Radiative equilibrium

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Definition of radiative equilibrium

The discovery of the nature of radiation of heat was gradual.

Prevost's 1791 definition

An important early contribution was made by Pierre Prévost in 1791^[1]. Prévost considered that what is nowadays called the photon gas or electromagnetic radiation was a fluid that he called "free heat". The present writer's translation of Prevost's 1791 definition is as follows:

Absolute equilibrium of free heat is the state of this fluid in a portion of space which receives as much of it as it lets escape. Relative equilibrium of free heat is the state of this fluid in two portions of space which receive from each other equal quantities of heat, and which moreover are in absolute equilibrium, or experience precisely equal changes.

Prevost went on to comment that (present author's translation) "The heat of several portions of space at the same temperature, and next to one another, is at the same time in the two species of equilibrium." This comment needs very reserved interpretation.

Prévost's contribution was often referred to as Prévost's exchange principle.

Radiative equilibrium, defined as above, is one of the several requirements for thermodynamic equilibrium. Radiative equilibrium is a kind of dynamic equilibrium.

Schwarzschild's 1906 Confusing Concept of Predominant Equilibrium

K. Schwarzschild in 1906^[2] confused the terminology by his introduction of the concept of predominant equilibrium. He considered a system in which convection and radiation both operated but radiation was so much more efficient than convection that convection could be, as an approximation, neglected, and radiation could be considered predominant. Milne in 1930^[3] noted that this led to a "logically indefensible" definition, but still he accepted its use.

Current definition

Nowadays, a radiative field is often described in terms of specific radiative intensity, which is a function of each geometrical point in a space region, at an instant of time^[4][5]. This is slightly different from Prevost’s mode of definition, which was for regions of space. It is also slightly conceptually different from Prevost’s definition: Prevost thought in terms of bound and free heat while today we think in terms of heat in kinetic and other dynamic energy of molecules, that is to say heat in matter, and the thermal photon gas. A detailed definition is given by Goody and Yung (1989) ^[5]. They think of the interconversion between thermal radiation and heat in matter. From the specific radiative intensity they derive , the monochromatic vector flux density of radiation at each point in a region of space. They define the monochromatic volume-specific rate of gain of heat by matter from radiation as the negative of the divergence of the monochromatic flux density vector; it is a scalar function of the position of the point:

.

They define monochromatic radiative equilibrium by

at every point of the region that is in radiative equilibrium.

They define radiative equilibrium by

at every point of the region that is in radiative equilibrium.

This means that, at every point of the region of space that is in radiative equilibrium, the total, for all frequencies of radiation, interconversion of energy between thermal radiation and heat in matter is nil.

Mihalas and Weibel-Mihalas (1984)^[4] emphasise that this definition applies to a static medium, in which the matter is not moving. They also consider moving media.

References

1. ^ Prévost, P. (1791). Mémoire sur l'equilibre du feu. Journal de Physique (Paris), vol 38 pp. 314-322.
2. ^ Schwarzschild, K. (1906). Ueber das Gleichgewicht der Sonnenatmosphaere. Nachrichten von der Koeniglichen Gessellschaft der Wissenschaften zu Goettingen. Math.-phys. Klasse 195: 41-53. Translation in Selected Papers on the Transfer of Radiation, ed. D.H. Menzel, Dover, New York, 1966.
3. ^ Milne, E.A. (1930). Thermodynamics of the Stars. In Handbuch der Astrophysik, 3 (1): 63-255. Reprinted in Selected Papers on the Transfer of Radiation, ed. D.H. Menzel, Dover, New York, 1966.
4. ^ ^{a b} Mihalas, D., Weibel-Mihalas, B. (1984). Foundations of Radiation Hydrodynamics, Oxford University Press, New York, ISBN 0195034376.
5. ^ ^{a b} Goody, R.M., Yung, Y.L. (1989). Atmospheric Radiation. Theoretical Basis, second edition, Oxford University Press, New York, 1989, ISBN 0195051343.