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| {{about|any type of [[electromagnetic radiation]] from an object related to its temperature|infrared light|Infrared}}
| | Most folks have this habit of doing all the stuff by themselves, regardless of how important or simple they are! These folks won't allow others interfere in their affairs. While this stance will work in different regions of existence, it happens to be really not the best way to reply whenever you want to fix a Windows registry. There are some jobs including removing spywares, virus in addition to obsolete registry entries, which are best left to expert softwares. In this particular article I can tell we why it is important to fix Windows registry NOW!<br><br>You are able to reformat the computer to make it run quicker. This might reset the computer to when you first used it. Always remember to back up all files and programs before doing this because this can remove the files from the database. Remember before we do this you need all drivers and installation files plus this could be a last resort in the event you are trying to find slow computer tips.<br><br>Your PC could also have a fragmented hard drive or the windows registry might have been corrupted. It might additionally be due to the dust and dirt which should be cleaned. Whatever the problem, you are able to constantly find a solution. Here are certain tricks on how to make your PC run quicker.<br><br>The 1328 error is a widespread issue caused by your program being unable to properly process various updates for the program or Microsoft Office. If you have this error, it commonly means which a computer is either unable to read the actual update file or a computer has issues with the settings it's using to run. To fix this issue, we first require to change / fix any problems which the computer has with its update files, plus then repair any of the issues which the program might have.<br><br>The [http://bestregistrycleanerfix.com/regzooka regzooka] could come because standard with a back up plus restore center. This ought to be an easy to apply process.That signifies that should you encounter a issue with your PC following using a registry cleaning you are able to just restore the settings.<br><br>If you think that there are issues with all the d3d9.dll file, then we have to substitute it with a brand-new functioning file. This is completed by performing a series of procedures and we can begin by obtaining "d3d9.zip" within the host. Next you must unzip the "d3d9.dll" file found on the hard drive of the computer. Proceed by locating "C:\Windows\System32" and then finding the existing "d3d9.dll" on the PC. When found, rename the file "d3d9.dll to d3d9BACKUP.dll" plus then copy-paste this new file to "C:\Windows\System32". After which, hit "Start" followed by "Run" or search "Run" on Windows Vista & 7. As soon as a box shows up, kind "cmd". A black screen will then appear and you must type "regsvr32d3d9.dll" plus then click "Enter". This procedure may help we to substitute the aged file with the fresh copy.<br><br>Maybe we are asking how come these windows XP error messages appear. Well, for you to be able to recognize the fix, you must first recognize where those errors come from. There is this software called registry. A registry is software which stores everything on the PC from a normal configuration, setting, info, plus logs of activities from installing to UN-installing, saving to deleting, along with a lot more alterations we do inside the program pass by it plus gets 'tagged' and saved because a easy file for recovery reasons. Imagine it because a big recorder, a registrar, of all a records in a PC.<br><br>So in summary, when comparing registry cleaning, make sure the one we choose gives you the following.A backup and restore center, swiftly surgery, automatic deletion center, start-up management, an easy method of contact along with a income back guarantee. |
| {{See also |Black body radiation|Planck's law}}
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| {{More footnotes|date=October 2007}}
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| [[Image:Wiens law.svg|300px|thumb|right|This diagram shows how the peak wavelength and total radiated amount vary with temperature according to [[Wien's displacement law]]. Although this plot shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero. Visible light is between 380 and 750 nm.]]
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| [[Image:Hot metalwork.jpg|250px|thumb|right|Thermal radiation in visible light can be seen on this hot metalwork. Its emission in the [[infrared]] is invisible to the human eye and the camera the image was taken with, but an [[infrared camera]] could show it (See [[Thermography]]).]]
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| '''Thermal radiation''' is [[electromagnetic radiation]] generated by the [[thermal motion]] of [[charged particles]] in [[matter]]. All matter with a [[temperature]] greater than [[absolute zero]] emits thermal radiation. When the temperature of the body is greater than absolute zero, interatomic collisions cause the [[kinetic energy]] of the atoms or molecules to change. This results in charge-acceleration and/or dipole oscillation which produces [[electromagnetic radiation]], and the wide spectrum of radiation reflects the wide spectrum of energies and accelerations that occur even at a single temperature.
