobile electrons that conduct heat extremely well.
Why: In each of the
umbrellas, heat is being conveyed from one end to the other via conduction in
the umbrella's components. Metals have mobile electrons and these electrons can
carry thermal energy long distances within a metal. That long-range transport
allows metals to conduct heat much better than most insulating solids.
2. As you sit in front of the fire, you find that your face is becoming unpleasantly hot while the back of your neck remains quite chilly. Explain that odd arrangement of heating.
Answer: Heat is being conveyed to your face via
thermal radiation. Since this radiation travels only in straight-line paths, it
can't reach the back of your neck to warm it.
Why: The fire emits a
great deal of invisible infrared thermal radiation (and some visible radiation
as well). Your face is bathed in this radiation and feels hot while your neck
is not exposed to much thermal radiation and feels cold.
3. The air in the room is finally beginning to warm up, so you move over to the bed. As you walk by the window and look out into the frigid night, you feel a rush of cold coming at your face. With your hand, you feel a flow of cold air falling toward the floor from the window's surface, but this cold air is not approaching your face. (a) What causes the flow of cold air falling downward from the window, and (b) why does your face feel cold when you look out the window, even though cold air is not hitting your face?
Answer: (a) Air cooled by contact with the cold
window contracts. Its density increases and because it is no longer supported
adequately by the buoyant force, it sinks downward. (b) Your face feels cold
because while it is radiating away heat toward the cold outdoors, the cold
outdoors is radiating much less heat toward your face. (Overall, your face is
losing heat to the outdoors via radiation.)
Why: The cold window
cools air that touches it and causes that air to fall downward as a convective
heat transfer. And there is also an invisible radiative heat transfer from your
face to the outside. Thermal radiation goes in both directions, but since your
face is warmer than the outside, the net flow of heat is toward the outside.
You send more thermal radiation to the outside than it sends to you.
4. Despite the fire, the room air is still cool. As you lie huddled under your blanket, trying to keep warm, you are glad that the blanket consists of tiny fibers that trap air. Assuming that your body is hotter than the room air, (a) why does exposure to the room air make you feel cold, and (b) why does the blanket's structure do such a good job of making you feel less cold?
Answer: (a) The room air is colder than your body,
so heat flows naturally from your hotter body to the colder air, and (b) the
blanket traps air so that convection cannot occur (to carry heat from your body
to the colder air in the room).
Why: When you are
exposed to cold air, heat flows out of you and into the air. This heat loss
makes you feel cold. But by blocking convection with the help of the blanket,
you make it much harder for heat to go from you to the room air. The blanket
also blocks thermal radiation and neither it nor the trapped air have good
thermal conductivities. Heat basically can't get from you to the room air, so
you feel less cold.
That
summer job as a video-game tester fell through, so you have decided to
apprentice as a glassblower in one of the boutiques at Kings Dominion. You
spend many a happy hour heating clear and colored glasses with a torch as you
fashion little glass poodles, spaceships, and circus clowns. Not surprisingly,
you have also been learning from painful experience that touching hot glass is
always a bad idea.
5. The torch operates on a mixture of propane and air. What is happening within this mixture that allows the torch to transfer thermal energy as heat to the glass? (Follow energy's movements from the time it arrives at Kings Dominion until it reaches the glass as heat.)
Answer: A chemical reaction converts the mixture's
chemical potential energy into thermal energy and the mixture becomes hotter.
Heat then flows naturally from the hot gas mixture to the colder glass.
Overall, energy arrives at Kings Dominion as chemical potential energy (in the
propane and air), becomes thermal energy when the mixture burns, and flows as
heat into the glass.
Why: Since energy is
conserved, it can be accounted for throughout its journeys. In this case,
energy enters the picture as chemical potential energy in the propane and
oxygen molecules, is released as thermal energy when those molecules rearrange
into carbon dioxide and water molecules, and flows as heat into the glass.
6. When you heat clear glass hot enough to melt it, it emits a dim reddish glow. However, when you heat black glass to the same temperature, it glows bright red. Why does hot black glass emit red light, and why is this light so much brighter than the red light emitted by hot clear glass?
Answer: The black glass is a good absorber and
emitter of thermal radiation. When heated hot enough, it emits thermal
radiation that includes reddish visible light and because of its blackness, it
does a better job of this emission than clear glass at the same temperature.
Why: Above about 500 C,
an object's thermal radiation begins to appear reddish. But the brightness of
that radiation depends in part on the object's ability to interact with
electromagnetic radiation. A black object interacts as well as possible and
therefore emits as much thermal radiation as possible. But a clear object is
terrible at absorbing and emitting visible light and so doesn't glow brightly
at all.
7. Which cools faster to room temperature: hot clear glass or hot black glass? Explain why.
Answer: The hot black glass cools most quickly
because it is the best at radiating away heat to its colder surroundings.
Why: Thermal radiation
truly transfers heat. If you put a black object in a colder environment, it
will do the best possible job of radiating away its thermal energy as heat. In
contrast, a clear object will do a miserable job of radiating away thermal
energy and will stay hot longer.
8. Knowing the temperature of hot glass aids in fabricating those little glass nick-knacks. Since touching the glass is out of the question, the only ways to judge its temperature are to look for melting behavior or to study the light emitted by the glass. What would you look for in this light to know if the glass is hot enough?
Answer: As the glass heats, the color of the
thermal radiation it emits will gradually shift from the reddish end of the
spectrum toward the bluish end of the spectrum. You simply look for the right
color in the thermal radiation.
Why: The hotter the
glass becomes, the more green and blue light it emits in its thermal radiation.
As the glass warms up, you can see this increased emission of short wavelength
light as a shift from reddish glow toward yellow or even white. At the same time,
the glow becomes brighter. You could use brightness to judge temperature, but
you would then have to take into account the efficiency of the glass at
emitting and absorbing light (i.e. its emissivity). As long as you took this
emissivity into account, brightness would also be a helpful guide in judging
the glass's temperature.