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In [[physics]], '''radiative equilibrium''' is the condition where a [[steady state]] system is in [[dynamic equilibrium]], with equal incoming and outgoing [[electromagnetic radiation|radiative]] [[heat flux]] and negligible heat transfer by [[conduction (heat)|conduction]] and [[convection]].<ref name=Modest2013>{{cite book|last=Modest|first=Michael F.|title=Radiative heat transfer|year=2013|publisher=Academic|location=Oxford|isbn=9780123869906|page=298|url=http://books.google.de/books?id=J2KZq0e4lCIC&pg=PA298|edition=3rd ed.}}</ref> In [[atmospheric physics]], under conditions of radiative equilibrium, total flux is constant with depth.<ref name=dePater2010>{{cite book|last=de Pater|first=Imke|title=Planetary sciences|year=2010|publisher=[[Cambridge University Press]]|location=New York|isbn=9780521853712|page=68|url=http://books.google.de/books?id=a_ijoTgDhnEC&pg=PA68|edition=2nd ed.|coauthors=Lissauer, Jack J.}}</ref> In [[astrophysics]], radiative equilibrium is used to determine atmospheric radiation of [[star]]s. In [[climate science]], the net change in the [[tropopause]] after temperatures readjust to radiative equilibrium in the [[stratosphere]], is used to determine the [[radiative forcing]], as part of an assessment of natural and anthropogenic climate change.<ref>{{Cite book | |||
|author=IPCC | |||
| title = Climate Change 2007: Working Group I: The Physical Science Basis | |||
| publisher = Cambridge University Press | |||
| year = 2007 | |||
| chapter = 2.2 Concept of Radiative Forcing | |||
| chapterurl = http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-2.html | |||
}}</ref> | |||
==Definitions== | |||
===History=== | |||
In 1791 [[Pierre Prevost]] showed that all bodies radiate heat and concluded, ''Radiation will exactly compensate absorption''. He used the terms absolute and relative equilibrium to describe changes.<ref name="Prevost 1791">[http://books.google.fr/books?id=7ZLOAAAAMAAJ&pg=PA314&lpg=PA314#v=onepage&q&f=false Prevost, P. (1791). Mémoire sur l'equilibre du feu. ''Journal de Physique'' (Paris), vol 38 pp. 314–322.]</ref> Prevost considered that what is nowadays called the [[photon gas]] or [[electromagnetic radiation]] was a fluid that he called "free heat" ({{lang-fr|le feu}}). Prevost proposed that free radiant heat is a very rare fluid, rays of which, like light rays, pass through each other without detectable disturbance of their passage. Prevost's called his theory ''movable equilibrium of heat'', now designated as the theory of exchanges, which stated that each body radiates to, and receives radiation from, other bodies. The radiation from each body is emitted regardless of the presence or absence of other bodies.<ref>{{cite book |last=Maxwell |first=J.C. | year=1871 |title=Theory of Heat| publisher=Longmans, Green and Co, London | pages = 221–222 |url=[http://archive.org/details/theoryofheat00maxwrich Abstract][http://ia700504.us.archive.org/6/items/theoryofheat00maxwrich/theoryofheat00maxwrich.pdf PDF]}}</ref><ref>{{cite book |last= |first= | year=1901 |title=The Laws of Radiation and Absorption: Memoirs by Prévost, Stewart, Kirchhoff, Bunsen| publisher=American Book Company |url=[http://archive.org/details/lawsradiationan00bunsgoog Abstract][http://archive.org/stream/lawsofradiationa00bracrich/lawsofradiationa00bracrich_djvu.txt Full Text]}}</ref><ref>Partington, J.R. (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co, London, p. 467.</ref> | |||
In 1906 [[Karl Schwarzschild]] postulated the radiative equilibrium (German: ''Strahlungsgleichgewicht'') dependent on [[Kirchhoff's law of thermal radiation]], when he studied the sun.<ref>Schwarzschild, K. (1906). Über das Gleichgewicht der Sonnenatmosphäre.[https://eudml.org/doc/58631 Download PDF]</ref> | |||
===Pointwise radiative equilibrium=== | |||
Following [[Max Planck|Planck]] (1914),<ref name="Planck 1914"/> 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.<ref name="Mihalas Mihalas 1984">[http://www.filestube.com/9c5b2744807c2c3d03e9/details.html Mihalas, D., Weibel-Mihalas, B. (1984). ''Foundations of Radiation Hydrodynamics'', Oxford University Press, New York, ISBN 0-19-503437-6.]</ref><ref name="Goody Yung 1989">Goody, R.M., Yung, Y.L. (1989). ''Atmospheric Radiation. Theoretical Basis'', second edition, Oxford University Press, New York, 1989, ISBN 0-19-505134-3.</ref> A detailed definition is given by Goody and Yung (1989).<ref name="Goody Yung 1989"/> They think of the interconversion between thermal radiation and heat in matter. From the specific radiative intensity they derive <math>\mathbf{F}_\nu</math>, the monochromatic vector flux density of radiation at each point in a region of space, which is equal to the time averaged monochromatic [[Poynting vector]] at that point (Mihalas 1978<ref name="Mihalas 1978">Mihalas, D. (1978). ''Stellar Atmospheres'', 2nd edition, Freeman, San Francisco, ISBN 0-7167-0359-9.</ref> on pages 9–11). 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: | |||
::: <math>h_\nu = - \nabla \cdot \mathbf{F}_\nu</math>. | |||
They define '''(pointwise) monochromatic radiative equilibrium''' by | |||
::: <math>\nabla \cdot \mathbf{F}_\nu = 0 </math> at every point of the region that is in radiative equilibrium. | |||
They define '''(pointwise) radiative equilibrium''' by | |||
