Radiation from a black body

As shown in 5.1.6, the laws of thermodynamics demand that there must be an upper limit for the spectral intensity Lx(X,(3,(p,T) for all bodies. This maximum emission is associated with an ideal radiator, the black body. Its radiation properties shall be dealt with in the following. 

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The radiation from a black body is proportional to the fourth power of the adiabatic flame temperature, according to the Stefan-Boltzmann s law ... 

The quantum concept was introduced by Max Planck in 1900 to explain the distribution of energy radiated from a black body in thermal equilibrium with the surrounding. The idea that light travels as photons was originated by Einstein in 1905. 

Boltzmann s Law. The law of the equipartition of energy to a molecular system. Stef an-Boltzmann Law states that the total energy radiated from a black body is proportional to its absolute temp raised to the fourth power. It is expressed by E= a (T4 - T ) where E - total energy in ergs,... 

If hf, is the coefficient equivalent to radiation from a black body, hr = 0.95hb W/m2 K The outer diameter is 0.036 m and hence ... 

As a first approach, extraterrestrial solar radiation can be taken to be radiation from a black body at this temperature, see also section 5.3.5. 

Switzerland, yielded the spectrum reproduced in Fig. 5.40. The numerical values upon which this diagram is based can be found in M. Iqbal [5.34]. The maximum of EfAn lies in the visible light region at A pa 0.45 /tm. 99 % of the irradiance falls in the wavelength band A < 3.8 fim. Fig. 5.40 also shows the spectral irradiance EXa of the radiation emitted by a black sun at Ts = 5777 K. The areas under the two curves (up to A —> oo) are equal — they each yield the solar constant E0 —, but the spectrum of the extraterrestrial solar radiation deviates significantly at some points, in particular at A < 0.6//.in, from the spectrum of radiation from a black body. 

According to section 5.3.2.2, the hemispherical total absorptivity of a body with any radiative properties is equal to its hemispherical total emissivity, if radiation from a black body at the same temperature strikes the body. This is the case here. It therefore follows from (5.160) that A2F21 = A. This corresponds to the reciprocity rule (5.132) with F 2 = 1. Its application to this case was however not assured from the start as the intensity of body 1 is not constant. 

In 1900 Planck derived an empirical relationship for data from a black body radiation by introducing a concept of quantisation of energy he was able to prove the relationship theoretically. It had been shown that at a specific temperature the spectrum of radiation from a black body was unparalleled in its characteristics and the energy varied... 

The difference between the absorbed solar radiation and the net infrared radiation. Experimental data show that radiation from the earth s natural surfaces is rather close to the radiation from a black body at the corresponding temperature the ratio of the observed values of radiation to black body radiation is generally 0.90 -1.0. radiative-convective models... 

Joseph Stel (1835-1893), a Slovene-Austrian physicist, is best known for originating the law that the radiation from a black-body is proportional to the fourth power of temperature. In 1884, this law was theoretically derived by his student Ludwig Boltzmann and is known as the Stefan-Boltzmann law. Stefan s electromagnetic equations are also important, as his work on the kinetic theory of heat. He was among the first physicists who understood Maxwell s electromagnetic theory. 

Black body radiation The characteristic radiation from a black body surface at a specific temperatme. 

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