Black-body radiation

Cavity under radiation refers to electromagnetic radiation within a sealed cavity is in thermal equilibrium.

Both the energy density as well as their spectral distribution are independent of the wall material and any other characteristics of the cavity at a given temperature. Because of this universality, the cavity radiation is of fundamental importance for theoretical investigations of the thermal radiation and as a reference source for thermal radiation measurements.

Universal properties

Consider an evacuated cavity with walls made ​​of any non-transparent material, which are kept at a constant temperature T. The walls give off heat radiation and it will, after sufficient time to adjust a thermal equilibrium state. The electromagnetic radiation that meets the cavity in the equilibrium state is called cavity radiation.

The energy density in the cavity is not dependent on the nature of the walls. To prove you connect two cavities, the walls of different radiation properties but have identical temperatures, through an opening with one another. A color filter in the opening let pass only radiation of frequency. Radiation through the opening between the cavities is changed. If the spectral energy density is higher at the frequency in a cavity, as more radiation would flow into the cavity as a lower energy vice versa, and the energy density, and therefore the temperature would increase in the second cavity. But this spontaneous emergence of a temperature difference would contradict the second law of thermodynamics. Therefore, the spectral energy density at all frequencies, and thus the total energy density in the two cavities must be identical.

Similarly, it can be shown that the radiation in the cavity homogeneous, isotropic, unpolarized and the volume of the cavity must be independent.

The spectral energy density in the cavity thus represents a dependent only on the frequency and temperature universal function is:

Similarly, universal must be because of the constant conversion factor and the spectral density of blackbody radiation:

Cavity radiation and black body

One of introduced into the cavity of non-transparent body does not change the properties of the cavity radiation, as this reduced the radiation properties of the newly added surface and the cavity volume is independent. The spectral radiation density of the body is exposed is equal to the spectral radiance of the radiation field, in which it is located. The body may absorb the radiation incident on it complete; such an idealized black body absorber means. So as to maintain the thermal equilibrium in the cavity radiation energy density, homogeneity and isotropy, the body must emit as much energy as it absorbs radiation from the cavity at every frequency and in any spatial angle. The spectral radiance of the black body, therefore, must be of a direction -independent and identical to the spectral radiance of the blackbody radiation.

This relationship has allowed Max Planck to derive from the properties of the cavity radiation, the spectral radiance of the black body. Both the cavity radiation and the radiation of the black body subject to the Planckian radiation law.

Kirchhoff's law of radiation

→ Main article: Kirchhoff's radiation law

If placed in the body cavity (e.g., an absorbent gas) does not absorb all of the incident radiation, it must emit less radiation to replace the absorbed radiation. It possesses the directional spectral absorption coefficient, that is, it may absorb at the temperature T and the frequency of the radiation which comes from the direction described by the polar angle and the azimuth angle, the fraction. The body must radiate as much energy as it absorbs from the cavity radiation in turn to maintain the thermal equilibrium at each frequency and angle in any room. Its spectral radiance is therefore

This is the Kirchhoff's law of radiation: any body temperature radiates at each frequency and in each element of solid angle as much radiation power as it is absorbed therein by the radiation of a black body. The radiation power at the frequency that is greater the greater is the absorption coefficient at that frequency. The maximum absorption coefficient has a black body, which therefore also the maximum thermal radiation power emits: no body temperature can emit more thermal radiation as a black body. The black body therefore has great importance as a universal reference for radiation- technical investigations.

Since the emission of any body can never be greater than that of a black body, the following applies:

Where the directional spectral emissivity of the body is (). Comparison with the preceding equation shows:

A good absorber is also a good emitter.

Note that with the radiation spectrum of a black body radiator is adjusted in the cavity, although the wall materials may be of any radiation properties. Has a wall, for example, only an emissivity of 0.7, it is absorbed in the thermal equilibrium constantly only 70 % of the incident cavity radiation and reflects the rest If, for example, after a disturbance, the spectral radiance of the cavity is less than the black body radiation in equilibrium corresponds, as it absorbed the portion of 70 % would be less than 70 % of ideal body radiation. The wall emits but still due to their temperature 70 % of the radiant power that would emit a black body. Since the wall more radiation emitted as absorbed, the energy density in the cavity rises, until it has reached the required value by the Planck's law of radiation. Thus, the cavity due to the Kirchhoff 's law also contains at any walls in balance just as much radiation as it would contain at blackbodies as walls.

In thermal equilibrium, the thermal radiation emitted from the walls still has the spectral characteristics of the wall material (for example, particularly strong emission at specific characteristic wavelengths, low emission at other ). However, the wall of the total outgoing radiation is the sum of the thermal emission and the reflected portion of the taken out of the cavity to the radiant wall. At the wavelengths in which the well wall itself emits it absorbs a large proportion of the incident radiation and reflects little; at the wavelengths in which the little wall itself emits it reflects to compensate a large fraction of the incident radiation. The spectral characteristics of the wall material are compensated in this way and the total emitted by emission and reflection radiation has independently because of Kirchhoff 's law of radiation from the wall material is a Planck's spectrum.

Measuring importance and realization

From a drilled hole in a cavity occurs cavity radiation which have the same intensity and the same spectrum as that of the thermal radiation of a black body of the same temperature. Since the production of a black body is difficult because the required over all frequencies as possible the ideal absorption coefficient, the radiation cavity but does not depend on the radiation properties of the wall materials, is generally used as a source for voids blackbody radiation.

Real cavities are never quite perfect ( for example, the walls may be partially transparent at certain frequencies ), but with careful construction, a good approximation of an ideal cavity can be achieved. In particular, the opening must be kept as small as possible in order not to disturb the thermal equilibrium in the cavity due to excessive radiation loss.

The opening must be small in order to allow to enter as little as possible interference radiation from the outside into the cavity and to prevent yet penetrated radiation from leaving the cavity as long as possible. The longer the extraneous radiation remains in the cavity, the more it is reflected at the cavity walls and the more it is absorbed. As an illustrative example of this will appear window openings in a wall dark, even when the room walls are brightly painted: the penetrated light is reflected in the space under jedesmaligem loss of intensity several times back and forth and can only partially escape out the window again. In practice, the support absorption by blackening of the cavity walls. If a significant portion of the penetrated radiation leaving the cavity again, he would distort the measured Planck spectrum. Contamination by short-wave radiation (light ) would be indeed avoided by darkening the laboratory, but the laboratory ubiquitous heat radiation can not be turned off.

Common materials are depending on the temperature requirements of copper, aluminum, stainless steel or a continuously stirred water.

Deviations of an actual cavity radiator from ideal behavior may be (for example, the influence of the opening diameter to the effective emissivity ) so that appropriate computational adjustments can be applied to the measurement results may collect by calibration measurements or by calculation.