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| Examples of thermal radiation include the [[visible light]] and [[infrared light]] emitted by an [[incandescent light bulb]], the [[infrared]] radiation emitted by animals and detectable with an [[infrared camera]], and the [[cosmic microwave background radiation]]. Thermal radiation is different from [[thermal convection]] and [[thermal conduction]]—a person near a raging bonfire feels [[radiant heating]] from the fire, even if the surrounding air is very cold.
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| [[Sunlight]] is part of thermal radiation generated by the hot [[Plasma (physics)|plasma]] of the [[Sun]]. The [[Earth]] also emits thermal radiation, but at a much lower [[intensity (physics)|intensity]] and different [[Electromagnetic spectrum|spectral distribution]] (infrared rather than [[visible light|visible]]) because it is cooler. The Earth's absorption of solar radiation, followed by its outgoing thermal radiation are the two most important processes that determine the temperature and climate of the Earth.
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| If a radiation-emitting object meets the physical characteristics of a [[black body]] in [[thermodynamic equilibrium]], the radiation is called blackbody radiation.<ref>K. Huang, ''Statistical Mechanics'' (2003), p.278</ref> [[Planck's law]] describes the spectrum of blackbody radiation, which depends only on the object's temperature. [[Wien's displacement law]] determines the most likely frequency of the emitted radiation, and the [[Stefan–Boltzmann law]] gives the radiant intensity.<ref>K. Huang, ''Statistical Mechanics'' (2003), p.280</ref>
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| Thermal radiation is one of the fundamental mechanisms of [[heat transfer]].
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| ==Overview==
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| Thermal radiation is the emission of [[electromagnetic waves]] from all matter that has a [[temperature]] greater than [[absolute zero]].<ref name=blundell>{{cite book
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| |author=S. Blundell, K. Blundell
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| |title=Concepts in Modern Physics
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| |isbn=978-0-19-856769-1
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| |year=2006
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| |publisher=Oxford University Press
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| |page=247
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| }}</ref> It represents a conversion of [[thermal energy]] into [[electromagnetic energy]]. Thermal energy results in kinetic energy in the random movements of atoms and molecules in matter. All matter with a temperature by definition is composed of particles which have kinetic energy, and which interact with each other. These atoms and molecules are composed of charged particles, i.e., [[proton]]s and [[electron]]s, and kinetic interactions among matter particles result in charge-acceleration and dipole-oscillation. This results in the electrodynamic generation of coupled electric and magnetic fields, resulting in the emission of [[photon]]s, radiating energy away from the body through its surface boundary. Electromagnetic radiation, including light, does not require the presence of matter to propagate and travels in the [[vacuum]] of space infinitely far if unobstructed.
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| The characteristics of thermal radiation depend on various properties of the surface it is emanating from, including its temperature, its spectral [[Absorbance|absorptivity]] and spectral emissive power, as expressed by [[Kirchhoff's law of thermal radiation|Kirchhoff's law]].<ref name=blundell/> The radiation is not monochromatic, i.e., it does not consist of just a single frequency, but comprises a continuous dispersion of photon energies, its characteristic spectrum. If the radiating body and its surface are in [[thermodynamic equilibrium]] and the surface has perfect absorptivity at all wavelengths, it is characterized as a [[black body]]. A black body is also a perfect emitter. The radiation of such perfect emitters is called [[black-body radiation]]. The ratio of any body's emission relative to that of a black body is the body's [[emissivity]], so that a black body has an emissivity of unity.
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| Absorptivity, [[reflectivity]], and emissivity of all bodies are dependent on the wavelength of the radiation. The temperature determines the wavelength distribution of the electromagnetic radiation. For example, fresh snow, which is highly reflective to visible light (reflectivity about 0.90), appears white due to reflecting sunlight with a peak wavelength of about 0.5 micrometers. Its emissivity, however, at a temperature of about -5 °C, peak wavelength of about 12 micrometers, is 0.99.
