Information about Black Body
In physics, a black body is an object that absorbs all electromagnetic radiation that falls onto it. No radiation passes through it and none is reflected. It is this lack of both transmission and reflection to which the name refers. These properties make black bodies ideal sources of thermal radiation. That is, the amount and wavelength (color) of electromagnetic radiation they emit is directly related to their temperature. Black bodies below around 700 K (430 °C) produce very little radiation at visible wavelengths and appear black (hence the name). Black bodies above this temperature however, produce radiation at visible wavelengths starting at red, going through orange, yellow, and white before ending up at blue as the temperature increases.
The term "black body" was introduced by Gustav Kirchhoff in 1860. The light emitted by a black body is called black-body radiation (or cavity radiation), and has a special place in the history of quantum mechanics.[1]
In the laboratory, a black-body 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.[2]
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 black-body radiation.[3] 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 black-body cavity may be thought of as containing a gas of photons. In addition, it led to the development of quantum versions of statistical mechanics, called Fermi-Dirac statistics and Bose-Einstein statistics, each applicable to a different class of particles. 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 Stefan-Boltzmann 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 ultra-violet 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.[4]
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 full-ideal 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 non-black surfaces, the deviations from ideal black-body 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 black-body spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is black-body radiation emitted by black holes.
where
at which the intensity of the radiation it produces is at a maximum is
The nanometer is a convenient unit of measure for optical wavelengths. Note that 1 nanometer is equivalent to 10−9 meters.
The total energy radiated per unit area per unit time
(in watts per square meter) by a black body is related to its temperature T (in kelvins) and the Stefan-Boltzmann constant 
as follows:
Black-body 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:
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.[11] 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
The surface temperature of a planet depends on a few factors:
then we can derive a formula for the relationship between the Earth's surface temperature and the Sun's surface temperature.
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:
Even though the earth only absorbs as a circular area
, it emits equally in all directions as a sphere:
Now, in the first assumption the earth is in thermal equilibrium, so the power absorbed must equal the power emitted:
Many factors cancel from both sides and this equation can be greatly simplified.
The term "black body" was introduced by Gustav Kirchhoff in 1860. The light emitted by a black body is called black-body radiation (or cavity radiation), and has a special place in the history of quantum mechanics.[1]
Explanation
In the laboratory, a black-body 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.[2]
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 black-body radiation.[3] 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 black-body cavity may be thought of as containing a gas of photons. In addition, it led to the development of quantum versions of statistical mechanics, called Fermi-Dirac statistics and Bose-Einstein statistics, each applicable to a different class of particles. See also fermion and boson.
)
The temperature of a Pahoehoe lava flow can be estimated by observing its colour. The result agrees well with the measured temperatures of lava flows at about 1,000 to 1,200 °C.
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 Stefan-Boltzmann 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 ultra-violet 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.[4]
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 full-ideal 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 non-black surfaces, the deviations from ideal black-body 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.
)
WMAP image of the cosmic microwave background radiation anisotropy. It has the most perfect thermal emission spectrum known and corresponds to a temperature of 2.725 kelvin (K) with an emission peak at 160.2 GHz.
In astronomy, objects such as stars are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect black-body spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is black-body radiation emitted by black holes.
Equations governing black bodies
Planck's law of black-body radiation
- :
where
- *
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;
- *
is the temperature of the black body;
- *
is Planck's constant;
- *
is the speed of light; and
- *
is Boltzmann's constant.
Wien's displacement law
at which the intensity of the radiation it produces is at a maximum is
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
(in watts per square meter) by a black body is related to its temperature T (in kelvins) and the Stefan-Boltzmann constant as follows:
- :
Radiation emitted by a human body
) |
) |
| Much of a person's energy is radiated away in the form of infrared energy. Some materials are transparent to infrared light, while opaque to visible light (note the plastic bag). Other materials are transparent to visible light, while opaque to the infrared (note the man's eyeglasses). |
The net power radiated is the difference between the power emitted and the power absorbed:
.
.
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.[11] 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
.
