Radiation hollow enclosure

This diagram shows the radiation emitted by black-bodies at specific temperature. A black-body is one that has a uniform temperature over all of its surface. One way to make a black-body is to form an hollow enclosure and to heat it to a given temperature. If a small hole is made in the side of the enclosure, radiation characteristic of the temperature will be emitted. 

In order to derive these we will consider an adiabatic evacuated enclosure, like that shown in Fig. 5.19, with walls of any material. In this enclosure a state of thermodynamic equilibrium will be reached The walls assume the same temperature T overall and the enclosure is filled with radiation, which is known as hollow enclosure radiation. In the sense of quantum mechanics this can also be interpreted as a photon gas in equilibrium. This equilibrium radiation is fully homogeneous, isotropic and non-polarised. It is of equal strength at every point in the hollow enclosure and is independent of direction it is determined purely by the temperature T of the walls. Due to its isotropic nature, the spectral intensity L x of the hollow enclosure radiation does not depend on / and universal function of wavelength and temperature L x = L x X,T), which is also called Kirchhoff s function. As the enclosure is filled with the same diffuse radiation, the incident spectral intensity Kx for every element of any area that is oriented in any position, will, according... 

According to this, the spectral intensity of the black body is independent of direction and is the same as the spectral intensity of hollow enclosure radiation at the same temperature ... 

Hollow enclosure radiation and radiation of a black body (a x = 1) have identical properties. The black body radiates diffusely from (5.18) it holds for its hemispherical spectral emissive power that... 

We will now consider an enclosure with a body that has any radiation properties, Fig. 5.21. Thermodynamic equilibrium means that this body must also emit exactly the same amount of energy in every solid angle element and in every wavelength interval as it absorbs from the hollow enclosure radiation. It therefore holds for the emitted radiative power that... 

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. 

Fig. 5.22 Isothermal hollow enclosure for the realisation of a black body. 1 insulation 2 heating 3 copper cylinder 4 reflected radiation 5 polished surface 6 black surface 7 incident beam 8 strongly absorbing surface...

Fig. 5.55 a Hollow enclosure bounded by black radiating edges, b Illustration of the energy balance for the zone i... 

The following balance equations are valid for this hollow enclosure with three black radiating zones ... 

If the bodies participating in radiative exchange cannot be assumed to be black bodies, then the reflected radiation flows also have to be considered. In hollow enclosures, multiple reflection combined with partial absorption of the incident radiation takes place. A general solution for radiative exchange problems without simplifying assumptions is only possible in exceptional cases. If the boundary walls of the hollow enclosure are divided into isothermal zones, like in 5.5.2, then a relatively simple solution is obtained, if these zones behave like grey Lambert radiators. Each zone is characterised purely by its hemispherical total emissivity si — whilst at = is valid for its absorptivity, and for the reflectivity... 

Fig. 5.57 Hollow enclosure bounded by isothermal surfaces (zones) each of which is a grey Lambert radiator...

The setup for ESR spectroscopy is a cross between NMR and micro-wave techniques (Section 5.8). The source is a frequency-stabilized klystron, whose frequency is measured as in microwave spectroscopy. The microwave radiation is transmitted down a waveguide to a resonant cavity (a hollow metal enclosure), which contains the sample. The cavity is between the poles of an electromagnet, whose field is varied until resonance is achieved. Absorption of microwave power at resonance is observed using the same kind of crystal detector as in microwave spectroscopy. Sensitivity is enhanced, as in microwave spectroscopy, by the use of modulation The magnetic field applied to the sample is modulated at, say, 100 kHz, thus producing a 100-kHz signal at the crystal when an absorption is reached. The spectrum is recorded on chart paper. 

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