Radiative equilibrium

Chemiluminescent processes occur in most combustion reactions, giving flames many of their characteristic colors. However, hot solid carbon particles in flames emit (usually yellow) thermal radiation in an equilibrium radiative process which therefore is not chemiluminescence,... 

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

The mechanism of radiative transfer in flares was found to depend on compn, flare diameter and pressure (Ref 69). The flare efficiency calcn is complicated by the drop-off in intensity at increasing altitudes and at very large diameters owing to the lower reaction temps (Ref 11, p 13) and the narrowing of the spectral emittance band (Ref 35). The prediction of the light output in terms of compn and pressure (ie, altitude) is now possible using a computer program which computes the equilibrium thermodynamic properties and the luminance (Ref 104) Flare Formulations... 

The greenhouse effect is a natural phenomenon whereby the earth s atmosphere is more transparent to solar radiation than terrestrial infixed radiation (emitted by the earth s surface and atmosphere). Consequently, the planet s mean surface temperature is about 33 K higher than the planet s radiative equilibrium temperature (the temperature at which the earth comes into equilibrium with the energy received from the sun). 

The concept of global radiative equilibrium is useful in identifying the various factors that govern climatic variability. At radiative equilibrium, the flux of solar radiation absorbed by the planet equals the flux of infrared radiation to space. That is. 

Hence, the radiative equilibrium temperature is sensitive to changes in the solar constant, planetary albedo, and the radiative properties of the earth-atmosphere-ocean system. In addition, changes internal to the earth-atmosphere-ocean system may alter the climate. Table I is an incomplete list of phenomena that individually or in concert could alter climate. 

Thus if one starts with one pure isomer of a substance, this isomer can undergo first-order transitions to other forms, and in turn these other forms can undergo transitions among themselves, and eventually an equilibrium mixture of different isomers will be generated. The transitions between atomic and molecular excited states and their ground states are also mostly first-order processes. This holds both for radiative decays, such as fluorescence and phosphorescence, and for nonradiative processes, such as internal conversions and intersystem crossings. We shall look at an example of this later in Chapter 9. 

Our multi-level carbon model atom is adapted from D. Kiselman (private communication), with improved atomic data and better sampling of some absorption lines. The statistical equilibrium code MULTI (Carlsson 1986), together with ID MARCS stellar model atmospheres for a grid of 168 late-type stars with varying Tefj, log g, [Fe/H] and [C/Fe], were used in all Cl non-LTE spectral line formation calculations, to solve radiative-transfer and rate equations and to find the non-LTE solution for the multi-level atom. We put particular attention in the study of the permitted Cl lines around 9100 A, used by Akerman et al. (2004). 

Minima in Ti are usually above the So hypersurface, but in some cases, below it (ground state triplet species). In the latter case, the photochemical process proper is over once relaxation into the minimum occurs, although under most conditions further ground-state chemistry is bound to follow, e.g., intermolecular reactions of triplet carbene. On the other hand, if the molecule ends up in a minimum in Ti which lies above So, radiative or non-radiative return to So occurs similarly as from a minimum in Si. However, both of these modes of return are slowed down considerably in the Ti ->-So process, because of its spin-forbidden nature, at least in molecules containing light atoms, and there will usually be time for vibrational motions to reach thermal equilibrium. One can therefore not expect funnels in the Ti surface, at least not in light-atom molecules. 

Some insight into the structure of stellar atmospheres can be obtained by considering the simple case of a plane parallel grey atmosphere (k+o independent of wavelength) in radiative equilibrium. 

Equation (3.19) gives a first approximation to the temperature structure of an atmosphere in radiative equilibrium, and departures from greyness can also be treated approximately by defining a suitable mean absorption coefficient (see Chapter 5). The emergent monochromatic intensity at an angle 9 to the normal (relevant to some point on the solar disk) is also found by integrating the equation of transfer (3.11) ... 

D. Mihalas, Stellar Atmospheres, W. H. Freeman Co., San Francisco, 1970, 1978. The first edition of this classic text deals with radiative and convective equilibrium and line formation in normal stellar atmospheres, while the second treats non-LTE effects in more detail. 

From radiative equilibrium, Eq. (5.23), and hydrostatic equilibrium with the ideal-gas equation of state Eq. (5.15),... 

A. S. Eddington develops theory of radiative equilibrium (building on earlier work by A. Schuster and K. Schwarzschild) and applies it to internal constitution of stars. He also pioneers physics of interstellar gas. 

W. H. McCrea develops models of atmospheres of A-type stars in radiative equilibrium with opacity due to H I. 

Anthropogenic addition to radiative forcing at stabilisation (W/m2) Stabilisation level for C02 only (ppm C02) Multi-gas concentration level (ppm C02-eq.) Global mean temperature °C increase above pre-industrial at equilibrium," using best estimate climate sensitivity of 3°C Peaking year for C02 emissions Change in C02 emissions in 2050 (% of 2000 emissions) ... 

Let N(j,Ni,N2, and Nj, be the equilibrium population densities of the states 0, 1,2, and 3, respectively (reached under continuous wave excitation intensity Iq), and let N = NQ + Ni+N2 + N3he the total density of optical absorbing centers. The up-converted luminescence intensity ho (corresponding to the transition 2 0) depends on both N2 and on the radiative emission probability of level 2, A2. This magnitude, which is dehned below, is proportional to the cross section a20 (called the emission cross section and equal to the absorption cross section ao2, as shown in Chapter 5). Thus we can write... 

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