Temperature relation between a planet and its star
Here is an application of black-body laws. It is a rough derivation that gives an order of magnitude answer. See p. 380-382 of Planetary Science, for further discussion.[12]Factors
)
Earth's longwave thermal radiation intensity, from clouds, atmosphere and ground
- 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 (This is more important for planets like Jupiter)
Assumptions
If we assume the following:- # The Sun and the Earth both radiate as spherical black bodies in thermal equilibrium with themselves.
- # 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:)
The Earth only has an absorbing area equal to a two dimensional circle, rather than the surface of a sphere.
- :
- where
- :
is the Stefan-boltzmann constant,
- :
is the surface temperature of the Sun, and
- :
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:
- :
- where
- :
is the radius of the Earth and
- :
is the distance between the Sun and the Earth.
Even though the earth only absorbs as a circular area
, it emits equally in all directions as a sphere:
- :
- where
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:
- :
- So plug in equations 1, 2, and 3 into this and we get
- :
Many factors cancel from both sides and this equation can be greatly simplified.
The result
After canceling of factors, the final result is- :
where is the surface temperature of the Sun, is the radius of the Sun, is the distance between the Sun and the Earth, and
is the average surface temperature of the Earth.
In other words, 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,- :
- :
- :
we'll find the effective temperature of the Sun to be- :
This is within three percent of the standard measure of 5780 kelvins which makes the formula valid for most scientific and engineering applications.See also
- Effective temperature
- Color temperature
- Infrared thermometer
- Photon polarization
- Ultraviolet catastrophe
References
1. ^ When used as a compound adjective, the term is typically hyphenated, as in "black-body radiation", or combined into one word, as in "blackbody radiation". The hyphenated and one-word forms should not generally be used as nouns.
2. ^ Huang, Kerson (1967). Statistical Mechanics. New York: John Wiley & Sons.
3. ^ Planck, Max (1901). "On the Law of Distribution of Energy in the Normal Spectrum" (HTML). Annalen der Physik 4: 553.
4. ^ Landau, L. D.; E. M. Lifshitz (1996). Statistical Physics, 3rd Edition Part 1, Oxford: Butterworth-Heinemann.
5. ^ Infrared Services. Emissivity Values for Common Materials. Retrieved on 2007-06-24.
6. ^ Omega Engineering. Emissivity of Common Materials. Retrieved on 2007-06-24.
7. ^ Elert, G. (ed.). Temperature of a Healthy Human. Retrieved on 2007-06-24.
8. ^ Lee, B.. Theoretical Prediction and Measurement of the Fabric Surface Apparent Temperature in a Simulated Man/Fabric/Environment System. Retrieved on 2007-06-24.
9. ^ Harris J, Benedict F (1918). "A Biometric Study of Human Basal Metabolism.". Proc Natl Acad Sci U S A 4 (12): 370-3. PMID 16576330.
10. ^ Levine, J (2004). "Nonexercise activity thermogenesis (NEAT): environment and biology". Am J Physiol Endocrinol Metab 286: E675-E685.
11. ^ DrPhysics.com. Heat Transfer and the Human Body. Retrieved on 2007-06-24.
12. ^ Cole, George H. A.; Woolfson, Michael M. (2002). Planetary Science: The Science of Planets Around Stars (1st ed.). Institute of Physics Publishing. ISBN 0-7503-0815-X.
Other textbooks
- Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.
- Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman. ISBN 0-7167-4345-0.
External links
- Cooling Mechanisms for Human Body - From Hyperphysics
- Descriptions of radiation emitted by many different objects
- Black Body Emission Calculator
- BlackBody Emission Applet
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
..... Click the link for more information.In physics, a physical body (sometimes called simply a body or even an object) is a collection of masses, taken to be one. For example, a cricket ball can be considered an object but the ball also consists of many particles (pieces of matter).
..... Click the link for more information.Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
..... Click the link for more information.Reflection is the change in direction of a wave front at an between two dissimilar media so that the wave front returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves.
