Wien's distribution law - encyclopedia article about Wien's distribution law.

Comparison of Wien's Distribution law with the Rayleigh-Jeans Law and Planck's law, for a body of 8 mK temperature.

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.<ref name="MehraRechenberg1982" >J. Mehra, H. Rechenberg (1982). "1", The Historical Development of Quantum Theory. New York: Springer-Verlag. ISBN 0-387-90642-8. <ref name="bowleysanchez1999" >R. Bowley, M. Sánchez (1999). Introductory Statistical Mechanics, 2nd edition, Oxford: Clarendon Press. ISBN 0-19-850576-0. The equation does accurately describe the short wavelength (high frequency) spectrum of thermal emission from objects, but it fails to accurately fit the experimental data for long wavelengths (low frequency) emission.<ref name="bowleysanchez1999" />

The law may be written as

$\text{[math]}$ ^[1]

where

* $\text{[math]}$ is the amount of energy per unit surface area per unit time per unit solid angle per unit frequency emitted at a frequency ν.

* $\text{[math]}$ is the temperature of the black body.

* $\text{[math]}$ is Planck's constant.

* $\text{[math]}$ is the speed of light.

* $\text{[math]}$ is Boltzmann's constant.

This equation may also be written as

$\text{[math]}$ <ref name="bowleysanchez1999" />^[2]

where $\text{[math]}$ is the amount of energy per unit surface area per unit time per unit solid angle per unit wavelength emitted at a wavelength λ.

Relation to Planck's law

The Wien approximation was originally proposed as a description of the complete spectrum of thermal radiation, although it failed to accurately describe long wavelength (low frequency) emission. However, it was soon superseded by Planck's law, developed by Max Planck. Unlike the Wien approximation, Plank's law accurately describes the complete spectrum of thermal radiation. Planck's law may be given as

$\text{[math]}$ <ref name="rybickilightman1979" />

The Wien approximation may be derived from Planck's law by assuming $\text{[math]}$ . When this is true, then

$\text{[math]}$ <ref name="rybickilightman1979" />

and so Planck's law approximately equals the Wien approximation at high frequencies.

Other approximations of thermal radiation

The Rayleigh-Jeans law developed by Lord Rayleigh may be used to accurately describe the long wavelength spectrum of thermal radiation but fails to describe the short wavelength spectrum of thermal emission.<ref name="bowleysanchez1999" /><ref name="rybickilightman1979" />

References

1. ^ G. B. Rybicki, A. P. Lightman (1979). Radiative Processes in Astrophysics. New York: John Wiley & Sons. ISBN 0-471-82759-2.
2. ^ Equation derived using u=4π/c; see Rybicki, Lightman (1979) reference.

Wien's law or Wien law may refer to:

Wien approximation, an equation used to describe the short-wavelength (high frequency) spectrum of thermal radiation.

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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.
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spectrum (plural spectra) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a
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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.
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Wilhelm Wien

Wilhelm Carl Werner Otto Fritz Franz Wien
Born January 13 1864
Fischhausen, East Prussia
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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.
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FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. A sequel, titled Amplitude was released in 2003.
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energy (from the Greek ενεργός, energos, "active, working")^[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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Area is the measure of how much exposed area any two dimensional object has. It is expressed in square units, and is calculated by adding together the areas of all the faces of the object.

Area formulas

Note: For 2D figures, the surface area and the area are the same.
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time.

One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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The solid angle, Ω, is the angle that an object subtends at a point. It is a measure of how big that object appears to an observer at that point. For instance, a small object nearby could subtend the same solid angle as a large object far away.
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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.
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Planck constant (denoted ) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory.
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speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".^[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
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The Boltzmann constant (k or k_B) is the physical constant relating temperature to energy.

It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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Area is the measure of how much exposed area any two dimensional object has. It is expressed in square units, and is calculated by adding together the areas of all the faces of the object.

Area formulas

Note: For 2D figures, the surface area and the area are the same.
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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 .
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Max Planck

Max Karl Ernst Ludwig Planck
Born March 23 1858
Kiel, Germany
Died September 4 1947 (aged 89)
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Rayleigh-Jeans Law, first proposed in the early 20th century, attempts to describe the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature.
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Lord Rayleigh

John William Strutt, 3rd Baron Rayleigh
Born 12 November 1842
Langford Grove, Maldon, Essex, UK
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Wien approximation (redirected from Wien's distribution law)

Relation to Planck's law

Other approximations of thermal radiation

References

Area formulas

Area formulas

Wien approximation
(redirected from Wien's distribution law)