Question Board -- Questions about Temperature and Heat

These are questions and reports sent in by participants in the Virtual Workshop on Temperature Light Heat, and answers and comments. If you have a question or an answer or a comment, send it in!
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The questions (Click on a line to jump to the entry)
Questions about temperature and heat
Is blue light warmer than red light?
How can you measure the temperature of the sun?
A thermometer in the spectrum
Why don't white objects heat their surroundings?
How are thermal energy, temperature, and kinetic energy of molecules related?
What do liquid crystals do?
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My Question: Is blue light warmer than red light?
Does each color wavelength have a certain amount of heat or are they all equal in the amount of heat distributed? For example are shorter blue wavelengths going to cause more heat if absorbed than longer red wavelengths?

Joe's answer
Blue light is better able to cause chemical reactions, because it delivers more energy to a molecule all at once when it is absorbed. However, there is a problem relating this to the ability to warm something: the light can be bright or dim, and we have to compare the red light to the blue light on an equal basis. The easiest way to measure brightness (and thus the most common way to do it) is to measure the amount of energy delivered. By that rule, a blue light and a red light of the same brightness will have the same heating effect -- by definition.

So accidentally we have asked a version of the question "Which weighs more, a pound of feathers or a pound of lead?" And just like in that example, we could imagine a different way to measure the quantities (like comparing a box of feathers to a box of lead). We could ask whether the blue part of light from some source provides more or less heating than the red part. If the source is an incandescent light, the answer is that the red light wins by a large margin, because there really isn't much blue there; but if the source is sunlight, I think it is close to a tie.

There are still other ways to compare red light to blue light. Light delivers its energy in lumps (very tiny lumps, from our point of view) called photons. A blue photon delivers almost twice as much energy as a red photon, and that is why it is more able to cause chemical reactions and physical effects. On the per-photon basis, blue light is the easy winner. But there are twice as many red photons as blue photons in white light to make up for this.

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My Question: How do you measure the temperature of the sun?

Joe's answer
There are two ways that I can think of that are used to measure the temperature of the sun and other stars:

*The color of the light given off by a hot object is an indication of its temperature. A red hot object is cooler than a white hot object, for example. With a good measurement of the brightness of the sun for different wavelengths of light (which means roughly, for different colors of light) we can estimate the temperature of the surface of the sun.

*We can tell which atoms are in the atmosphere of the sun using a spectroscope. This also reveals how many atoms are excited. It has to be really hot to excite an atom, and by looking at which kinds of atoms are excited and which are not, we get a measurement of the temperature of the "atmosphere" of the sun.

However, this does not determine the temperature inside the sun. Astronomers have theories for this that they are very certain of, because there is an indirect test of it: the sun makes its power by nuclear reactions, and the center of the sun has to be a certain temperature for these reactions to take place.

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My Question: If I take a ray of sunlight and put it through a prism and project the spectrum on a wall. Would a very sensitive thermometer find that the red is warmer than the violet? I think it would be, because the red is nearer to the infrared part of the spectrum.

Sally says
The sun is very hot, and the result is that the brightest part of the spectrum is in the visible. It depends a little bit on how you make the spectrum (i.e. what the prism is made of).

There are two standard ways to represent a spectrum. One shows how much power arrives in each wavelength. The other shows how much power arrives in each photon energy or frequency. Since wavelength is the reciprocal of frequency, the two ways don't look very much alike. Either way, the peak turns out to be in the middle of the sun's spectrum.

However, the spectrum of a cooler object, like an incandescent light bulb, has relatively less visible light, and the warmest part of the spectrum would indeed be in the infrared (this is how infrared light was discovered!).

My Question: If something that is white reflects all light, then why doesn't it (the white object), rather than something that is black, make the area around it hotter?

Joe's answer
Under the right circumstances, it probably does. Here are the concepts that combine to have this effect:

* Light carries energy
-- to us, from the sun, in the form of visible light
-- and also away from the earth, in the form of infrared (invisible) light
* Dark objects absorb visible light, but they also participate in the second step, where light leaves again.
* Light colored objects reflect light, and don't have any effect on it.
* Adding energy to something makes it hotter, almost always.

So when the sun is out, a dark object is going to be hotter than everything else, because it absorbs the light and gains the energy. A parking lot in July can get really hot! Not only does it make you hot when you touch it, but it heats up the air and radiates invisible light at you to make you hot.

