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<!--This article is written for readers without specialized technical education, but who want to know what the term emissivity means in contexts such as "low-e" coatings for windows.-->
{{short description|Capacity of an object to radiate electromagnetic energy}}
[[Image:Blacksmith at work02.jpg|thumb|right|[[Blacksmith]]s work [[iron]] when it is hot enough to emit plainly visible [[thermal radiation]].]]
The '''emissivity''' of the surface of a material is its effectiveness in emitting energy as [[thermal radiation]]. Thermal radiation is [[electromagnetic radiation]] that most commonly includes both visible radiation (light) and [[infrared]] radiation, which is not visible to human eyes. A portion of the thermal radiation from very hot objects (see photograph) is easily visible to the eye. 

The emissivity of a surface depends on its chemical composition and geometrical structure.  Quantitatively, it is the ratio of the thermal radiation from a surface to the radiation from an [[black body|ideal black surface]] at the same temperature as given by the [[Stefan–Boltzmann law]]. (A comparison with [[Planck's law]] is used if one is concerned with particular wavelengths of thermal radiation.) The ratio varies from 0 to 1. 

The surface of a perfect black body (with an emissivity of 1) emits thermal radiation at the rate of approximately 448 watts per square metre (W/m{{sup|2}}) at a room temperature of {{convert|25|C|K F}}.  

Objects generally have emissivities less than 1.0, and emit radiation at correspondingly lower rates.<ref>The [[Stefan–Boltzmann law]] is that the rate of emission of thermal radiation is ''σT''<sup>4</sup>, where ''σ'' = 5.67×10<sup>−8</sup>&nbsp;W/m<sup>2</sup>·K<sup>4</sup>, and the temperature ''T'' is in [[kelvin]]s. See {{cite book |title=The Nature of Science: An A-Z Guide to the Laws and Principles Governing Our Universe |first=James S. |last=Trefil
|publisher=[[Houghton Mifflin Harcourt]] |year=2003 |isbn=9780618319381 |page=[https://archive.org/details/natureofsciencea00tref/page/377 377] |url=https://archive.org/details/natureofsciencea00tref|url-access=registration }}</ref> 

However, wavelength- and subwavelength-scale particles,<ref name="Bohren">
{{cite book
 |last1=Bohren |first1=Craig F.
 |last2=Huffman |first2=Donald R.
 |year=1998
 |title=Absorption and scattering of light by small particles
 |url=https://books.google.com/books?id=ib3EMXXIRXUC
 |publisher=Wiley
 |isbn=978-0-471-29340-8
 |pages=123–126
}}</ref> [[metamaterial]]s,<ref>
{{Cite conference
 |last1=Narimanov |first1=Evgenii E.
 |last2=Smolyaninov |first2=Igor I.
 |year=2012
 |chapter=Beyond Stefan–Boltzmann Law: Thermal Hyper-Conductivity
 |arxiv=1109.5444
 |title=Conference on Lasers and Electro-Optics 2012
 |series=OSA Technical Digest
 |publisher=Optical Society of America
 |pages=QM2E.1
 |doi=10.1364/QELS.2012.QM2E.1
 |isbn=978-1-55752-943-5
 |citeseerx=10.1.1.764.846
 |s2cid=36550833
 }}</ref> and other nanostructures<ref name="Golyk2012">{{cite journal |last1=Golyk |first1=V. A. |last2=Krüger |first2=M. |last3=Kardar |first3=M. |title=Heat radiation from long cylindrical objects |journal=Phys. Rev. E |date=2012 |volume=85 |issue=4 |page=046603 |doi=10.1103/PhysRevE.85.046603 |pmid=22680594 |arxiv=1109.1769 |bibcode=2012PhRvE..85d6603G |url=https://link.aps.org/accepted/10.1103/PhysRevE.85.046603|hdl=1721.1/71630 |s2cid=27489038 |hdl-access=free }}</ref> may have an emissivity greater than 1.

