Black body

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Comparison between the irradiation of the solar phoosphere (yellow) and the theoretical emission curve of a black body (grey) to 5777 K, the estimated temperature for the solar phoosphere.

A black body is an ideal physical body that absorbs all incident radiant energy, regardless of frequency or angle of incidence. The name of "black body" It is given to it because it absorbs all the colors of the light that falls on its surface. This absorption results in thermal agitation which causes the emission of thermal radiation. This electromagnetic energy emitted by a black body is called black body radiation. The name black body was introduced by Gustav Kirchhoff in 1860.

Every body emits energy in the form of electromagnetic waves, even in a vacuum. However, the radiant energy emitted by a body at room temperature is low and corresponds to longer wavelengths than those of visible light (ie, lower frequency). By raising the temperature, not only does the energy emitted increase, but it does so at shorter wavelengths; This is why a body changes color when heated. Bodies do not emit with the same intensity at all frequencies or wavelengths, but rather they do so following Planck's law.

At the same temperature, the energy emitted also depends on the nature of the surface; Thus, a matte or black surface has a emitting power greater than a glossy surface. Thus, the energy emitted by an incandescent carbon filament is greater than that of a platinum filament at the same temperature. Kirchhoff's law establishes that a body that is a good emitter of energy is also a good absorber of said energy. Thus, black color bodies are good absorbers.

Classical and quantum blackbody models

The physical principles of classical mechanics and quantum mechanics lead to mutually exclusive predictions about black bodies or physical systems that approach them. The evidence that the classical model made predictions of the emission at small wavelengths in open contradiction with what was observed led Planck to develop a heuristic model that was the germ of quantum mechanics. The contradiction between classical predictions and empirical results at low wavelengths is known as the ultraviolet catastrophe.

Planck's law (quantum model)

${displaystyle I(nuT)={frac {2hnu ^{3}}{c^{2}}}{frac {1}{e^{frac {hnu }{kT}}-1}}}$

where ${displaystyle scriptstyle I(nuT){text{d}}nu ,}$ is the amount of energy per area unit, time unit and solid angle unit; $scriptstyle h$ is a constant that is known as Planck constant; $scriptstyle c$ is the speed of light; and $scriptstyle k$ It's Boltzmann's constant.

His name is emissive power of a body ${displaystyle scriptstyle E(nuT)}$ to the amount of radiant energy emitted by the surface unit and time:

${displaystyle E(nuT)=4pi I(nuT)={frac {8pi hnu ^{3}}{c^{2}}}{frac {1}{e^{frac {hnu }{kT}}-1}}}$

The wavelength at which the maximum emission occurs is given by Wien's displacement law; therefore, as the temperature increases, the brightness of a body adds smaller and smaller wavelengths, and it goes from red to white as it adds radiation from yellow to violet. The power emitted per unit area is given by the Stefan-Boltzmann law.

Rayleigh-Jeans Law (classical model)

Before Planck, the Rayleigh-Jeans Law modeled the behavior of the black body using the classical model. In this way, the model that defines the radiation of the black body at a specific wavelength:

${displaystyle B_{lambda }(T)={frac {2ckT}{lambda ^{4}}}}$

where c is the speed of light, k is Boltzmann's constant and T is the absolute temperature. This law predicts an infinite power output at very small wavelengths. This situation that is not corroborated experimentally is known as the ultraviolet catastrophe.

Physical approximations to a black body

The black body is a theoretical or ideal object, but it can be approximated in several ways, including an isolated cavity and other somewhat more complex systems.

Isolated cavity

It is possible to study objects in the laboratory with behavior very close to that of the black body. For this, the radiation coming from a small hole in an isolated chamber is studied. The camera absorbs very little energy from the outside, since it can only affect the small hole. However, the cavity radiates energy like a black body. The emitted light depends on the temperature inside the cavity, producing the emission spectrum of a black body. System works this way:

The light that enters through the hole falls on the farthest wall, where part of it is absorbed and part of it is reflected at a random angle and falls again on another part of the wall. In it, part of the light is again absorbed and another part reflected, and in each reflection a part of the light is absorbed by the walls of the cavity. After many reflections, all the incident energy has been absorbed.

Alloys and nanotubes

According to the Guinness Book of Records, the substance that least reflects light (in other words, the blackest substance) is a phosphor-nickel alloy, with chemical formula NiP. This substance was originally produced by Indian and American researchers in 1980, but perfected (made darker) by Anritsu (Japan) in 1990. This substance reflects only 0.16% of visible light; that is, 25 times less than conventional black paint.

In 2008 an article was published in the scientific journal Nanoletters with experimental results about a material created with carbon nanotubes that is the most absorbent material created by man, with a reflectance of 0.045 %, almost three times less than the mark achieved by Anritsu.

Real bodies and gray body approximation

Real objects never behave like ideal black bodies. Instead, the radiation emitted at a given frequency is a fraction of the ideal emission. The emissivity of a material specifies what fraction of blackbody radiation the real body is capable of emitting. The emissivity depends on the wavelength of the radiation, the surface temperature, surface finish (polished, oxidized, clean, dirty, new, weathered, etc.) and emission angle.

In some cases it is convenient to assume that there is a constant value of emissivity for all wavelengths, always less than 1 (which is the emissivity of a black body). This approximation is called the gray body approximation. Kirchhoff's Law indicates that in thermodynamic equilibrium, the emissivity is equal to the absorptivity, so that this object, which is not capable of absorbing all the incident radiation, also emits less energy than an ideal black body.

Astronomical applications

In astronomy, the emission from stars approximates that of a black body. The associated temperature is known as the Effective Temperature, a fundamental property for characterizing stellar emission.

The cosmic microwave background radiation from the Big Bang behaves almost like a black body. The small variations detected in this emission are called anisotropies and are very important to know the differences in mass that existed at the origin of the universe.

Hawking radiation is blackbody radiation emitted by black holes.

The emission of gas, cosmic dust, and protoplanetary disks is also associated with black bodies, mainly in the infrared and millimeter region of the electromagnetic spectrum. They are important tools for searching for planetary systems.

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