Radiation equilibrium with matter

Optical Pyrometers. The optical pyrometer can be used for the determination of temperatures above 900 K, where blackbody radiation in the visible part of the spectrum is of sufficient intensity to be measured accurately. The blackbody emitted radiation intensity at a given wavelength A in equilibrium with matter at temperature Tis given by the Planck radiation law,... 

The generality of the Second Law gives us a powerful means to understand the thermodynamic aspects of real systems through the usage of ideal systems. A classic example is Planck s analysis of radiation in thermodynamic equilibrium with matter (blackbody radiation) in which Planck considered idealized simple... 

A simple thought experiment due to Einstein gives a basic idea of the interaction of electromagnetic radiation with matter. Consider a space surrounded on all sides by perfectly reflecting mirrors (Figure 2.9). Inside this cavity there is a hot material body which is in thermal equilibrium with the radiation which fills the cavity. This radiation is then isotropic, as it fills, in a random manner, all the space of the cavity its intensity can be defined as an energy per unit volume. 

Figure 2.9 In the thought-experiment of the basic interaction of radiation with matter, a material body at vanishing density is in thermal equilibrium with monochromatic electromagnetic radiation held within a perfectly reflecting enclosure...

However, we would like to point here not to the differences between the equilibrium tunneling mechanism and the above examples of mechanisms of the nonequilibrium type in low-temperature chemical conversions, but, on the contrary, to a simplifying assumption which relates them but which has to be rejected in a number of cases—and that is the subject matter of this chapter. In the above models the solid matrix itself was considered, in essence, from a special point of view, namely, as an ideal system, devoid of defects, which is in mechanical equilibrium. In other words, the fact that the systems in question are significantly out of equilibrium with respect to their mechanoenergetic state was ignored. This property of the experimentally studied samples was the result of both their preparation conditions and the ionizing radiation. 

This section deals with the fundamental nature of the interactions of high-energy radiations with matter, from the absorption of the radiations to the eventual establishment ofchemical equilibrium in the system. The process may bedivided into three stages which are illustrated in Fig. 1. 

Note that weak interaction processes remain out of equilibrium as long as neutrinos are not equilibrated with matter and radiation. This is the case as long as the density remains lower than about 1011 g/cm3. At higher densities, a state of so-called complete equilibrium is obtained. 

Having studied the material equihbrium of particles, it will be advantageous to turn attention briefly to the equilibrium of matter itself with the radiation which bathes it. 

Electromagnetic radiation which interacts with matter also reaches a state of thermal equilibrium with a definite temperature. This state of electromagnetic radiation is called thermal radiation, also called heat radiation in earlier literature. In fact, today we know that our universe is filled with thermal radiation at a temperature of about 2.8 K. 

At ordinary temperatures, this thermal particle density is extremely small. But quantum field theory has now revealed the thermod5mamic importance of the state p = 0. It is a state of thermal equilibrium that matter could reach indeed matter was in such a state during the early part of the universe. Had matter stayed in thermal equilibrium with radiation, at the current temperature of the universe the density of protons and electrons, given by (11.6.5) or its modifications, would be virtually zero. The existence of particles at their present temperatures has to be viewed as a nonequilibrium state. As a result of the particular way in which the universe has evolved, matter was not able to convert to radiation and stay in thermal equilibrium with it. 

As emphasized earlier, we live in a world that is not in thermodynamic equilihrium. The 2.8 K thermal radiation that fills the universe is not in thermal equilibrium with the matter in the galaxies. On a smaller scale, the earth, its atmosphere, biosphere and the oceans are all in a nonequilibrium state due to the constant influx of energy from the sun. In the laboratory, most of the time we encounter phenomena exhibited by systems not in thermodynamic equilibrium, while equilibrium systems are the exception. 

Much of the radiation with which we are familiar in everyday life is of thermal origin, arising by definition from matter in thermal equilibrium. In an ideal atomic gas in thermal equilibrium, for example, the upward versus downward transitions of bound electrons between energy levels in individual atoms are in close balance due to the exchange of energy between particles via collisions and the absorption and emission of radiation. The velocities of particles in an ideal thermal gas follow the well-known Maxwellian distribution, and the collective continuous spectrum of the radiating particles is described by the familiar Planck black-body radiation curve with its characteristic temperature-dependent profile and maximum. 

It should be noted that where the preparative method involves realtively low temperatures and the biimidazole (dimer) is substantially insoluble in the reaction medium as in the above Hayashi et al. procedure, the product precipitates as formed. Sometimes the crude product comprises mixtures of biimidazoles and may contain one or more biimidazoles that are relatively easily dissociated by heat, such as, for example, the 4,4 -isonier. Such thermal instability is, in general, more readily apparent in the liquid, e.g. in solution, than in the soiid. Ihus whereas the solid dimer may be essentially uncolored, i.e. undissociated at room and ordinary storage temperatures, it may become extensively colored, i.e. dissociated to imidazolyl radicals, almost immediately on being dissolved in an inert solvent such as benzene. As the radicals in solntion are in equilibrium with all possible dimeric structures, in time, in the absence of exciting light radiation, the radical color fades as the radicals dimerize to biimidazoles that are not thermally dissociable at that temperature in the particular solvent used. In other words, on equilibration, the system tends to produce biimidazoles that are thermodynamically stable at the temperatures employed. Thus no matter which of the above methods is used to oxidize a particular imidazole, substantially the same dimeric product is obtained on recrystallization under the same conditions. The l,2 -lsomer is such a product, obtained under the conditions described in Example 1. 

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... 

An unknown event disturbed the equilibrium of the interstellar cloud, and it collapsed. This process may have been caused by shock waves from a supernova explosion, or by a density wave of a spiral arm of the galaxy. The gas molecules and the particles were compressed, and with increasing compression, both temperature and pressure increased. It is possible that the centrifugal forces due to the rotation of the system prevented a spherical contraction. The result was a relatively flat, rotating disc of matter, in the centre of which was the primeval sun. Analogues of the early solar system, i.e., protoplanetary discs, have been identified from the radiation emitted by T Tauri stars (Koerner, 1997). 

We assume that the absorbing gas is of a uniform composition and in thermal equilibrium. The absorption coefficient, which is defined by Lambert s law, Eq. 3.1, is expressed in terms of the probabilities of transitions between the stationary states of the supermolecular system, in response to the incident radiation. Assuming the interaction of radiation and matter may be approximated by electric dipole interaction, i.e., assuming the wavelengths of the radiation are large compared with the dimensions of molecular complexes, the transition probability between the initial and... 

Consider a system in which matter and radiation are in equilibrium in a closed cavity at temperature T. (This equilibrium situation does not generally hold in spectroscopy, but the transition probabilities are fundamental properties of the interaction between radiation and matter and cannot be affected by the presence or absence of equilibrium.) As before, let be greater than (0). The probability of absorption from state n to state m is proportional to the number of photons with frequency near vmn the number of photons is proportional to the radiation density u(vmn). Hence the rate of absorption is given by Bn t,mNnu(i mn)t where Nn is the number of molecules in state n and Bn m is a proportionality constant called the Einstein coefficient for absorption. From the discussion following (3.46) and from (3.47), it follows that... 

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