Dictionary Definition
blackbody n : a hypothetical object capable of
absorbing all the electromagnetic radiation falling on it; "a black
body maintained at a constant temperature is a full radiator at
that temperature because the radiation reaching and leaving it must
be in equilibrium" [syn: black body,
full
radiator]
User Contributed Dictionary
English
Pronunciation
Noun
blackbody a theoretical body, approximated by a hole in a hollow black sphere, that absorbs all incident electromagnetic radiation and reflects none; it has a characteristic emission spectrum
Translations
 Finnish: musta kappale
 German: schwarzer Körper
 Russian: чёрное тело (čórnoje t'élo)
 Spanish: cuerpo negro
 Swedish: svartkropp
Alternative spellings
See also
Extensive Definition
In physics, a black body is an
object that
absorbs all light
that falls on it. No electromagnetic radiation passes through it
and none is reflected.
Because no light is reflected or transmitted, the object appears
black when it is cold.
If the black body is hot, these properties make
it an ideal source of thermal
radiation. If a perfect black body at a certain temperature is
surrounded by other objects in thermal
equilibrium at the same temperature, it will on average emit
exactly as much as it absorbs, at every wavelength. Since the
absorption is easy to understand—every ray that hits the body is
absorbed—the emission is just as easy to understand.
A black body at temperature T emits exactly the
same wavelengths and intensities which would be present in an
environment at equilibrium at temperature T, and which would be
absorbed by the body. Since the radiation in such an environment
has a spectrum that depends only on temperature, the temperature of
the object is directly related to the wavelengths of the light that
it emits. At room temperature, black bodies emit infrared
light, but as the temperature increases past a few hundred
degrees Celsius, black
bodies start to emit at visible wavelengths, from red, through
orange, yellow, and white before ending up at blue, beyond which
the emission includes increasing amounts of ultraviolet.
The term "black body" was introduced by Gustav
Kirchhoff in 1860. The light
emitted by a black body is called blackbody radiation.
If a small window is opened into an oven, any
light that enters the window has a very low probability of leaving
without being absorbed. Conversely, the hole acts as a nearly ideal
blackbody radiator. This makes peepholes into furnaces good
sources of blackbody radiation, and some people call it cavity
radiation for this reason.
Blackbody emission gives insight into the
thermal equilibrium state of a continuous field. In classical
physics, each different Fourier mode
in thermal equilibrium should have the same
energy, leading to the nonsense
prediction that there would be an infinite amount of energy in
any continuous field. Black bodies could test the properties of
thermal equilibrium because they emit radiation which is
distributed thermally. Studying the laws of the black body
historically led to
quantum mechanics.
Explanation
In the laboratory, blackbody radiation is
approximated by the radiation from a small hole entrance to a large
cavity, a hohlraum. Any
light entering the hole would have to reflect off the walls of the
cavity multiple times before it escaped, in which process it is
nearly certain to be absorbed. This occurs regardless of the
wavelength of the
radiation entering (as long as it is small compared to the hole).
The hole, then, is a close approximation of a theoretical black
body and, if the cavity is heated, the spectrum
of the hole's radiation (i.e., the amount of light emitted from the
hole at each wavelength) will be
continuous, and will not depend on the material in the cavity
