Black Body

Category: Photometry In Physical, a black body indicates an ideal object whose electromagnetic Specter depends only on its Température. In practice, such a material object does not exist, but it represents a case idealized being used as reference for the physicists. As opposed to what its name suggests, a black body does not appear inevitably black. Indeed the “black” Adjectif means here that the object itself absorbs all the external light which would fall on him, and does not reflect any radiation either. Only radiation coming from the black body is thermal radiation, depending only on the temperature of the body. The name black body was introduced by the Physicien Gustav Kirchhoff in 1860. The model of the black body made it possible max Planck to discover the quantification of the electromagnetic interactions, which was one of the bases of the Quantum physics.

The model of the black body

The black body is an ideal object which would absorb all the electromagnetic energy that it receives, without reflecting some or transmitting some. It is not made any different Hypothèse on the nature of the object. The light being a electromagnetic Wave, it is absorbed completely and the object should thus appear black, from where its name.

The real object which approaches more this model is the interior of a furnace. In order to be able to study the radiation in this cavity, it is bored on one of its faces of a small hole letting escape a tiny fraction from the Rayonnement intern. It is besides a furnace which was used by Wien to determine the laws of electromagnetic emission according to the Température. The walls of the interior of the enclosure emit a radiation with all the wavelengths: theoretically waves radio with the x-rays. This emission is due to the agitation of the Atome S. Indeed, the temperature measures the agitation of the atoms (those “oscillate” around their position). By doing this, each atom behaves like a vibrating Dipôle (dipole formed by the core and the electronic cloud), which thus radiates energy.

By reflecting wall in wall, this radiation will be seen absorbed and re-emitted continuously on the internal walls of the furnace, until the object reaches thermal balance. The form of this spectrum (i.e. the distribution of the quantity of energy according to the Wavelength) is the signature of a purely thermal radiation, is thus called spectrum of the black body , and depends only on the Température of the furnace.

Perhaps paradoxically, the “continuous” spectrum (thus by neglecting the spectral lines) star S (or in any case for the large majority of too cold stars neither nor too heats) is a spectrum of black body. It is a good approximation of the temperature of surface of star. For the Sun for example, the temperature of surface east of approximately 5800 degrees. Let us note that an object seldom behaves like a black body, because it reflects part of electromagnetic energy and transmits some another part, it does not absorb all. In addition, the Atome S have also a clean emission mode of Photon S, the characteristic lines (this phenomenon is used for the chemical analysis in Spectrométrie of emission, Fluorescence and absorption); the color depends there on the chemical nature of the object.

Laws of the black body

Electromagnetic spectrum

The monochromatic energy exitance $M^o_ {\ lambda}$ for a Wavelength $\ lambda$ given is given by the Loi of Planck:

$M^o_ {\ lambda} = \ frac {2 \ pi H c^2} {\ lambda^5} \ cdot \ frac {1} {e^ {hc/\ lambda kT} - 1}$ with $M^o_ {\ lambda}$ in W.m^-2.sr^-1.m^-1

where C is the Speed of light in the vacuum, H is the Constante of Planck and K is the Boltzmann constant.

Law of Wien

The maximum of this spectrum is given by the Loi of Wien:

\ lambda_ {max} = \ frac {hc} {4,965 \ cdot kT} = \ frac {2,898 \ cdot 10^ {- 3}} {T}

with $\ lambda_ {max}$ in meters and T in Kelvin S. This last law expresses the fact that for a black body, the product of the Température and Wavelength of the peak of the curve are always equal to a constant. This very simple law thus makes it possible to know the temperature of a body compared to a black body by the only form of its spectrum and the position of its maximum.

Law of Stefan-Boltzmann

According to the Law of Stefan-Boltzmann, the density flux of energy or density of power or exitance energy $M^o (T)$ (out of W m^-2) emitted by the black body vary according to the absolute Température T (expressed in Kelvin) according to the formula:

M^o (T) = \ sigma T^4 \,

where σ is the Constante of Stefan-Boltzmann.

A body radiates more especially as it is hotter.

Small history

To the beginning of work on the black body, calculations of the total energy emitted gave a surprising result: the object emitted an infinite quantity of energy! As calculated energy grew at the time of the Intégration spectrum for the short wavelengths, one called that the “ultraviolet catastrophe”. The traditional Mécanique is taken there at fault and max Planck concluded from it that the model used to calculate total energy was erroneous; the model of Rayleigh and Jeans considered a continuous spectrum indeed.

In a report entitled On the theory of the law of energy distribution on a normal spectrum and presented the December 14th 1900, Planck exposes its deductions made on this problem and proposes then the assumption of the quanta: energy is not emitted in a continuous way, but by packages whose size E depends on the wavelength:

E=\frac{hc}{\lambda}

that was worth the to him Nobel Prize of physics in 1918. The discovery of this quantification of the energy exchanges was one of the bases of the Quantum physics; in particular, correlated with work of Hertz on the photoelectric Effect, that made it possible Einstein to invent the concept of Photon in 1905, which was worth its to him Nobel Prize of physics in 1921.

External bond

Page “Black Body” on the site of the Observatory of Paris;
a video explanatory on the laws of the black body.

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