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| The distribution of power that a black body emits with varying frequency is described by [[Planck's law]]. At any given temperature, there is a frequency ''f<sub>max</sub>'' at which the power emitted is a maximum. Wien's displacement law, and the fact that the frequency of light is inversely proportional to its wavelength in vacuum, mean that the peak frequency ''f<sub>max</sub>'' is proportional to the absolute temperature ''T'' of the black body. The photosphere of the sun, at a temperature of approximately 6000 K, emits radiation principally in the (humanly) visible portion of the electromagnetic spectrum. Earth's atmosphere is partly transparent to visible light, and the light reaching the surface is absorbed or reflected. Earth's surface emits the absorbed radiation, approximating the behavior of a black body at 300 K with spectral peak at ''f<sub>max</sub>''. At these lower frequencies, the atmosphere is largely opaque and radiation from Earth's surface is absorbed or scattered by the atmosphere. Though some radiation escapes into space, most is absorbed and subsequently re-emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary [[greenhouse effect]], contributing to [[global warming]] and [[climate change]] in general (but also critically contributing to climate stability when the composition and properties of the atmosphere are not changing).
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| The common household [[incandescent light bulb]] has a spectrum overlapping the black body spectra of the sun and the earth. Some of the photons emitted by a tungsten light bulb filament at [[color temperature|3000 K]] are in the visible spectrum. However, most of the energy is associated with photons of longer wavelengths; these do not help a person see, but still transfer heat to the environment, as can be deduced empirically by observing a household incandescent light bulb. Whenever EM radiation is emitted and then absorbed, heat is transferred. This principle is used in [[microwave oven]]s, [[laser cutting]], and [[Electrolysis (cosmetology)|RF hair removal]].
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| Unlike conductive and convective forms of heat transfer, thermal radiation can be concentrated in a tiny spot by using reflecting mirrors. [[Concentrating solar power]] takes advantage of this fact. In many such systems, mirrors are employed to concentrate sunlight into a smaller area. In lieu of mirrors, [[Fresnel lens#Generating solar power|Fresnel lenses]] can also be used to concentrate heat flux. (In principle, any kind of lens can be used, but only the Fresnel lens design is practical for very large lenses.) Either method can be used to quickly vaporize water into steam using sunlight. For example, the sunlight reflected from mirrors heats the [[PS10 Solar Power Plant]], and during the day it can heat water to 285 °C (558.15 K) or 545 °F.
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| ===Surface effects===
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| Lighter colors and also whites and metallic substances absorb less illuminating light, and thus heat up less; but otherwise color makes small difference as regards heat transfer between an object at everyday temperatures and its surroundings, since the dominant emitted wavelengths are nowhere near the visible spectrum, but rather in the far infrared. Emissivities at those wavelengths have little to do with visual emissivities (visible colors); in the far infra-red, most objects have high emissivities. Thus, except in sunlight, the color of clothing makes little difference as regards warmth; likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit.
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| The main exception to this is shiny metal surfaces, which have low emissivities both in the visible wavelengths and in the far infrared. Such surfaces can be used to reduce heat transfer in both directions; an example of this is the [[multi-layer insulation]] used to insulate spacecraft.
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| [[Low-emissivity]] windows in houses are a more complicated technology, since they must have low emissivity at thermal wavelengths while remaining transparent to visible light.
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| ==Properties==
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| There are four main properties that characterize thermal radiation (in the limit of the far field):
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| *Thermal radiation emitted by a body at any temperature consists of a wide range of frequencies. The frequency distribution is given by [[Planck's law of black-body radiation]] for an idealized emitter as shown in the diagram at top.
