Black-body radiation

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Revision as of 05:03, 18 September 2007 by imported>Niek Sanders (Minor clarifications.)
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Planck's blackbody equation describes the spectral exitance of an ideal blackbody.

where:

Symbol Units Description
Input wavelength
Input temperature
Planck's constant
Speed of light in vacuum
Boltzmann constant

Note that the input is in meters and that the output is a spectral irradiance in . Omitting the term from the numerator gives the blackbody emission in terms of radiance, with units where "sr" is steradians. There is a different formulation of the Planck equation in terms of frequency.

Taking the first derivative leads to the wavelength with maximum exitance. This is known as the Wien Displacement Law.

A closed form solution exists for the integral of the Planck blackbody equation over the entire spectrum. This is the Stefan-Boltzmann equation. In general, there is no known closed-form solution for the definite integral of the Planck blackbody equation; numerical integration techniques must be used.

The relationship between the ideal blackbody exitance and the actual exitance of a surface is given by emissivity.

Spectral Exitance for 300K Blackbody

An ideal blackbody at 300K (~30 Celsius) has a peak emission 9.66 microns. It has virtually no self-emission before 2.5 microns, hence self-emission is typically associated with the "thermal" regions of the EM spectrum. However, the Sun has a peak emission around 0.49 microns which is in the visible region of spectrum.