What is the perfect black body

Black body

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A Black body (also: Black body, Planckian radiator, ideal black body) is an idealized source of thermal radiation. The idealization is that such a body completely absorbs all incident electromagnetic radiation of any wavelength, while real bodies always reflect part of it. At the same time, it emits electromagnetic radiation as heat radiation, which, in terms of intensity and spectral distribution, is independent of the further nature of the body and its surface and only depends on its temperature.

The thermal radiation of the black body is stronger in every wavelength range than that of any real body of the same area and the same temperature. she will Blackbody radiation called, or also due to the realization of the black body through a cavity Cavity radiation. In the literature of the late 19th and early 20th centuries, the designation is black radiation to find.

The black body serves as a basis for theoretical considerations as well as a reference for practical investigations into electromagnetic radiation. The term "black body" was coined in 1860 by Gustav Robert Kirchhoff.

properties

Spectral distribution of the intensity of the black body radiation at different temperatures of the black body.
Spectral distribution of the intensity of black body radiation in a double-logarithmic plot

A black body completely absorbs incident electromagnetic radiation, including light. It does not let any radiation through and does not reflect or scatter anything. Except at the temperature of absolute zero, the black body sends one as thermal radiation or Black radiation designated electromagnetic radiation. The intensity and spectral distribution of the thermal radiation depend only on the temperature of the black body. In particular, its material properties have no influence, so it is the reference for numerous theoretical and practical purposes.

The ideal properties of the black body can only be approximated, e.g. B. in limited frequency ranges. According to Kirchhoff's law of radiation, the emissivity for thermal radiation for every real body at every wavelength and in every direction is proportional to its absorption capacity. Since the absorption capacity of the blackbody assumes the greatest possible value at every wavelength, its emissivity is also the greatest possible at all wavelengths. Any real body cannot emit more thermal radiation than a black body at any wavelength. It is the ideal source of thermal radiation.

The intensity and frequency distribution of the electromagnetic radiation emitted by a black body are described by the radiation law established by Max Planck. As the temperature rises, the maximum of the frequency distribution shifts to higher frequencies, i.e. to shorter wavelengths, in accordance with Wien's law of displacement. The Stefan-Boltzmann law describes that the total emitted energy is proportional to the fourth power of the absolute temperature of the black body.

A black body emits at a temperature of 300 K (this corresponds to a temperature of approx. 27 ° C) a radiant power of around 460 watts per square meter of surface. The eye is not sensitive to the wavelength range corresponding to this temperature and the black body appears dark. At a temperature of 5800 K (temperature of the sun's surface), a black body emits a radiation output of 64 MW / m². At this temperature, part of the radiation is in the visible spectral range, the body appears to be shining white to the eye. It is still called a black body because it absorbs all incident radiation.

The emissivity of the black body is independent of the direction of emission (Lambert radiator). It radiates evenly in all directions and emits completely diffuse radiation of the maximum possible strength.

Historical meaning

The attempt to describe blackbody radiation in theory contributed significantly to the birth of quantum physics. In a purely classical description, blackbody radiation diverges in the UV range (the so-called ultraviolet catastrophe). Only the assumption by Max Planck in 1900 that matter can only absorb and release radiation energy in the form of certain energy quanta was able to solve this riddle.

realization

A more ideal Black body cannot be realized. There are no known materials which completely absorb electromagnetic waves regardless of frequency. Even making a body that comes close to the ideal of the black body is difficult. A soot-covered surface has an absorption coefficient of approx. 0.96 in the visible spectral range - but not at other wavelengths. Many non-metallic substances have a high degree of absorption in the mid-infrared, but can appear white in the visible (e.g. wall paint).

As a rule, only the absorption and emission properties of the radiation source are of interest for practical applications, but not their shape. Instead of a surface, the opening of a cavity radiator or simply a long blind hole is used. This allows the ideal properties of a blackbody to be better represented, even if the inner surfaces have a low degree of absorption.

Cavity radiation

In a warm cavity with walls any Non-transparent material that is kept at a constant temperature, the walls give off heat radiation against each other and a radiation equilibrium is established. The electromagnetic radiation that fills the cavity is called cavity radiation. The energy density and the frequency distribution of the cavity radiation do not depend on the nature of the walls, but only on their temperature. In addition, the radiation is homogeneous, isotropic, unpolarized and independent of the volume of the cavity.