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| *The dominant frequency (or color) range of the emitted radiation shifts to higher frequencies as the temperature of the emitter increases. For example, a ''red hot'' object radiates mainly in the long wavelengths (red and orange) of the visible band. If it is heated further, it also begins to emit discernible amounts of green and blue light, and the spread of frequencies in the entire visible range cause it to appear white to the human eye; it is ''white hot''. However, even at a white-hot temperature of 2000 K, 99% of the energy of the radiation is still in the infrared. This is determined by [[Wien's displacement law]]. In the diagram the peak value for each curve moves to the left as the temperature increases.
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| *The total amount of radiation of all frequencies increases steeply as the temperature rises; it grows as ''T''<sup>4</sup>, where ''T'' is the absolute temperature of the body. An object at the temperature of a kitchen oven, about twice the room temperature on the absolute temperature scale (600 K vs. 300 K) radiates 16 times as much power per unit area. An object at the temperature of the filament in an [[incandescent light bulb]]—roughly 3000 K, or 10 times room temperature—radiates 10,000 times as much energy per unit area. The total radiative intensity of a black body rises as the fourth power of the absolute temperature, as expressed by the [[Stefan–Boltzmann law]]. In the plot, the area under each curve grows rapidly as the temperature increases.
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| *The rate of electromagnetic radiation emitted at a given frequency is proportional to the amount of absorption that it would experience by the source. Thus, a surface that absorbs more red light thermally radiates more red light. This principle applies to all properties of the wave, including [[wavelength]] (color), direction, [[Polarization (waves)|polarization]], and even [[Coherence (physics)|coherence]], so that it is quite possible to have thermal radiation which is polarized, coherent, and directional, though polarized and coherent forms are fairly rare in nature far from sources (in terms of wavelength). See section below for more on this qualification.
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| ===Near-field and far-field===
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| The general properties above apply if the distances considered are much larger than the wavelengths contributing to the spectrum (most significant from 8-25 micrometres at 300 K). Indeed, thermal radiation as discussed above takes only radiating waves (far-field, or [[electromagnetic radiation]]) into account. A more sophisticated framework involving electromagnetic theory must be used for smaller distances from the thermal source or surface ([[near-field thermal radiation]]). For example, although [[near and far field|far-field]] thermal radiation at distances from surfaces of more than one wavelength is generally not coherent to any extent, near-field thermal radiation (i.e., radiation at distances of a fraction of various radiation wavelengths) may exhibit a degree of both temporal and spatial coherence.<ref>[http://www.tandfonline.com/doi/abs/10.1080/00107510701690380#preview] Review of coherrent thermal radiation</ref>
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| ===Subjective color to the eye of a black body thermal radiator===
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| {| class="wikitable"
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| |-
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| ! °C (°F)
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| ! Subjective color<ref>[http://web.archive.org/web/20110721181740/http://cc.oulu.fi/~kempmp/colours.html The Physics of Coloured Fireworks<!-- Bot generated title -->]</ref>
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| |-
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| | {{convert|480|C}} || faint red glow
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| |-
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| | {{convert|580|C}} || dark red
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| |-
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| | {{convert|730|C}} || bright red, slightly orange
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| |-
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| | {{convert|930|C}} || bright orange
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| |-
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| | {{convert|1100|C}} || pale yellowish orange
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| |-
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| | {{convert|1300|C}} || yellowish white
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| |-
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| | > {{convert|1400|C}} || white (yellowish if seen from a distance through atmosphere)
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| |}
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| ===Selected radiant heat fluxes===
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| (1 W/cm<sup>2</sup> = 10 kW/m<sup>2</sup>)
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| {| class="wikitable"
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| ! kW/m<sup>2</sup> !! Effect
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| | 170 || Maximum flux measured in a post-[[flashover]] compartment
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| |-
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| | 80 || Thermal Protective Performance test for [[personal protective equipment]]
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| |-
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| | 52 || [[Fiberboard]] ignites at 5 seconds
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| |-
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| | 29 || [[Wood]] ignites, given time
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| | 20 || Typical beginning of [[flashover]] at floor level of a residential room
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| |-
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| | 16 || [[Human skin]]: Sudden pain and second-degree [[burn]] [[blister]]s after 5 seconds
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| |-
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| | 12.5 || [[Wood]] produces ignitable volatiles by [[pyrolysis]]
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| |-
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| | 10.4 || Human skin: Pain after 30 seconds, second-degree burn blisters after 9 seconds
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| |-
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| | 6.4 || Human skin: Second-degree burn blisters after 18 seconds
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| |-
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| | 4.5 || Human skin: Second-degree burn blisters after 30 seconds
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| |-
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| | 2.5 || Human skin: Burns after prolonged exposure, radiant flux exposure typically encountered during [[firefighting]]
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| |-
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| | 1.4 || [[Sunlight]], [[sunburn]]s potentially within 30 minutes
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| |}<ref>John J. Lentini - Scientific Protocols for Fire Investigation, CRC 2006, ISBN 0849320828, table from NFPA 921, Guide for Fire and Explosion Investigations</ref>
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| ==Interchange of energy==
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| [[Image:Radiant heat panel nrc ottawa.jpg|thumb|right|300px|Radiant heat panel for testing precisely quantified energy exposures at [[National Research Council (Canada)|National Research Council]], near [[Ottawa]], [[Ontario]], [[Canada]].]]
