black body


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Black-body radiation curves for different temperaturesclick for a larger image
Black-body radiation curves for different temperatures

black body

A body that absorbs all the radiation falling on it, i.e. a body that has no reflecting power. It is also a perfect emitter of radiation. The concept of a black body is a hypothetical ideal. The radiation from stars, and their effective and color temperatures, can however be described by assuming that they are black bodies.

Black-body radiation is the thermal radiation (see thermal emission) that would be emitted from a black body at a particular temperature. It has a continuous distribution of wavelengths. The graph of the energy, or intensity, of the radiation has a characteristic shape (see illustration) with a maximum value at a given wavelength, λmax. At lower temperatures the black-body radiation is mainly in the infrared region of the spectrum. As the temperature increases the maximum of the curve moves to shorter wavelengths. Curves at different temperatures follow the relationship

λmax T = 2.9 × 103

where the wavelength is measured in micrometers. This is known as the Wien displacement law. The radiation from a hot black body is greater at every wavelength than the radiation from a cooler black body. The total radiation flux thus increases rapidly with increasing temperature, as described by Stefan's law.

Stefan's law gives the total energy emitted over all wavelengths per second per unit area of a black body. The energy emitted at a particular wavelength by a black body can be predicted from Planck's radiation law. This law was derived by Max Planck from his quantum theory, propounded in 1900. If E (λ,T) is the energy emitted per unit wavelength interval at wavelength λ, per second, per unit area, into unit solid angle, by a body at thermodynamic temperature T , then

E (λ,T) = (2πhc 25)[ehc kT – 1]–1

h is the Planck constant, k the Boltzmann constant, and c the speed of light. Stefan's law and the Wien displacement law can both be derived from Planck's law.

Planck's radiation law describes only the continuous spectrum emitted by a black body. The continuous radiation from a star, as opposed to a black body, does not usually follow Planck's law exactly, although over a broad region of the spectrum the law is a good approximation.

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