Tutorial

A black body is a theoretical object absorbing all the electromagnetic energy it receives, which creates thermal agitation. At equilibrium, ie at constant temperature, all the energy absorbed is re-emitted in electromagnetic radiation also called thermal radiation. Indeed, the black body absorption coefficient as well as its emissivity are equal to "1". The emission depends then only on the temperature. A black body is a Lambertian source radiating therefore identically in all directions.

The emittance of a black body is given by the Stefan-Boltzman law:

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T is the temperature.

Its radiance is :

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The radiance is also calculated as follows :

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is the spectral radiance at T. It is given by the following formula :

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The spectral radiance as a function of the wavelength is shown for different temperature on the left curves.

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is maximum for a wavelength λ_M satisfying :

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Thus, λ_M decreases with temperature.

For "real" bodies, the spectral emissivity ε_λ is not equal to unity. It is calculated as follows, and being the spectral radiances respectively of the "real" body and of the black body at the same temperature :

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The total emissivity of the "real" body is :

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It is smaller than 1.

Grey bodies have a spectral emissivity ε which is not dependant on the wavelength. Therefore, their spectral radiance is:

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The wavelength for the maximum spectral radiance remains the same than for a black body at the same temperature :

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The radiance and emittance are :

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