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| Thermal radiation is one of the principal mechanisms of [[heat transfer]]. It entails the emission of a spectrum of electromagnetic radiation due to an object's temperature. Other mechanisms are [[convection]] and [[Heat conduction|conduction]]. The interplay of energy exchange by thermal radiation is characterized by the following equation:
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| :<math>\alpha+\rho+\tau=1. \,</math>
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| Here, <math>\alpha \,</math> represents the spectral absorption component, <math>\rho \,</math> spectral reflection component and <math>\tau \,</math> the spectral transmission component. These elements are a function of the wavelength (<math>\lambda\,</math>) of the electromagnetic radiation. The spectral absorption is equal to the [[emissivity]] <math>\epsilon \,</math>; this relation is known as [[Kirchhoff's law of thermal radiation]]. An object is called a black body if, for all frequencies, the following formula applies:
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| :<math>\alpha = \epsilon =1.\,</math>
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| In a practical situation and room-temperature setting, humans lose considerable energy due to thermal radiation. However, the energy lost by emitting [[infrared]] light is partially regained by absorbing the heat flow due to conduction from surrounding objects, and the remainder resulting from generated heat through metabolism. Human skin has an emissivity of very close to 1.0 .<ref>{{cite journal |journal=Science |date=24 May 1963 |volume= 140 |issue= 3569 |pages= 870–877 |title= Thermography of the Human Body Infrared-radiant energy provides new concepts and instrumentation for medical diagnosis |author=R. Bowling Barnes |doi=10.1126/science.140.3569.870 |bibcode = 1963Sci...140..870B |pmid=13969373 }}</ref> Using the formulas below shows a human, having roughly {{nowrap|2 square meter}} in surface area, and a temperature of about 307 [[kelvin|K]], continuously radiates approximately {{nowrap|1000 watts.}} However, if people are indoors, surrounded by surfaces at {{nowrap|296 K,}} they receive back about {{nowrap|900 watts}} from the wall, ceiling, and other surroundings, so the net loss is only about {{nowrap|100 watts.}} These heat transfer estimates are highly dependent on extrinsic variables, such as wearing clothes, i.e. decreasing total thermal circuit conductivity, therefore reducing total output heat flux. Only truly ''gray'' systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in ''all'' control volume bodies considered) can achieve reasonable steady-state heat flux estimates through the Stefan-Boltzmann law. Encountering this "ideally calculable" situation is virtually impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "gray" approximations will get you ''close'' to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most [[Standard conditions for temperature and pressure|STP]]<!--STP assumed to be Standard temp-pressure--> lab controlled environments).