(compare with emission
spectrum). By a
theorem proved by Kirchhoff, this curve depends only on the
temperature of the
cavity walls.
Calculating this curve was a major challenge in
theoretical physics during the late nineteenth century. The problem
was finally solved in 1901 by Max Planck as
Planck's law of blackbody radiation. By making changes to
Wien's
Radiation Law (not to be confused with Wien's
displacement law) consistent with thermodynamics and
electromagnetism, he
found a mathematical formula fitting the experimental data in a
satisfactory way. To find a physical interpretation for this
formula, Planck had then to assume that the energy of the
oscillators in the cavity was quantized (i.e., integer multiples of
some quantity). Einstein
built on this idea and proposed the quantization of electromagnetic
radiation itself in 1905 to explain the photoelectric
effect. These theoretical advances eventually resulted in the
superseding of classical electromagnetism by quantum
electrodynamics. Today, these quanta are called photons and the blackbody cavity
may be thought of as containing a gas of
photons. In addition, it led to the development of quantum
probability distributions, called FermiDirac
statistics and BoseEinstein
statistics, each applicable to a different class of particle,
which are used in quantum mechanics instead of the classical
distributions. See also fermion and boson.
The wavelength at which the radiation is
strongest is given by Wien's
displacement law, and the overall power emitted per unit area
is given by the StefanBoltzmann
law. So, as temperature increases, the glow color changes from
red to yellow to white to blue. Even as the peak wavelength moves
into the ultraviolet, enough radiation continues to be emitted in
the blue wavelengths that the body will continue to appear blue. It
will never become invisible — indeed, the radiation of
visible light increases monotonically
with temperature.
The radiance or observed intensity
is not a function of direction. Therefore a black body is a perfect
Lambertian
radiator.
Real objects never behave as fullideal black
bodies, and instead the emitted radiation at a given frequency is a
fraction of what the ideal emission would be. The emissivity of a material
specifies how well a real body radiates energy as compared with a
black body. This emissivity depends on factors such as temperature,
emission angle, and wavelength. However, it is typical in
engineering to assume that a surface's spectral emissivity and
absorptivity do not depend on wavelength, so that the emissivity is
a constant. This is known as the grey body assumption.
Although Planck's formula predicts that a black
body will radiate energy at all frequencies, the formula is only
applicable when many photons are being measured. For example, a
black body at room temperature (300 K) with one square meter of
surface area will emit a photon in the visible range once every
thousand years or so, meaning that for most practical purposes, the
black body does not emit in the visible range.
When dealing with nonblack surfaces, the
deviations from ideal blackbody behavior are determined by both
the geometrical structure and the chemical composition, and follow
Kirchhoff's Law: emissivity equals absorptivity, so that an
object that does not absorb all incident light will also emit less
radiation than an ideal black body.
In astronomy, objects such as
stars are frequently
regarded as black bodies, though this is often a poor
approximation. An almost perfect blackbody spectrum is exhibited
by the
cosmic microwave background radiation. Hawking
radiation is blackbody radiation emitted by black
holes.
Equations governing black bodies
Planck's law of blackbody radiation