:::<math>h = \int_0^{\infty} h_\nu d\nu = 0</math> 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 (pointwise) radiative equilibrium, the total, for all frequencies of radiation, interconversion of energy between thermal radiation and energy content in matter is nil. | |||
====Approximate pointwise radiative equilibrium==== | |||
[[Subrahmanyan Chandrasekhar|Chandrasekhar]] (1950, p. 290)<ref>Chandrasekhar, S. (1950). ''Radiative Transfer'', Oxford University Press, Oxford, 1950.</ref> writes of a model of a [[stellar atmosphere]] in which "there are no mechanisms, other than radiation, for transporting heat within the atmosphere ... [and] there are no sources of heat in the atmosphere." This is hardly different from Schwarzschild's 1906 approximate concept, but is more precisely stated. | |||
=== Exchange equilibrium between systems=== | |||
{{see also|Thermodynamic equilibrium #Relation of exchange equilibrium between systems}} | |||
Radiative exchange equilibrium occurs with thermodynamic systems. [[Max Planck|Planck]] (1914)<ref name="Planck 1914">Planck, M. (1914). ''The Theory of Heat Radiation'' p. 40</ref> refers to a condition of [[thermodynamic equilibrium]], in which "any two bodies or elements of bodies selected at random exchange by radiation equal amounts of heat with each other." | |||
The term '''radiative exchange equilibrium''' can also be used to refer to two specified regions of space that exchange equal amounts of radiation by emission and absorption (even when the steady state is not one of thermodynamic equilibrium, but is one in which some sub-processes include net transport of matter or energy including radiation). | |||
==Radiative equilibrium in astrophysics== | |||
Radiative equilibrium for a [[star]], is taken as a whole and not confining attention only to its atmosphere. And when the rate of heat transfer from nuclear reactions plus [[viscosity]] to the microscopic motions of the material particles of the star is ''balanced'' by the transfer of energy by electromagnetic radiation from the star to space. | |||
A star that is radiating energy to space cannot be in a steady state of temperature distribution unless there is a steady supply of energy from nuclear reactions within the star, to support the radiation to space.<ref name="Cox 1968">Cox, J.P. with Giuli, R.T. (1968, reprint 1984). ''Principles of Stellar Structure'', Gordon and Breach, New York, ISBN 0-677-01950-5, p. 134.</ref> | |||
[[Planetary equilibrium temperature]] is the theoretical temperature for a [[blackbody]], which does not consider a radiative atmosphere. | |||
==Radiative equilibrium in Earth sciences== | |||
{{see also|Earth's radiation balance}} | |||
'''Radiative equilibrium''' or '''radiative balance''' or just '''energy balance''', describe a [[steady state]] net change of [[infrared]] radiation from Earth and [[shortwave radiation]] from [[outer space]]. | |||
==See also== | |||
* [[Earth's energy budget]] | |||
* [[Earth's radiation balance]] | |||
* [[Non-equilibrium thermodynamics]] | |||
* [[Planetary equilibrium temperature]] | |||
* [[Thermal equilibrium]] | |||
* [[Thermodynamic equilibrium]] | |||
==References== | |||
<references/> | |||
[[Category:Thermodynamics]] | |||
Revision as of 19:37, 21 June 2013
In physics, radiative equilibrium is the condition where a steady state system is in dynamic equilibrium, with equal incoming and outgoing radiative heat flux and negligible heat transfer by conduction and convection.[1] In atmospheric physics, under conditions of radiative equilibrium, total flux is constant with depth.[2] In astrophysics, radiative equilibrium is used to determine atmospheric radiation of stars. In climate science, the net change in the tropopause after temperatures readjust to radiative equilibrium in the stratosphere, is used to determine the radiative forcing, as part of an assessment of natural and anthropogenic climate change.[3]
Definitions
History
In 1791 Pierre Prevost showed that all bodies radiate heat and concluded, Radiation will exactly compensate absorption. He used the terms absolute and relative equilibrium to describe changes.[4] Prevost considered that what is nowadays called the photon gas or electromagnetic radiation was a fluid that he called "free heat" (Template:Lang-fr). Prevost proposed that free radiant heat is a very rare fluid, rays of which, like light rays, pass through each other without detectable disturbance of their passage. Prevost's called his theory movable equilibrium of heat, now designated as the theory of exchanges, which stated that each body radiates to, and receives radiation from, other bodies. The radiation from each body is emitted regardless of the presence or absence of other bodies.[5][6][7]
In 1906 Karl Schwarzschild postulated the radiative equilibrium (German: Strahlungsgleichgewicht) dependent on Kirchhoff's law of thermal radiation, when he studied the sun.[8]
Pointwise radiative equilibrium
Following Planck (1914),[9] 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.[10][11] A detailed definition is given by Goody and Yung (1989).[11] 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, which is equal to the time averaged monochromatic Poynting vector at that point (Mihalas 1978[12] on pages 9–11). 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 (pointwise) monochromatic radiative equilibrium by
- at every point of the region that is in radiative equilibrium.
