Listed are some examples of blackbody
radiators, and applications of blackbody radiation.
Remember that all objects are blackbody radiators, and that the spectrum
of an object's blackbody radiation is determined by the object's temperature, and by its
emissivity. The examples we discuss here are ones where the radiation is either visible
radiation, or where the radiation is put to some use.
The Sun (and other stars)
The high temperatures and pressures in the cores of stars, including our own Sun, smash
atomic nuclei together to form heavier nuclei in a process called nuclear fusion.
When this occurs, gamma rays (high-energy photons) are produced, and these gamma rays
collide with all the various particles in the star's core. When a gamma ray collides with
a particle (an electron, or an atomic nucleus), it can lose energy in the collision: the
gamma ray leaves the collision with somewhat less energy, the missing energy appearing as
a greater kinetic energy for the particle. This process is called Compton scattering.
Because the material in the star is so dense, this process happens many, many times, and
before the gamma ray can reach the surface of the star its energy is comparable to the
kinetic energies the particles already have. The outer region (about the outer 1/3 or so)
of the star is a convective zone, which is heated below by the material heated by the
gamma rays, and cooled above by the blackbody radiation from the star's surface. In the
convective zone, the cooler material being formed at the surface is denser than the hotter
material below, and so it tends to sink toward the star's center, displacing the hotter
material and squeezing it upward to the surface.
The surface of the star (called the photosphere) is rather nonuniform in its
temperature. If you were to look at small areas on the star's surface, you would find some
areas with higher temperatures, where convecting hot material had just been brought to the
surface, and other areas with lower temperature, where the material has had time to cool
by blackbody radiation that escapes into space. How would you measure the different
temperatures? By analyzing the spectra of the blackbody radiation emitted by the different
regions. The average temperature of the Sun's photosphere is about 5600 K. Other stars are
hotter (and so appear bluer), or cooler (and so appear redder). Generally, very young
stars are very hot and have a noticeable blue color. Older stars, including red giants,
are cooler, and have a noticeable color. In the Northern Hemisphere winter sky, the
constellation Orion's brightest star, Betelgeuse, a red giant, appears quite red. Nearby,
the brightest star in the constellation Canis Major, just at Orion's heels, is the star
Sirius, which is actually a binary star. The brightest of the two stars in Sirius is a
very hot, blue star, whose color is also quite noticeable.
The spectrum of a star, including the Sun, is not quite that of an ideal blackbody. The
fact that the photosphere contains materials at different temperatures produces a spectrum
that is not quite the shape of the ideal blackbody spectrum. Furthermore, the above the
photosphere is the star's atmosphere, which contains many gases consisting of both
electrically neutral and ionized chemicals. Most prominent among these are hydrogen and
helium. However, the atmospheres of stars such as the Sun also contain a wide variety of
heavier elements, including carbon, nitrogen, oxygen, silicon, potassium, sodium, iron and
nickel. The temperature of the atmosphere is somewhat lower than that of the photosphere,
but, because they are more tenuous than the material in the photosphere, the atmosphere's
emissivity is much lower than the photosphere's emissivity. However, these materials
absorb some of the radiation at certain wavelengths. These absorption lines were first
noticed by Fraunhofer in 1814, who cataloged some 700 in the visible region of the
electromagnetic spectrum. Using these absorption lines it is possible to learn much about
the chemical composition of a star's atmosphere.
Beyond the atmosphere of most stars is a corona. Interestingly, the temperature of the
corona is much greater than even that of the photosphere. It is not currently known why
that is. Again, the material in the corona is much more tenuous than that in the
photosphere, and so its emissivity is much smaller than the photosphere's.
The Sun is a relatively strong source of x-rays and radio-frequency radiation, which
are both connected with storm and magnetic activity on the sun, and whose spectra deviate
considerably from blackbody radiation.
Incandescent light
bulbs, electric heaters and stoves
When electric current is passed through a resistive material (that is, through an
imperfect conductor), it heats the material. The electrical current (I) flows in
response to an applied electrical potential difference (voltage difference, V)
between two points (like two ends of a segment of wire). The resistance (R)
of the material is defined by the ratio of the electrical potential difference to the
current:
This is known as Ohm's Law. The amount of energy the current deposits in the
material per unit time is given by the formula is called the power dissipation (P),
and is given by the expression
(The second equality follows by rearranging the previous expression to read V=IR.).
The units of P is Watts (W), or Joules/sec (J/s), or Volt-Amperes (VA). All of these are
equivalent. P is the number of Joules per second that is added to the kinetic
energy of the atoms making up the material. Increased atomic kinetic energy means
increased temperature. If the material were not at the same time getting rid of some of
this energy at the same time, its temperature would just keep on increasing and increasing
until it melted or vaporized.
A conductor (whether highly resistive or not) contains electrons that are quite free to
move about. When the voltage difference is established across a region of the material, an
electric field is established at all places in the material. The electrons, being
electrically charged, experience a force when they are in this field, and so they begin to
accelerate toward the electrically relatively positive end of the material. While they are
in motion, the electrons will inevitably start to crash into the atoms making up the
material, and in these collisions some kinetic energy will be lost by the electrons and
gained by whatever they are crashing into. The increased kinetic energy (eventually of the
whole material) means that the material's temperature is increasing. This is a familiar
phenomenon; when electrical current is run through a wire, the wire starts to become warm.
If it is not too resistive, and if the current being drawn through it, it will not warm up
very much. If this is an extension cord, you do not want it to warm up too much, of
course.