..... Click the link for more information.Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature. Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the light emitted by a glowing
..... Click the link for more information.The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero — the coldest possible temperature — is zero kelvins
..... Click the link for more information.Gustav Robert Kirchhoff
Gustav Kirchhoff
Born 12 March 1824
Königsberg, East Prussia
..... Click the link for more information.18th century - 19th century - 20th century
1830s 1840s 1850s - 1860s - 1870s 1880s 1890s
1857 1858 1859 - 1860 - 1861 1862 1863
:
Subjects: Archaeology - Architecture -
..... Click the link for more information.In physics, Black-body radiation may refer to:- Black body, an object that emits light (black-body radiation)
- Planck's law of black-body radiation, Intensity vs. Wavelength and Temperature
- Stefan-Boltzmann law of black-body radiation, Total Intensity vs. Temperature
..... Click the link for more information.The history of quantum mechanics as this interlaces with history of quantum chemistry began essentially with the 1838 discovery of cathode rays by Michael Faraday, the 1859 statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig
..... Click the link for more information.In radiation thermodynamics, a hohlraum (a German loanword, originally a non-specific word for "hollow area" or "cavity") is a cavity whose walls are in radiative with the radiant energy within the cavity.
..... Click the link for more information.In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek letter lambda (λ). Examples of wave-like phenonomena are light, water waves, and sound waves.
..... Click the link for more information.In statistical signal processing and physics, the spectral density, power spectral density, or energy spectral density is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has
..... Click the link for more information.In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek letter lambda (λ). Examples of wave-like phenonomena are light, water waves, and sound waves.
..... Click the link for more information.An element's emission spectrum is the relative intensity of electromagnetic radiation of each frequency it emits when it is heated (or more generally when it is excited).
When the electrons in the element are excited, they jump to higher energy levels.
..... Click the link for more information.Kirchhoff's law of thermal radiation, or Kirchhoff's law for short, is a general statement equating emission and absorption in heated objects, proposed by Gustav Kirchhoff in 1859 (and proved in 1861), following from general considerations of thermodynamic equilibrium.
..... Click the link for more information.trillion fold).]]
Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
..... Click the link for more information.Max Planck
Max Karl Ernst Ludwig Planck
Born March 23 1858
Kiel, Germany
Died September 4 1947 (aged 89)
..... Click the link for more information.For a general introduction, see black body.
In physics, Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature .
..... Click the link for more information.Wien's approximation (also sometimes called Wien's law or the Wien distribution law) is a law of physics used to describe the spectrum of thermal radiation (frequently called the blackbody function). This law was first derived by Wilhelm Wien in 1896.
..... Click the link for more information.wavelength corresponding to the peak emission in various black body spectra as a function of temperature|right|300px]] Wien's displacement law is a law of physics that states that there is an inverse relationship between the wavelength of the peak of the emission of a
..... Click the link for more information.Thermodynamics (from the Greek θερμη, therme, meaning "heat" and δυναμις, dynamis, meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on
..... Click the link for more information.Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
..... Click the link for more information.Editing of this page by unregistered or newly registered users is currently disabled due to vandalism.
If you are prevented from editing this page, and you wish to make a change, please discuss changes on the talk page, request unprotection, log in, or .
..... Click the link for more information.photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation such as x-rays or visible light.
..... Click the link for more information.Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s.[1]
..... Click the link for more information.Photon
Photons emitted in a coherent beam from a laser
Composition: Elementary particle
Family: Boson
Group: Gauge boson
Interaction: Electromagnetic
Theorized: Albert Einstein (1905–17)
Symbol: or
Mass: 0[1]
..... Click the link for more information.In physics, a photon gas is a gas-like collection of photons, which has many of the same properties of a conventional gas like hydrogen or neon - including pressure, temperature, and entropy. The most common example of a photon gas in equilibrium is black body radiation.
..... Click the link for more information.In particle physics, fermions are particles with half-integer spin, such as protons and electrons. They are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons.
..... Click the link for more information.In particle physics, bosons are force carrier particles, such as the photon. They may be either elementary or composite. They are distinguished from fermions (matter particles) by their integer spin. Bosons are named after Indian physicist Satyendra Nath Bose.
..... Click the link for more information. - :
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