A body introduced into the cavity does not change the properties of the cavity radiation, since this is independent of the radiation properties of the newly added surface and of the reduced cavity volume. This applies in particular to a fictitious black body that has been introduced: it completely absorbs the radiation falling on it and reaches thermal equilibrium. The thermal balance of energy density, frequency distribution, homogeneity and isotropy of the cavity radiation is maintained. The black body emits just as much energy as its own emission at every frequency and in every direction as it absorbs from the cavity radiation. In particular, the cavity radiation and the emission of the black body have the same energy density and the same spectrum - they are equivalent.

Thus, a cavity used as a radiation source has the same radiation properties as a black body.

Cavity radiator

If an opening is made in the cavity wall that is small enough not to disturb the thermal equilibrium noticeably, the hole absorbs the incident radiation almost ideally, and only thermal radiation emerges through the opening.

The radiation emanating from the opening has the properties of a black body if the opening is small compared to the internal volume. The degree of reflection of the inner cavity surface can be significantly greater than zero. Radiation incident from the outside into the cavity is then reflected back and forth in the interior many times, mostly being absorbed and only a small remainder being re-emitted through reflections. Such openings appear practically completely black. To support the absorption, the cavity walls are made black and rough if possible. Black bodies used in practice are hollow spheres with an opening or hollow cylinders that are open on one side. Blind holes can be made in bodies for measuring purposes. Black heaters for high temperatures (e.g. up to 1800K) consist of ceramic materials on the inside. For the thermal determination of the radiation power of laser beams, absorption bodies in the form of hollow cones are often used. Absorbent coatings depend on the wavelength to be measured.

Color temperature

Basically there is an equilibrium temperature for all bodies, which is reached after a long time, as long as absorption and emission remain constant.

Color temperature according to Planck's law of radiation

The color temperature is a comparative value that describes the maximum intensity curve of a black body according to Planck's law of radiation and Wien's law of displacement. This intensity maximum shifts to shorter wavelengths with increasing temperature.

Incandescent lamps with a filament temperature of around 2700 to 2800 K, such as the classic incandescent lamp or the halogen lamps of 3100 to 3200 K, have their radiation maximum in the near infrared. The spectral component in the visible range gives a yellowish impression. The color impression of the radiation of a thermal radiator as well as a black radiator can be used to determine its temperature.

At around 5500 Kelvin, the maximum intensity is in the middle of the visible range and roughly corresponds to bright sunlight in a clear sky. If the temperature rises further, the intensity maximum is in the ultraviolet range and, at further increased temperatures, reaches the range of X-rays.

With increasing temperature, the maximum radiation intensity of a black body shifts to shorter wavelengths, the color impression changes from red to bluish-white. The color of a (heat) light source can be specified as the temperature of a comparable black body. This gives the color temperature of the light source. This also applies analogously to other self-emitters. The prerequisite is that their properties do not deviate too much from a gray body.

For the visible range, an approximation of Rayleigh and Jeans applies at high temperatures. The spectral radiance, that is the power per unit area and solid angle and per frequency interval, is proportional to the square of the frequency.

An increase in temperature over a certain range no longer influences the relative radiation distribution in the visible, the color impression remains "white". In the CIE standard color table, the "black body curve" ends at a point that is a very unsaturated violet-tinged hue. This point corresponds to the color temperature "infinite".

Emissivities

The radiation of the black body only depends on its temperature - at each frequency and at the temperature in question, the greatest physically possible thermal radiation output is emitted. The black body is therefore suitable as a radiation reference. The ratio of the radiation intensity emitted thermally from any surface and the radiation intensity from a black body is the emissivity of the surface. The emissivity is always between 0 and 1 and is usually dependent on the wavelength - unless it is a gray body. The black body itself always has emissivity 1 and can therefore be used to calibrate pyrometers.

A real body usually has different emissivities at different frequencies and possibly even in different radiation directions. For a complete characterization, the emissivity must be given as a function of the frequency and the beam angle.

A Lambert radiator is a body with a direction-independent emissivity, it radiates completely diffuse. A gray body is a body whose emissivity is the same at all frequencies. For both cases, the radiation calculations are simplified so that real bodies - as far as possible - are approximately viewed as diffuse radiators and gray bodies.

According to Kirchhoff's law of radiation, the directed spectral emissivity for every body is equal to the directed spectral absorption. For the other degrees of emission and absorption integrated via the directions and frequencies, equality only applies under additional conditions.