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| If objects appear white (reflective in the [[visual spectrum]]), they are not necessarily equally reflective (and thus non-emissive) in the thermal infrared. Most household radiators are painted white but this is sensible given that they are not hot enough to radiate any significant amount of heat, and are not designed as thermal radiators at all - they are actually convectors, and painting them matt black would make virtually no difference to their efficacy. Acrylic and urethane based white paints have 93% blackbody radiation efficiency at room temperature<ref>S. Tanemura, M. Tazawa, P. Jing, T. Miki, K. Yoshimura, K. Igarashi, M. Ohishi, K. Shimono, M. Adachi,
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| Optical Properties and Radiative Cooling Power of White Paints,[http://wire0.ises.org/wire/doclibs/SWC1999.nsf/id/D33990A41EA63969C1256920003D6148/$File/038.pdf]
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| ISES 1999 Solar World Congress</ref> (meaning the term "black body" does not always correspond to the visually perceived color of an object). These materials that do not follow the "black color = high emissivity/absorptivity" caveat will most likely have functional spectral emissivity/absorptivity dependence.
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| Calculation of radiative heat transfer between groups of object, including a 'cavity' or 'surroundings' requires solution of a set of [[simultaneous equations]] using the [[Radiosity (heat transfer)|Radiosity]] method. In these calculations, the geometrical configuration of the problem is distilled to a set of numbers called [[view factor]]s, which give the proportion of radiation leaving any given surface that hits another specific surface. These calculations are important in the fields of [[solar thermal energy]], [[boiler]] and [[furnace]] design and [[Ray tracing (graphics)|raytraced computer graphics]].
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| A selective surface can be used when energy is being extracted from the sun. For instance, when a green house is made, most of the roof and walls are made out of glass. Glass is transparent in the visible (approximately 0.4 µm<λ<0.8 µm) and [[near-infrared]] wavelengths, but opaque to mid- to far-wavelength infrared (approximately λ>3 µm).<ref name="ReferenceA">Heat and Mass Transfer, Yunus A. Cengel and Afshin J. Ghajar, 4th Edition</ref><ref>[[Infrared#Different regions in the infrared]] Short-wavelength infrared is 1.4-3µm, Mid-wavelength infrared is 3-8µm</ref> Therefore glass lets in radiation in the visible range, allowing us to be able to see through it, but doesn’t let out radiation that is emitted from objects at or close to room temperature. This traps what we feel as heat. This is known as the greenhouse effect and can be observed by getting into a car that has been sitting in the sun. Selective surfaces can also be used on solar collectors. We can find out how much help a selective surface coating is by looking at the equilibrium temperature of a plate that is being heated through solar radiation. If the plate is receiving a solar irradiation of {{nowrap|1350 W/m²}} (minimum is {{nowrap|1325 W/m²}} on July 4 and maximum is {{nowrap|1418 W/m²}} on January 3) from the sun the temperature of the plate where the radiation leaving is equal to the radiation being received by the plate is {{nowrap|393 K}} (248 °F). If the plate has a selective surface with an emissivity of 0.9 and a cut off wavelength of {{nowrap|2.0 µm,}} the equilibrium temperature is approximately {{nowrap|1250 K}} (1790 °F). Note that the calculations were made neglecting convective heat transfer and neglecting the solar irradiation absorbed in the clouds/atmosphere for simplicity, however, the theory is still the same for an actual problem. | |
| If we have a surface, such as a glass window, with which we would like to reduce the heat transfer from, a clear reflective film with a low emissivity coating can be placed on the interior of the wall. “Low-emittance (low-E) coatings are microscopically thin, virtually invisible, metal or metallic oxide layers deposited on a window or skylight glazing surface primarily to reduce the U-factor by suppressing radiative heat flow”.<ref>[http://www.efficientwindows.org/lowe.cfm The Efficient Windows Collaborative: Window Technologies<!-- Bot generated title -->]</ref> By adding this coating we are limiting the amount of radiation that leaves the window thus increasing the amount of heat that is retained inside the window.
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| ==Radiative heat transfer==
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| The radiative heat transfer from one surface to another is equal to the radiation entering the first surface from the other, minus the radiation leaving the first surface.