If we were surrounded by white objects, they would reflect light at us and make us hotter that way. This definitely would happen if the objects were like mirrors, and all arranged to reflect the sun's light at us. That would be a solar collector, and with enough mirrors you can melt steel.

So if we were standing on a desert of white sand, we would notice that we were getting extra energy from the sand. But white objects reflect light in all directions, and not preferentially at a particular object, and they bounce a lot of the light back into the sky, so there is less down here. The reflected light is still visible light, which does not warm the air (air doesn't notice visible light. That's why we can see through air). The simplest way to keep sunlight from making us hot is to refuse delivery of it, which is what a white object does.

The experiment to demonstrate your effect might be to have a thermometer in the shade of the house, in a place where there was sunlight nearby (the thermometer right at the corner of the house, or on the north side of the house close to noon) and then compare a pair of reflectors, one that is all white and one that is all black. We want the reflector to be nice and big, so that it will be redirecting a lot of energy, some at the thermometer. The top of the box that copier paper comes in might do -- still bigger would be better, but these are not easy to come by, and bigger isn't important if we can get within a foot or two of the thermometer and still be in the sunlight. (Another way to do this would be inside, late in the afternoon or early in the morning, using a sunbeam coming in a window to redirect with our reflector). Now I'm betting that a white object would cause a temperature rise, and that a black one would not.

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My Question: How are thermal energy, temperature, and the kinetic energy of molecules related? Are there equations defining their relationships?

Joe's answer
The kinetic energy of a molecule is closely related to temperature. For most molecules near room temperature, the average of the part of the kinetic energy that is due to motion of the center of mass is given to very good accuracy by KE = 3kT/2 where T is the temperature in Kelvin and k is a constant whose value is well known (1.38 x 10^(-23)) J/Kelvin. What it means is that the temperature is exactly the average kinetic energy except that we measure it in units of the wrong size.

However, molecules can rotate and vibrate as well as just move, and then the average kinetic energy can be several times larger when we include these other ways to move.

At very low temperatures, there is a complication called quantum mechanics, which means that atoms and molecules don't act quite the same as marbles or baseballs; as a consequence a molecule can have a certain amount of kinetic energy even though in a way it isn't moving at all. (If this part doesn't make sense, ignore it.)

Thermal energy can be defined as the sum of all the energy that an object has that is related to its temperature. Now in addition to the various kinds of motion there is a kind of energy that comes from molecules interacting with each other. This can be as big as the kinetic energy. Note that when I say "thermal energy" I mean the total energy of the object, rather than the energy per molecule or per atom or per gram. Then the Atlantic ocean has more thermal energy than a hot cup of coffee, just because there is more of it. But some of the time we will talk about the energy per gram -- we should say "thermal energy density" or "specific thermal energy" ("specific:" being an old-fashioned way to say "per unit of mass").

The chemists have a unit called "a mole" which is 6 x 10^23 particles. One mole of ordinary materials is a about a teaspoonful -- the unit exists so that we can translate atomic facts into measurable numbers. Then the average kinetic energy of a mole of almost anything is 12 Joules x the Kelvin temperature, and the thermal energy of a mole of almost anything is larger than this by at most a factor of 3 (due to the interaction energy contribution).

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My Question: I'm doing a project to detect temperatures, using liquid crystals. Will the crystals change color based on the heat applied?"

Joe's answer
Although the material is called a "liquid crystal," what you will actually be using is a plastic sheet that is slightly thicker than the cardstock they make file folders from. It will flex easily and can be cut with scissors. Inside the plastic are small droplets of the actual material, which is a liquid. The cut edges are slightly sticky, and you have to be careful to keep it between layers of waxed paper when you are not using it (or it will stick to something permanently).

The material has a temperature range that is set back at the factory. We use the 20-25 C (68F-77 F) and 25 C - 30 C (77 F -86 F) ranges a lot. At room temperature it is black (unless the room is really warm); it is black at all temperatures below its active range. Within the range it turns brown (a dull red, really) and then tan (or dull orange-yellow), and then green, and then blue, and finally violet as it warms through the range. Above the upper limit it remains violet, getting darker and darker. Within the range, you can detect temperature variations (from place to place) of as little as 1/2 degree F as a slight difference in color. It is hard to tell the actual temperature, but for comparing temperatures it works very well.

The word "heat" sometimes refers to an action (making something hot, by adding energy), and sometimes to the amount of energy in something. The liquid crystal doesn't measure those things -- just the temperature itself.

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