Black Body Radiation

Objects that absorb electromagnetic radiation well also emit radiation well. An object that absorbs all the radiation incident on it is called a black body. Such an object is also a perfect emitter of radiation; that is, no body at the same temperature emits more intensity per unit area.

In the figure above, the distribution of electromagnetic radiation emitted from a black body is shown as a function of wavelength for four different temperatures. One can see that objects at room temperature radiate in the infrared which is invisible to the eye but are easily detectable. As any object gets hotter, it radiates more strongly and its color changes. For example, as the element of an electric range heats up, it begins to take on a dull red color. As the temperature increases, the element glows brighter. This doesn't happen on your stove, but if the temperature would increase even more, the color would become white, and then as the peak moves into the ultraviolet, the color would turn blue.

The radiation emitted is not confined to a single wavelength but exists over a broad spectrum of wavelengths. As the temperature of the radiating body increases, the maximum of the distribution of wavelengths shifts toward shorter wavelengths. To explain this phenomenon in terms of classical physics, one approach is to assume the emitting body is a cavity with a small hole that emits radiation. One can then calculate the spectrum of radiation emitted in terms all of the standing waves possible inside the cavity. At long wavelengths, this method works. However, at short wavelengths, this model predicts that the amount of radiation increases strongly as the wavelength decreases. Experimentally one observes that the probability of emitting electromagnetic radiation goes to zero as the wavelength goes to zero. The divergence between the classical prediction and the experiment is often called the "ultraviolet catastrophe." It was a catastrophe for the classical physics of the 19th century.

As the temperature of the radiating body increases, the maximum of the distribution of wavelengths shifts toward shorter wavelengths, and intensity increases. The relation between the maximum of the wavelength distribution and temperature is called Wien's displacement law

$\lambda$maxT = 2.90·10-3 m·K.

It forms the basis of the optical pyrometer, a device which measures high temperatures, for example in a furnace, by observing their color. The intensity of radiation emitted from a black body is proportional to T4, with T in K, naturally.

 

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