It is sometimes desirable, however, to have a resistive conductor heat up. One example
is the incandescent light bulb. This consists of a sealed glass container with most of the
air taken out of it, in which is a coil of resistive wire. The ends of this coil are
connected to the outside of the container, so that a large voltage can be applied to it
from the household electric supply. When that electrical voltage is supplied (that is,
when someone turns on the light), the current flowing through the wire heats the wire to a
high temperature (2000-5500 K), and the wire glows. Light bulbs of inferior quality (whose
wire is not as resistive, or whose glass container still has a lot of gas in it) tend to
appear to have a reddish glow, since the wire filament is not as hot. When the electric
supply is turned off, the filament cools. Often this happens over a long enough period of
time that the glow can be observed to become both less and less intense, and redder, until
its glow finally cannot be perceived. The filament cools because its blackbody radiation
is carrying energy away into the space around the lightbulb.
Almost all electrical heating devices, including hair driers, clothes driers, space
heaters, electric baseboard heaters, electric stove and oven heating elements, work on
this same principle. When you turn a stove's burner on high, in a few moments, there is a
perceptible red glow from the heating element. As this gets hotter, the color appears more
and more orange. If the temperature were to be allowed to get high enough to give a
yellower glow, the burner would be hot enough to melt most cookware.
When you turn a stove's burner on a low setting, you will not see the burner glow, but
you can certainly feel the heat coming off of it, if you place your hand near (but at a
respectful distance from) the burner. This is not because the burner is heating the
air, which is heating your hand. It is because the molecules in your skin are absorbing
the infrared radiation that dominates the spectrum of the burner's blackbody radiation.
This is often called radiant heat. It is why you can walk by a parked car and sense
whether it has been driven quite recently (so its engine compartment is still warm). It's
also how radiators in older buildings heat the rooms they're in. Most of the heat
transferred into the room, and to the people in it, is transferred as blackbody radiation,
and not as a result of the radiator heating the air that is in contact with it, although
that certainly does happen as well. You also experience radiant heating when you are next
to hot coals, like the burning embers of a fire.
Candle Flames and Other Flames
The rate at which a candle burns is limited by the diffusion of oxygen into the
vicinity of the flame. The combustion process is an exothermic chemical reaction in which
the fuel (the paraffin), a mixture of chemical compounds comprised mostly of carbon and
hydrogen atoms, is combined with oxygen from the air to form carbon dioxide (CO2)
and water (H2O). The heat evolved by this process heats up and vaporizes some
of the fuel, and also heats up the oxygen, nitrogen, and other atmospheric gases. An
ordinary candle flame is actually quite oxygen-starved, and the vaporized fuel molecules,
at the elevated temperatures in the flame itself, wind up combining with other fuel
molecules. Incomplete combustion of fuel molecules also results in the formation of small
carbon particles. Together, the polymerized fuel and carbon particles make up soot. And
when the soot is formed, it is very hot, and emits a great deal of blackbody radiation.
This radiation appears reddish-orangish-yellowish. Chemical reactions in the flame plasma
also emit radiation, so the emission spectrum of a complete candle flame can be quite
complex. However, the characteristic continuum spectrum of the blackbody radiation from
the soot is the dominant feature.
You may have used, or watched other people use gas/oxygen torches, such as are used for
welding, plumbing, and glass sculpture. These torches have two supply hoses. One hose
feeds fuel (natural gas, propane, or acetylene) to the torch, while the other feeds a
supply of oxygen. When the torch is first lit, the oxygen feed is turned way down or even
off, and you will see a bright yellow flame shooting out of the torch. This is essentially
the same yellow flame as in the candle. The fuel is burning in oxygen-poor conditions,
relying on oxygen from the air diffusing in toward the region the previously-burned fuel
has depleted. When the oxygen supply is turned on, the flame is force-fed with oxygen, and
the flame now has a blue glow that is not nearly as bright as the yellow flame. In the
oxygen-rich flame there is essentially no soot production, so, even though there are gases
at a very high temperature, there is nothing there like the soot particles that have
sufficient emissivity to produce a great deal of blackbody radiation. The blue glow of the
flame is not blackbody radiation, but rather is due to chemical reactions going on in the
flame.
Warm-Blooded Animals
Humans, and other warm-blooded animals, tend to be warmer than their surroundings. As
blackbody radiators, they emit considerable amounts of energy (roughly 100 W for an
average adult at rest) in the infrared region of the spectrum. Of course, at the same
time, their surfaces are absorbing infrared radiation from their surroundings. But there
is a net energy loss, and this energy is continually being replaced by the animal's
metabolic processes.
Night vision equipment allows one to detect the presence of people and other warm
animals and objects by using a kind of video camera that is sensitive to infrared
radiation. The signal produced by that camera is fed into a video monitor that presents a
visible image. In this image, you see a person as a glowing object, rather than, as you
are accustomed to, an object that reflects the ambient light that falls on him.
The fact that people are emitters of infrared radiation is also used in a wide variety
of anti-intruder devices and in automatic light switches (usually for outdoor lighting).
These have infrared photosensors. When something emitting infrared radiation passes in
front, the photosensor causes an electrical circuit to close, and this is in turn used to
set off an alarm, turn on a light, or do something else.
The Cooling of the Earth at Night
The materials that make up the surface of the Earth absorb some of the Sun's radiation
during the daytime. This results in the warming of those materials. Since all materials
radiate blackbody radiation, the Earth's surface is always radiating energy (in the
infrared region). Of course, it is also absorbing energy from its surroundings, but as the
temperature of the Earth's surface increases, it ends up radiating more infrared radiation
than it is absorbing.
When the night comes, the surface is no longer being heated by the Sun, but it is still
radiating, and, since it is warmer than the air around it, it continues to radiate,
gradually cooling it off.
If clouds are present over the surface at night, their effect is to reflect some
fraction of the radiation that was emitted by the surface back down toward it. Over the
course of the night, this has the effect of causing the surface to cool much more slowly.
This is why clear-sky nights tend to be much colder than cloudy-sky nights.
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