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## Black body
In physics, a The term "black body" was introduced by Gustav Kirchhoff in 1860. The light emitted by a black body is called
## ExplanationIn the laboratory, 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 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.
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. 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 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. ## Equations governing black bodies## Planck's law of black-body radiationwhere - 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 lawThe relationship between the temperature The nanometer is a convenient unit of measure for optical wavelengths. Note that 1 nanometer is equivalent to 10 ## Stefan–Boltzmann lawThe total energy radiated per unit area per unit time (in watts per square meter) by a ## Radiation emitted by a human body
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: *P*_{net}=*P*_{emit}−*P*_{absorb}.
Applying the Stefan-Boltzmann law, - .
The total surface area of an adult is about 2 m², and the mid- and far-infrared emissivity of skin and most clothing is near unity, as it is for most nonmetallic surfaces. - .
The total energy radiated in one day is about 9 MJ (million joules), or 2000 kcal (food calories). Basal metabolic rate for a 40-year-old male is about 35 kcal/(m²·h), 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. Also, applying Wien's Law to humans, one finds that the peak wavelength of light emitted by a person is - .
This is why thermal imaging devices designed for human subjects are most sensitive to 7–14 micrometers wavelength. ## Temperature relation between a planet and its starHere is an application of black-body laws. It is a rough derivation that gives an order of magnitude answer. See p. 380-382 of ## FactorsThe 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 (This is more important for planets like Jupiter)
For the inner planets, incident and emitted radiation have the most significant impact on surface temperature. This derivation is concerned mainly with that. ## AssumptionsIf 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.
- The Sun and the Earth both radiate as spherical black bodies in thermal equilibrium
then we can derive a formula for the relationship between the Earth's ## DerivationTo begin, we use the Stefan-Boltzmann law to find the total power (energy/second) the Sun is emitting:
- 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 - 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 π - where
*T*_{E}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 resultAfter 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 SunIf 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
- Rayleigh-Jeans law
## References**^**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.**^**Huang, Kerson (1967).*Statistical Mechanics*. New York: John Wiley & Sons.**^**Planck, Max (1901). "On the Law of Distribution of Energy in the Normal Spectrum" (HTML).*Annalen der Physik***4**: 553.**^**Landau, L. D.; E. M. Lifshitz (1996).*Statistical Physics*, 3rd Edition Part 1, Oxford: Butterworth-Heinemann.**^**Infrared Services. Emissivity Values for Common Materials. Retrieved on 2007-06-24.**^**Omega Engineering. Emissivity of Common Materials. Retrieved on 2007-06-24.**^**Farzana, Abanty (2001). Temperature of a Healthy Human (Skin Temperature).*The Physics Factbook*. Retrieved on 2007-06-24.**^**Lee, B.. Theoretical Prediction and Measurement of the Fabric Surface Apparent Temperature in a Simulated Man/Fabric/Environment System. Retrieved on 2007-06-24.**^**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.**^**Levine, J (2004). "Nonexercise activity thermogenesis (NEAT): environment and biology".*Am J Physiol Endocrinol Metab***286**: E675-E685.**^**DrPhysics.com. Heat Transfer and the Human Body. Retrieved on 2007-06-24.**^**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__.
Categories: Thermodynamics | Electromagnetic radiation |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Black_body". A list of authors is available in Wikipedia. |