They define (pointwise) 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 (pointwise) radiative equilibrium, the total, for all frequencies of radiation, interconversion of energy between thermal radiation and energy content in matter is nil.
Approximate pointwise radiative equilibrium
Chandrasekhar (1950, p. 290)[13] writes of a model of a stellar atmosphere in which "there are no mechanisms, other than radiation, for transporting heat within the atmosphere ... [and] there are no sources of heat in the atmosphere." This is hardly different from Schwarzschild's 1906 approximate concept, but is more precisely stated.
Exchange equilibrium between systems
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Radiative exchange equilibrium occurs with thermodynamic systems. Planck (1914)[9] refers to a condition of thermodynamic equilibrium, in which "any two bodies or elements of bodies selected at random exchange by radiation equal amounts of heat with each other."
The term radiative exchange equilibrium can also be used to refer to two specified regions of space that exchange equal amounts of radiation by emission and absorption (even when the steady state is not one of thermodynamic equilibrium, but is one in which some sub-processes include net transport of matter or energy including radiation).
Radiative equilibrium in astrophysics
Radiative equilibrium for a star, is taken as a whole and not confining attention only to its atmosphere. And when the rate of heat transfer from nuclear reactions plus viscosity to the microscopic motions of the material particles of the star is balanced by the transfer of energy by electromagnetic radiation from the star to space.
A star that is radiating energy to space cannot be in a steady state of temperature distribution unless there is a steady supply of energy from nuclear reactions within the star, to support the radiation to space.[14]
Planetary equilibrium temperature is the theoretical temperature for a blackbody, which does not consider a radiative atmosphere.
Radiative equilibrium in Earth sciences
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Radiative equilibrium or radiative balance or just energy balance, describe a steady state net change of infrared radiation from Earth and shortwave radiation from outer space.
See also
- Earth's energy budget
- Earth's radiation balance
- Non-equilibrium thermodynamics
- Planetary equilibrium temperature
- Thermal equilibrium
- Thermodynamic equilibrium
References
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My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Prevost, P. (1791). Mémoire sur l'equilibre du feu. Journal de Physique (Paris), vol 38 pp. 314–322.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Partington, J.R. (1949). An Advanced Treatise on Physical Chemistry, volume 1, Fundamental Principles. The Properties of Gases, Longmans, Green and Co, London, p. 467.
- ↑ Schwarzschild, K. (1906). Über das Gleichgewicht der Sonnenatmosphäre.Download PDF
- ↑ 9.0 9.1 Planck, M. (1914). The Theory of Heat Radiation p. 40
- ↑ Mihalas, D., Weibel-Mihalas, B. (1984). Foundations of Radiation Hydrodynamics, Oxford University Press, New York, ISBN 0-19-503437-6.
- ↑ 11.0 11.1 Goody, R.M., Yung, Y.L. (1989). Atmospheric Radiation. Theoretical Basis, second edition, Oxford University Press, New York, 1989, ISBN 0-19-505134-3.
- ↑ Mihalas, D. (1978). Stellar Atmospheres, 2nd edition, Freeman, San Francisco, ISBN 0-7167-0359-9.
- ↑ Chandrasekhar, S. (1950). Radiative Transfer, Oxford University Press, Oxford, 1950.
- ↑ Cox, J.P. with Giuli, R.T. (1968, reprint 1984). Principles of Stellar Structure, Gordon and Breach, New York, ISBN 0-677-01950-5, p. 134.