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| *For a black body
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| :<math> \dot{Q}_{1 \rightarrow 2} = A_{1}E_{b1}F_{1 \rightarrow 2} - A_{2}E_{b2}F_{2 \rightarrow 1}</math><ref name="ReferenceA"/>
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| Using the reciprocity rule, <math>A_{1}F_{1 \rightarrow 2} = A_{2}F_{2 \rightarrow 1} </math>, this simplifies to:
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| :<math> \dot{Q}_{1 \rightarrow 2} = \sigma A_{1}F_{1 \rightarrow 2}(T_1^4-T_2^4) \!</math><ref name="ReferenceA"/>
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| where <math>\sigma</math> is the [[Stefan–Boltzmann constant]] and <math>F_{1 \rightarrow 2}</math> is the [[view factor]] from surface 1 to surface 2. | |
| | |
| *For a grey body with only two surfaces the heat transfer is equal to:
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| :<math> \dot{Q}= \dfrac{\sigma(T_1^4-T_2^4)}{\dfrac{1-\epsilon_1}{A_1\epsilon_1}+ \dfrac{1}{A_1F_{1 \rightarrow 2}}+ \dfrac{1-\epsilon_2}{A_2\epsilon_2}}</math>
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| | |
| where <math>\epsilon</math> are the respective emissivities of each surface. However, this value can easily change for different circumstances and different equations should be used on a case per case basis.
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| ==Radiative power==
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| Thermal radiation power of a black body per unit of [[solid angle]] and per unit [[frequency]] <math>\nu</math> is given by [[Planck's law]] as:
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| :<math>u(\nu,T)=\frac{2 h\nu^3}{c^2}\cdot\frac1{e^{h\nu/k_BT}-1}</math>
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| or in terms of wavelength
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| :<math>u(\lambda,T)=\frac{\beta}{\lambda^5}\cdot\frac1{e^{hc/k_BT\lambda}-1}</math>
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| where <math>\beta</math> is a constant.
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| This formula mathematically follows from calculation of spectral distribution of energy in [[Quantization (physics)|quantized]] electromagnetic field which is in complete [[thermal equilibrium]] with the radiating object. The equation is derived as an infinite sum over all possible frequencies. The energy, <math>E=h \nu</math>, of each photon is multiplied by the number of states available at that frequency, and the probability that each of those states will be occupied.
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| Integrating the above equation over <math>\nu</math> the power output given by the [[Stefan–Boltzmann law]] is obtained, as:
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| :<math>P = \sigma \cdot A \cdot T^4</math>
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| where the [[constant of proportionality]] <math>\sigma</math> is the [[Stefan–Boltzmann constant]] and <math>A</math> is the radiating surface area.
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| Further, the wavelength <math>\lambda \,</math>, for which the emission intensity is highest, is given by [[Wien's displacement law]] as:
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| :<math>\lambda_{max} = \frac{b}{T} </math>
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| For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor <math>\epsilon(\nu)</math>. This factor has to be multiplied with the radiation spectrum formula before integration. If it is taken as a constant, the resulting formula for the power output can be written in a way that contains <math>\epsilon</math> as a factor:
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| :<math>P = \epsilon \cdot \sigma \cdot A \cdot T^4</math>
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| This type of theoretical model, with frequency-independent emissivity lower than that of a perfect black body, is often known as a ''gray body''. For frequency-dependent emissivity, the solution for the integrated power depends on the functional form of the dependence, though in general there is no simple expression for it. Practically speaking, if the emissivity of the body is roughly constant around the peak emission wavelength, the gray body model tends to work fairly well since the weight of the curve around the peak emission tends to dominate the integral.
