Radiative between black bodies

Fig. 5.54 Radiation flows 12 and 21 in direct radiative exchange between black bodies 1 and 2...

Consider radiative exchange between a body of area A i and temperature Ti and black surroundings at To. The net interchange is given by... 

Fig. 5.8 Black body radiative transfer signals in Na located between parallel conducting plates for 29d —> 30p (left-hand side) and 28d —> 29p (right-hand side) as a function of the absorption frequency. The cutoff frequency is vc = 1/2d = 1.48 cm-1, where d is the plate separation. The increase in the transfer rate at v = vc (left-hand side) is due to the "switching on of the radiation polarized parallel to the plates (from ref. 24).

From the preceding discussions it is evident that at least four different temperatures have to be considered which under laboratory conditions are all equal the excitation temperature Tex of the molecule, defined by the relative populations of the levels, the kinetic temperature Tk, corresponding to the Maxwellian velocity distribution of the gas particles, the radiation temperature Traa, assuming a (in some cases diluted) black body radiation distribution, and the grain temperature 7, . With no thermodynamic equilibrium established, as is common in interstellar space, none of these temperatures are equal. These non-equilibium conditions are likely to be caused in part by the delicate balance between the various mechanisms of excitation and de-excitation of molecular energy levels by particle collisions and radiative transitions, and in part by the molecule formation process itself. Table 7 summarizes some of the known distribution anomalies. The non-equilibrium between para- and ortho-ammonia, the very low temperature of formaldehyde, and the interstellar OH and H20 masers are some of the more spectacular examples. 

Fig. 1.11 Radiative exchange between a body at temperature T and black surroundings at temperature...

As an introduction, a simple case of radiative exchange will be looked at. A radiator with area A, and at temperature T, is located in surroundings which are at temperature Ts, see Fig. 1.11. The medium between the two shall have no effect on the radiation transfer it shall be completely transparent for radiation, which is a very good approximation for atmospheric air. The surroundings shall behave like a black body, absorbing all radiation, as = 1. 

This is the law from G.R. Kirchhoff [5.5] Any body at a given temperature T emits, in every solid angle element and in every wavelength interval, the same radiative power as it absorbs there from the radiation of a black body (= hollow enclosure radiation) having the same temperature. Therefore, a close relationship exists between the emission and absorption capabilities. This can be more simply expressed using this sentence A good absorber of thermal radiation is also a good emitter. 

We will calculate first the direct radiative interchange between two black bodies of arbitrary shape with surfaces Ax and A2 and uniform temperatures 7 and T2, Fig. 5.54. In this case, all radiation flows emitted by one body that do not strike the other body will be ignored. The proportion of the radiation flow emitted by 1 and incident on 2 is given by... 

The net radiation flow transferred by direct radiative exchange between two black bodies is proportional to the difference of the fourth powers of their thermodynamic temperatures. 

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... 

The emissivity accounts for the properties of a radiating surface. An ideal radiator, or black body, has a value of e = 1. The rate of radiative heat transfer between two bodies is proportional to the difference between the fourth powers of their temperatures. In most commercial apparatus, not all the radiation from one body reaches the second. Radiation goes out in all directions, and only some of it reaches the intended receiver. The fraction that does is called the area factor or the view factor. Thus,... 

When considering the conditions of equilibrium between atomic particles and thermal radiation (black-body radiation), Einstein introduced another two elementary radiative processes whose rate depended on the radiation intensity. This was a... 

Fig. 2.3 Radiative processes of spontaneous emission and stimulated emission and absorption between quantum levels e) and i), which control the equilibrium (Boltzmann) population of levels due to radiative interaction with the equilibrium (Planck) distribution J(uj) of the photon energies of black-body radiation. Spontaneous emission happens in all directions, but stimulated emission occurs in the direction of the incident radiation.

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