 I(\nu)d\nu = \frac\frac\, d\nu
where

 I(\nu)d\nu \, is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν+dν;
 T \, is the temperature of the black body;
 h \, is Planck's constant;
 c \, is the speed of light; and
 k \, is Boltzmann's constant.
Wien's displacement law
The relationship between the temperature T of a black body, and wavelength \lambda_ at which the intensity of the radiation it produces is at a maximum is
 T \lambda_\mathrm = 2.898... \times 10^6 \ \mathrm. \,
The nanometer is a convenient unit
of measure for optical
wavelengths. Note that 1 nanometer is equivalent to 10−9
meters.
Stefan–Boltzmann law
The total energy radiated per unit area per unit
time j^ (in watts per
square
meter) by a black body is related to its temperature T (in
kelvins) and the
Stefan–Boltzmann constant \sigma as follows:

 j^ = \sigma T^4.\,
Radiation emitted by a human body
Blackbody laws can be applied to human beings. For example, some of a person's energy is radiated away in the form of electromagnetic radiation, most of which is infrared.The net power radiated is the difference between
the power emitted and the power absorbed:
 P_=P_P_.
 P_=A\sigma \epsilon \left( T^4  T_^4 \right) \,.
 P_ = 100 \ \mathrm \,.
There are other important thermal loss
mechanisms, including convection and evaporation. Conduction is
negligible since the Nusselt
number is much greater than unity. Evaporation (perspiration) is only
required if radiation and convection are insufficient to maintain a
steady state temperature. Free convection rates are comparable,
albeit somewhat lower, than radiative rates. Thus, radiation
accounts for about 2/3 of thermal energy loss in cool, still air.
Given the approximate nature of many of the assumptions, this can
only be taken as a crude estimate. Ambient air motion, causing
forced convection, or evaporation reduces the relative importance
of radiation as a thermal loss mechanism.
Also, applying Wien's
Law to humans, one finds that the peak wavelength of light
emitted by a person is
 \lambda_ = \frac = 9500 \ \mathrm \,.
Temperature relation between a planet and its star
Here is an application of blackbody laws. It is a rough derivation that gives an order of magnitude answer. The actual Earth is warmer due to the greenhouse effect.Factors
The surface temperature of a planet depends on a few factors: Incident radiation (from the Sun, for example)
 Emitted radiation (for example Earth's infrared glow)
 The albedo effect (the fraction of light a planet reflects)
 The greenhouse effect (for planets with an atmosphere)
 Energy generated internally by a planet itself (due to Radioactive decay, tidal heating and adiabatic contraction due to cooling).
For the inner planets, incident and emitted
radiation have the most significant impact on surface temperature.
This derivation is concerned mainly with that.
Assumptions
If we assume the following:
 The Sun and the Earth both radiate as spherical black bodies.
 The Earth is in thermal equilibrium.
 The Earth absorbs all the solar energy that it intercepts from the Sun.
then we can derive a formula for the relationship
between the Earth's surface temperature and the Sun's surface
temperature.
Derivation
To begin, we use the Stefan–Boltzmann law to find the total power (energy/second) the Sun is emitting:
 P_ = \left( \sigma T_^4 \right) \left( 4 \pi R_^2 \right) \qquad \qquad (1)
 where

 \sigma \, is the Stefan–boltzmann constant,
 T_S \, is the surface temperature of the Sun, and
 R_S \, is the radius of the Sun.
The Sun emits that power equally in all
directions. Because of this, the Earth is hit with only a tiny
fraction of it. This is the power from the Sun that the Earth
absorbs:

 P_ = P_ \left( \frac \right) \qquad \qquad (2)
 where

 R_ \, is the radius of the Earth and
 D \, is the distance between the Sun and the Earth.
Even though the earth only absorbs as a circular
area \pi R^2, it emits equally in all directions as a sphere:

 P_ = \left( \sigma T_^4 \right) \left( 4 \pi R_^2 \right) \qquad \qquad (3)
 where T_ is the surface temperature of the earth.
Now, in the first assumption the earth is in
thermal equilibrium, so the power absorbed must equal the power
emitted:

 P_ = P_\,
 So plug in equations 1, 2, and 3 into this and we get

 \left( \sigma T_^4 \right) \left( 4 \pi R_^2 \right) \left( \frac \right) = \left( \sigma T_^4 \right) \left( 4 \pi R_^2 \right).\,
Many factors cancel from both sides and this
equation can be greatly simplified.
The result
After canceling of factors, the final result isIn other words, given the assumptions made, the
temperature of the Earth depends only on the surface temperature of
the Sun, the radius of the Sun, and the distance between the Earth
and the Sun.
Temperature of the Sun
If we substitute in the measured values for Earth,
 T_ \approx 14 \ \mathrm = 287 \ \mathrm,
 R_ = 6.96 \times 10^8 \ \mathrm,
 D = 1.5 \times 10^ \ \mathrm,
we'll find the effective
temperature of the Sun to be

