Wien approximation
Wien's approximation (also sometimes called Wien's law or the Wien distribution law) is a law of
Details
Wien derived his law from thermodynamic arguments, several years before Planck introduced the quantization of radiation.[1]
Wien's original paper did not contain the Planck constant.
The law may be written as[5]
- is the amount of energy per unit surface area per unit time per unit solid angle per unit frequency emitted at a frequency ν, the so called spectral radiance,
- is the temperature of the black body,
- is the ratio of frequency over temperature,
- is the Planck constant,
- is the speed of light,
- is the Boltzmann constant.
This equation may also be written as[3][6]
The peak value of this curve, as determined by setting the derivative of the equation equal to zero and solving,[7] occurs at a wavelength
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 However, it was soon superseded by Planck's law, which accurately describes the full spectrum, derived by treating the radiation as a photon gas and accordingly applying Bose–Einstein in place of Maxwell–Boltzmann statistics. Planck's law may be given as[5]
The Wien approximation may be derived from Planck's law by assuming . When this is true, then[5]
Other approximations of thermal radiation
The
See also
- ASTM Subcommittee E20.02 on Radiation Thermometry
- Sakuma–Hattori equation
- Ultraviolet catastrophe
- Wien's displacement law
References
- ^ a b c d Wien, W. (1897). "On the division of energy in the emission-spectrum of a black body" (PDF). .
- ^
ISBN 978-0-387-90642-3.
- ^ a b c d
Bowley, R.; Sánchez, M. (1999). Introductory Statistical Mechanics (2nd ed.). ISBN 978-0-19-850576-1.
- ISBN 978-0-7918-4356-7.
- ^ ISBN 978-0-471-82759-7.
- ISBN 978-0-12-386944-9.
- ISBN 978-0-470-01306-9.