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| ===Constants===
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| Definitions of constants used in the above equations:
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| {| class="wikitable"
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| |-
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| | <math>h \,</math>
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| | [[Planck's constant]]
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| | 6.626 0693(11)×10<sup>−34</sup> J·s = 4.135 667 43(35)×10<sup>−15</sup> eV·s
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| |-
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| | <math>b \,</math>
| |
| | [[Wien's displacement law|Wien's displacement constant]]
| |
| | 2.897 7685(51)×10<sup>−3</sup> m·K
| |
| |-
| |
| | <math>k_B \,</math>
| |
| | [[Boltzmann constant]]
| |
| | 1.380 6505(24)×10<sup>−23</sup> J·K<sup>−1</sup> = 8.617 343(15)×10<sup>−5</sup> eV·K<sup>−1</sup>
| |
| |-
| |
| |<math>\sigma \,</math>
| |
| |[[Stefan–Boltzmann constant]]
| |
| | 5.670 373(21)×10<sup>−8</sup> W·m<sup>−2</sup>·K<sup>−4</sup>
| |
| |-
| |
| | <math>c \,</math>
| |
| | [[Speed of light]]
| |
| | 299,792,458 m·s<sup>−1</sup>
| |
| |}
| |
| | |
| ===Variables===
| |
| Definitions of variables, with example values:
| |
| {| class="wikitable"
| |
| |-
| |
| | <math>T \,</math>
| |
| | Absolute [[temperature]]
| |
| | For units used above, must be in [[kelvin]] (''e.g.'' Average surface temperature on Earth = 288 K)
| |
| |-
| |
| | <math>A \,</math>
| |
| | Surface [[area]]
| |
| | ''A''<sub>cuboid</sub> = 2''ab'' + 2''bc'' + 2''ac'';<br> ''A''<sub>cylinder</sub> = 2''π·r''(''h'' + ''r'');<br> ''A''<sub>sphere</sub> = 4''π·r''<sup>2</sup>
| |
| |}
| |
| | |
| ==See also==
| |
| *[[Black body]]
| |
| *[[Emissivity]]
| |
| *[[Incandescence]]
| |
| *[[Infrared photography]]
| |
| *[[Interior radiation control coating]]
| |
| *[[Planck radiation]]
| |
| *[[Sakuma–Hattori equation]]
| |
| *[[Thermal dose unit]]
| |
| *[[Thermography]]
| |
| *[[View factor]]
| |
| | |
| ==References==
| |
| {{Reflist|2}}
| |
| | |
| ==Further reading==
| |
| *{{cite book
| |
| | last = Siegel, John R. Howell
| |
| | first = Robert
| |
| | authorlink =
| |
| | coauthors = Howell. John R.
| |
| | title = Thermal radiation heat transfer
| |
| | publisher = Taylor & Francis, Inc.
| |
| | date = November 2001
| |
| | location = New York
| |
| | pages = (xix - xxvi ''list of symbols for thermal radiation formulas'')
| |
| | url = http://books.google.com/?id=O389yQ0-fecC&pg=PA1&dq=Thermal+radiation
| |
| | doi =
| |
| | accessdate = 2009-07-23
| |
| | isbn = 978-1-56032-839-1}}
| |
| *[[Ephraim M. Sparrow|E.M. Sparrow]] and [[Robert D. Cess|R.D. Cess]]. Radiation Heat Transfer. Hemisphere Publishing Corporation, 1978.
| |
| | |
| ==External links==
| |
| * [http://www.spectralcalc.com/blackbody_calculator/blackbody.php Black Body Emission Calculator]
| |
| * [http://sol.sci.uop.edu/~jfalward/heattransfer/heattransfer.html Heat Transfer]{{dead link|date=October 2013}}
| |
| * [http://panda.unm.edu/courses/finley/p262/ThermalRad/ThermalRad.html Thermal Radiation]
| |
| * [http://www.du.edu/~etuttle/weather/atmrad.htm Atmospheric Radiation]
| |
| * [http://www.hartscientific.com/publications/pdfs/3187781_A_w.pdf Infrared Temperature Calibration 101]
| |
| | |
| {{Radiation}}
| |
| {{Use dmy dates|date=December 2010}}
| |
| | |
| {{DEFAULTSORT:Thermal Radiation}}
| |
| [[Category:Electromagnetic radiation]]
| |
| [[Category:Heat transfer|Radiation]]
| |
| [[Category:Thermodynamics]]
| |