 T_ \approx 5960 \ \mathrm.
This is within three percent of the standard
measure of 5780 kelvins which makes the formula valid for most
scientific and engineering applications.
Doppler effect for a moving blackbody
The Doppler
effect is the well known phenomenon describing how observed
frequencies of light are "shifted" when a light source is moving
relative to the observer. If f is the emitted frequency of a
monochromatic light source, it will appear to have frequency f if
it is moving relative to the observer :
 f' = f \frac (1  \frac \cos \theta)
where v is the velocity of the source in the
observer's rest frame, θ is the angle between the velocity vector
and the observersource direction, and c is the speed of
light. This is the fully relativistic formula, and can be
simplified for the special cases of objects moving directly towards
( θ = π) or away ( θ = 0) from the observer, and for speeds much
less than c.
To calculate the spectrum of a moving blackbody,
then, it seems straightforward to simply apply this formula to each
frequency of the blackbody spectrum. However, simply scaling each
frequency like this is not enough. We also have to account for the
finite size of the viewing aperture, because the solid angle
receiving the light also undergoes a Lorentz
transformation. (We can subsequently allow the aperture to be
arbitrarily small, and the source arbitrarily far, but this cannot
be ignored at the outset.) When this effect is included, it is
found that a blackbody at temperature T that is receding with
velocity v appears to have a spectrum identical to a stationary
blackbody at temperature T , given by:
 T' = T \frac (1  \frac \cos \theta)
For the case of a source moving directly towards
or away from the observer, this reduces to

 T' = T \sqrt
Here v > 0 indicates a receding source, and v
< 0 indicates an approaching source.
This is an important effect in astronomy, where
the velocities of stars and galaxies can reach significant
fractions of c. An example is found in the
cosmic microwave background radiation, which exhibits a dipole
anisotropy from the Earth's motion relative to this blackbody
radiation field.
See also
References
Other textbooks
 Thermal Physics (2nd ed.)
 Modern Physics (4th ed.)
External links
 Calculating Blackbody Radiation Interactive calculator with Doppler Effect. Includes most systems of units.
 Cooling Mechanisms for Human Body  From Hyperphysics
 Descriptions of radiation emitted by many different objects
 BlackBody Emission Applet
 "Blackbody Spectrum" by Jeff Bryant, The Wolfram Demonstrations Project, 2007.
blackbody in Arabic: جسم أسود
blackbody in Azerbaijani: Mütləq qara
cisim
blackbody in Bulgarian: Абсолютно черно
тяло
blackbody in Catalan: Cos negre
blackbody in Czech: Absolutně černé těleso
blackbody in Danish: Sortlegeme
blackbody in German: Schwarzer Körper
blackbody in Estonian: Absoluutselt must
keha
blackbody in Modern Greek (1453): Μέλαν
σώμα
blackbody in Spanish: Cuerpo negro
blackbody in Esperanto: Nigra korpo
blackbody in Persian: جسم سیاه
blackbody in French: Corps noir
blackbody in Galician: Corpo negro
blackbody in Korean: 흑체
blackbody in Croatian: Crno tijelo
blackbody in Indonesian: Benda hitam
blackbody in Italian: Corpo nero
blackbody in Hebrew: קרינת גוף שחור
blackbody in Lithuanian: Absoliučiai juodas
kūnas
blackbody in Hungarian:
Feketetestsugárzás
blackbody in Mongolian: Хар бие
blackbody in Dutch: Zwart lichaam
blackbody in Japanese: 黒体
blackbody in Norwegian: Svart legeme
blackbody in Norwegian Nynorsk: Svart
lekam
blackbody in Polish: Ciało doskonale
czarne
blackbody in Portuguese: Corpo negro
blackbody in Russian: Абсолютно чёрное
тело
blackbody in Slovak: Absolútne čierne
teleso
blackbody in Slovenian: Črno telo
blackbody in Finnish: Musta kappale
blackbody in Swedish: Svartkroppsstrålning
blackbody in Thai: วัตถุดำ
blackbody in Vietnamese: Vật đen
blackbody in Turkish: Kara cisim ışınımı
blackbody in Ukrainian: Абсолютно чорне
тіло
blackbody in Chinese: 黑体 (热力学)