Applications

  • Black emitters are used as a radiation source or radiation standard for physical examinations (here mostly cavity emitters) and in interferometers (ceramic emitters for the mid-infrared).
  • Laser power meters often use cavity absorbers for the thermal or calorimetric determination of the laser beam power: such good absorbers not only increase the measurement accuracy, but also avoid dangerous scattered radiation. They are therefore also used as "radiation traps".
  • In kilns, temperatures can be determined very precisely with pyrometers directed through small viewing windows - the furnace chamber forms a black body radiator (cavity radiator). The surface of bodies can be provided with a pyrometer with a blind hole into which the pyrometer “looks” for temperature measurement independent of the emission level.
  • Many non-metallic materials have a high emissivity in the range from 0.85 to 0.95 for wavelengths that are greater than about 3… 5 μm. If the radiation behavior is to be determined at temperatures that are not too high (at room temperature the thermal radiation maximum is 10 μm and thus in the relevant wavelength range), they can often be regarded as gray bodies to a good approximation, and even black bodies if the accuracy requirements are lower. This is important, for example, for temperature measurement with low-temperature pyrometers or the radiation of heat from heating or cooling elements: non-metallic coatings (paint, anodizing - any color!) Increase the low emissivity of bare metals in the mid-infrared to almost one, allow precise pyrometric temperature measurement and improve heat radiation.
  • Soot is a good approximation of a blackbody in a certain wavelength range. However, depending on its consistency, it only achieves an absorption or emissivity of approx. 0.96. However, its emissivity is almost independent of the wavelength, so that it represents a gray body as a good approximation.
  • Human skin has a relatively constant emissivity between approx. 0.97 and 0.98 in the wavelength range between 2 and 14 μm,[1] at body temperature (emission maximum 9.4 μm) it radiates almost like a black body and absorbs practically all of the long-wave heat radiation from the environment (the absorption properties in the visible spectral range, on the other hand, behave significantly differently). The pyrometric fever measurement in the ear (measuring wavelength in the middle infrared) finds an almost ideal black cavity radiator.
  • Knowledge of the radiation behavior (color impression, intensity) of glowing metals was important for the processing and hardening of steel, especially at a time when pyrometric temperature measurement was not yet available.
  • The cosmic background radiation is a very good approximation of a black body radiation (more precisely: cavity radiation) with a temperature of 2.725 ± 0.002 Kelvin. Their detailed analysis is of interest to cosmology.
  • According to the Stefan-Boltzmann law, the total thermal radiation energy of a black body is proportional to the fourth power of its absolute temperature. This law is used by radiation thermometers to determine the temperature of a body if the emissivity is known. Usually only the radiation in a certain wavelength range is evaluated; then the emissivity in this area must be known.
  • The effective temperature of the sun is 5777 K.
    The temperature that a black body would have to have according to the Stefan-Boltzmann law in order to emit the same radiant power per unit area as a given radiator is called Effective temperature this spotlight. The less the radiator corresponds to a black body, the more it deviates from the actual temperature. The term “effective temperature” therefore only makes sense for radiators whose radiation properties are not too different from those of a black body, i.e. for stars and filaments. The term color temperature is used for fluorescent lamps, polar lights and other light sources with a pronounced line spectrum.
  • The solar radiation heats up the earth. The earth radiates the heat in the deep infrared range on average at 228K with an average output of 235 W / m².
  • In astronomy, stars are often approximated by black bodies, from which their effective surface temperature is determined. The difference between the frequency distribution according to the thermal emission and the real star spectrum provides information about the chemical composition and properties such as the star's magnetic field.

Color impression

The term “black” body can lead to the erroneous assumption that in general all are black looking Materials have a high degree of absorption or emissivity, even in the infrared wavelength range. However, the “black” in “black body” refers as a generalized term to the entire electromagnetic spectrum, not to a black impression in the range of light that is visible to humans. Specifically, this means:

  • Every (cold) black body actually appears black because it also absorbs all radiation in the visible wavelength range.
  • Not every black object is also a black body in the sense of the physical term, since it could absorb radiation well in the visible wavelength range, but poorly in the infrared. Materials that have this property are used, for example, to coat solar panels. Many black textiles also appear light in the near infrared.
  • A non-black object could nevertheless absorb and emit radiation well in the infrared wavelength range, for example white paint or window glass. Both substances have a high emissivity in the mid-infrared.

literature

  • Max Planck: About the law of energy distribution in the normal spectrum. In: Annals of Physics. Volume 309, No. 3, 1901, ISSN 0003-3804, pp. 553-563, doi: 10.1002 / andp.19013090310 (free PDF available on the publisher's website).

Web links

 Wikibooks: Planck's law of radiation formulas - Learning and teaching materials

Individual evidence

  1. ↑ B.F. Jones: A reappraisal of the use of infrared thermal image analysis in medicine. In: IEEE Transactions on Medical Imaging. Volume 17, No. 6, December 1998, pp. 1019-1027, doi: 10.1109 / 42.746635.