Equilibrium radiation

Consider an enclosure of dimensions large compared with any wavelengths under consideration, which is opaque but otherwise arbitrary in shape and composition (Fig. 4.11). If the enclosure is maintained at a constant absolute temperature T, the equilibrium radiation field will be isotropic, homogeneous, and unpolarized (see Reif, 1965, p. 373 et seq. for a good discussion of equilibrium radiation in an enclosure). At any point the amount of radiant energy per unit frequency interval, confined to a unit solid angle about any direction, which crosses a unit area normal to this direction in unit time is given by the Planck function... 

Besides the equilibrium radiation considered in this article, the concentration limits can also be affected by chemiluminescence which arises if, in the combustion, chemical compounds form with a non-equilibrium energy distribution along the degrees of freedom of molecules or an atom. The chemiluminescence itself cannot lead to the appearance of a flame propagation limit if only one specific energy fraction is emitted. However, forced luminescence in an optical resonator (in combustion lasers) can lead to quenching of the flame. 

The processes of scattering and absorption of radiation in the atmosphere so significantly alter the spectral distribution that any similarity to extra terrestrial radiation is almost coincidental. Experiments with radiation between surfaces have shown that blackbody radiation theory can be extended successfully to many radiation heat transfer situations. In these situations the strict equilibrium requirements of the initial model have so far not proved to be necessary for practical designs. Most importantly the concept of temperature has proved useful in non-equilibrium radiation flux situations(3). 

When studying the limits of solar energy conversion, either by thermal or quantum processes, the sun has traditionally been treated as a blackbody (thermal equilibrium) radiator with surface temperature 5 800 K and distance 1.5 x 1011 m from Earth. A blackbody absorbs all incident radiation irrespective of its wavelength and direction of incidence and is represented classically by a hole in a cavity. 

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... 

For coherent states (9.86) of the radiation field, and also for a thermal-equilibrium radiation field one obtains the symmetric relations... 

If the emissivity of the radiative shield 2 is much lower than unity, the level of equilibrium radiation emitted by the detector must drop (suppression of spontaneous radiation) and thus its BLIP detectivity will increase. The ideal result would be obtained for an aperture of the hght pipe close to zero, but in that case diffractive effect completely change the behavior of the whole system. 

The average equilibrium radiation dose aquivalent rate per pCi I contained within the thyroid is calculated to be 0.57, 0.24, 0.08, and 0.061 mrem y for 1-, 4-, and 14-year olds, and adults, respectively. As the effective energy absorbed per disintegration (c) remains fairly constant with age (0.061 — 0.065 MeV par disintegration) (Soldat, 1976), the substantial decrease in dose equivalent per pCi with increasing age results almost entirely from the rapid increase in thyroid gland size. 

Dust radiates in the infrared. By Kirchhoff s law, solid material in thermal equilibrium radiates like a blackbody. Most of the incident energy falling on the grain is scattered, hence the blueness of reflection nebulae and the reddening of starlight. The absorbed photons are reradiated at a rate approximated by = where k, ... 

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

In this chapter, the foundations of equilibrium statistical mechanics are introduced and applied to ideal and weakly interacting systems. The coimection between statistical mechanics and thennodynamics is made by introducing ensemble methods. The role of mechanics, both quantum and classical, is described. In particular, the concept and use of the density of states is utilized. Applications are made to ideal quantum and classical gases, ideal gas of diatomic molecules, photons and the black body radiation, phonons in a hannonic solid, conduction electrons in metals and the Bose—Einstein condensation. Introductory aspects of the density... 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

The acronym LASER (Light Amplification via tire Stimulated Emission of Radiation) defines the process of amplification. For all intents and purjDoses tliis metliod was elegantly outlined by Einstein in 1917 [H] wherein he derived a treatment of the dynamic equilibrium of a material in a electromagnetic field absorbing and emitting photons. Key here is tire insight tliat, in addition to absorjDtion and spontaneous emission processes, in an excited system one can stimulate tire emission of a photon by interaction witli tire electromagnetic field. It is tliis stimulated emission process which lays tire conceptual foundation of tire laser. 

We can sample the energy density of radiation p(v, T) within a chamber at a fixed temperature T (essentially an oven or furnace) by opening a tiny transparent window in the chamber wall so as to let a little radiation out. The amount of radiation sampled must be very small so as not to disturb the equilibrium condition inside the chamber. When this is done at many different frequencies v, the blackbody spectrum is obtained. When the temperature is changed, the area under the spechal curve is greater or smaller and the curve is displaced on the frequency axis but its shape remains essentially the same. The chamber is called a blackbody because, from the point of view of an observer within the chamber, radiation lost through the aperture to the universe is perfectly absorbed the probability of a photon finding its way from the universe back through the aperture into the chamber is zero. 

J. W. Pyper and C. K. Briggs, The Ortho-Para Forms of Hydrogen, Deuterium and Tritium Radiation and Self-induced Conpersion Kinetics and Equilibrium, Eawrence Eipermore Eaboratoy Report UCRE-52278, 1977. 

Stratospheric ozone is in a dynamic equilibrium with a balance between the chemical processes of formation and destruchon. The primary components in this balance are ultraviolet (UV) solar radiation, oxygen molecules (O2), and oxygen atoms (O) and may be represented by the following reactions ... 

Fig. 6. Radiation damage in graphite showing the induced crystal dimensional strains. Impinging fast neutrons displace carbon atoms from their equilibrium lattice positions, producing an interstitial and vacancy. The coalescence of vacancies causes contraction in the a-direction, whereas interstitials may coalesce to form dislocation loops (essentially new graphite planes) causing c-direction expansion.

When a damp cloth is laid in an air flow, it settles after a certain time ic an equilibrium temperature, the so-called wet bulb temperature (0 ), which is determined through heat and mass transfer. Negotiating the heat flow obtained by radiation and conduction, the heat balance of the wet cloth in a stationary situation can be expressed as... 

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