- Wien approximation
Wien's approximation (also sometimes called "
Wien's law " or the "Wien distribution law") is a law ofphysics used to describe thespectrum of thermal radiation (frequently called theblackbody function). This law was first derived byWilhelm Wien in 1896.cite book
author=J. Mehra, H. Rechenberg
year=1982
title=The Historical Development of Quantum Theory
volume=1
chapter=1
publisher=Springer-Verlag
location=New York
id=ISBN 0-387-90642-8] cite book
author=R. Bowley, M. Sánchez
year=1999
title=Introductory Statistical Mechanics
edition=2nd edition
publisher=Clarendon Press
location=Oxford
id=ISBN 0-19-850576-0] The equation does accurately describe the shortwavelength (highfrequency ) spectrum of thermal emission from objects, but it fails to accurately fit the experimental data for longwavelengths (lowfrequency ) emission.The law may be written as
cite book
author=G. B. Rybicki, A. P. Lightman
year=1979
title=Radiative Processes in Astrophysics
publisher=John Wiley & Sons
location=New York
id=ISBN 0-471-82759-2]where
:* is the amount of
energy per unitsurface area per unittime per unitsolid angle per unitfrequency emitted at a frequency ν.:* is thetemperature of the black body.:* isPlanck's constant .:* is thespeed of light .:* isBoltzmann's constant .This equation may also be written as
Equation derived using u=4π/c; see Rybicki, Lightman (1979) reference.]
where is the amount of
energy per unitsurface area per unittime per unitsolid angle per unitwavelength 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 However, it was soon superseded by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 byMax Planck . Unlike the Wien approximation, Planck's law accurately describes the complete spectrum of thermal radiation. Planck's law may be given asThe Wien approximation may be derived from Planck's law by assuming . When this is true, then
and so Planck's law approximately equals the Wien approximation at high frequencies.
Other approximations of thermal radiation
The
Rayleigh-Jeans law developed byLord 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.References
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