== Practical applications ==
Emissivities are important in a variety of contexts:
; [[Insulated windows]]: Warm surfaces are usually cooled directly by air, but they also cool themselves by emitting thermal radiation. This second cooling mechanism is important for simple glass windows, which have emissivities close to the maximum possible value of 1.0. "Low-E windows" with transparent [[low-emissivity]] coatings emit less thermal radiation than ordinary windows.<ref name=roadmap>{{cite book |chapter=The Low-E Window R&D Success Story |title=Windows and Building Envelope Research and Development: Roadmap for Emerging Technologies |publisher=[[U.S. Department of Energy]] |date=February 2014 |page=5 |chapter-url=http://energy.gov/sites/prod/files/2014/02/f8/BTO_windows_and_envelope_report_3.pdf#page=15 }}</ref> In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window.<ref name=Fricke>{{cite book |title=Essentials of Energy Technology |last1=Fricke |first1=Jochen |last2=Borst |first2=Walter L. |publisher=[[Wiley-VCH]] |date=2013 |isbn=978-3527334162 |page=37 |url=https://books.google.com/books?id=zn1nAgAAQBAJ&pg=PA37 }}</ref>
[[Image:Capteur a tubes sous vide 001.JPG|right|thumb|[[Solar water heating]] system based on [[evacuated tube solar hot water heater|evacuated glass tube collectors]]. [[Sunlight]] is absorbed inside each tube by a selective surface. The surface absorbs sunlight nearly completely, but has a low thermal emissivity so that it loses very little heat. Ordinary black surfaces also absorb sunlight efficiently, but they emit thermal radiation copiously.]]
; [[Solar thermal collector|Solar heat collectors]]: Similarly, solar heat collectors lose heat by emitting thermal radiation. Advanced solar collectors incorporate [[selective surface]]s that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation.<ref name=Fricke1>{{cite book |title=Essentials of Energy Technology |chapter=9. Solar Space and Hot Water Heating |last1=Fricke |first1=Jochen |last2=Borst |first2=Walter L. |publisher=Wiley-VCH |date=2013 |isbn=978-3527334162 |page=249 |chapter-url=https://books.google.com/books?id=zn1nAgAAQBAJ&pg=PA249 }}</ref>
; [[Heat shield|Thermal shielding]]: For the protection of structures from high surface temperatures, such as reusable [[spacecraft]] or [[hypersonic]] aircraft, high-emissivity coatings (HECs), with emissivity values near 0.9, are applied on the surface of insulating ceramics.<ref name="rtps">{{cite journal |url=https://www.sciencedirect.com/science/article/abs/pii/S0010938X1830605X| last1=Shao| first1=Gaofeng|display-authors=etal| title= Improved oxidation resistance of high emissivity coatings on fibrous ceramic for reusable space systems | journal= Corrosion Science | year=2019 | volume=146| pages= 233–246 | doi= 10.1016/j.corsci.2018.11.006 | arxiv=1902.03943 | s2cid=118927116}}</ref> This facilitates [[radiative cooling]] and protection of the underlying structure and is an alternative to ablative coatings, used in single-use [[reentry capsule]]s.
; [[Passive daytime radiative cooling]]: Daytime passive radiative coolers use the extremely cold temperature of outer space (~2.7 K) to emit heat and lower ambient temperatures while requiring zero energy input.<ref name=":212">{{Cite journal |last1=Aili |first1=Ablimit |last2=Yin |first2=Xiaobo |last3=Yang |first3=Ronggui |date=October 2021 |title=Global Radiative Sky Cooling Potential Adjusted for Population Density and Cooling Demand |journal=Atmosphere |volume=12 |issue=11 |page=1379 |doi=10.3390/atmos12111379 |doi-access=free }}</ref> These surfaces minimize the absorption of [[Solar Radiation|solar radiation]] to lessen heat gain in order to maximize the emission of LWIR thermal radiation.<ref name=":213">{{Cite journal |last1=Aili |first1=Ablimit |last2=Yin |first2=Xiaobo |last3=Yang |first3=Ronggui |date=October 2021 |title=Global Radiative Sky Cooling Potential Adjusted for Population Density and Cooling Demand |journal=Atmosphere |volume=12 |issue=11 |page=1379 |doi=10.3390/atmos12111379 |doi-access=free }}</ref> It has been proposed as a solution to global warming.<ref name=":5">{{Cite journal |last1=Chen |first1=Meijie |last2=Pang |first2=Dan |last3=Chen |first3=Xingyu |last4=Yan |first4=Hongjie |last5=Yang |first5=Yuan |title=Passive daytime radiative cooling: Fundamentals, material designs, and applications |journal=EcoMat |year=2022 |volume=4 |doi=10.1002/eom2.12153 |s2cid=240331557 |quote=Passive daytime radiative cooling (PDRC) dissipates terrestrial heat to the extremely cold outer space without using any energy input or producing pollution. It has the potential to simultaneously alleviate the two major problems of energy crisis and global warming. |doi-access=free }}</ref>
; [[Earth's energy budget|Planetary temperatures]]: The planets are solar thermal collectors on a large scale. The temperature of a planet's surface is determined by the balance between the heat absorbed by the planet from sunlight, heat emitted from its core, and thermal radiation emitted back into space. [[#Emissivities of planet Earth|Emissivity of a planet]] is determined by the nature of its surface and atmosphere.<ref name="ACS">{{cite web |title=Climate Sensitivity |url=http://www.acs.org/content/acs/en/climatescience/atmosphericwarming/climatsensitivity.html |access-date=2014-07-21 |publisher=[[American Chemical Society]]}}</ref>
[[Image:Emissivity differences on Chopfab beer can.png|right|thumb|Due to differences in emissivity, this [[thermography|infrared]] picture of a cold beer can shows vastly different (and incorrect) temperature values depending on the surface material. Reflections (like on the blank end of the can and the countertop) make accurate measurements of reflective surfaces impossible.]]
; Temperature measurements: [[Pyrometer]]s and [[thermography|infrared cameras]] are instruments used to measure the temperature of an object by using its thermal radiation; no actual contact with the object is needed. The calibration of these instruments involves the emissivity of the surface that's being measured.<ref name="Siegel" />

==Mathematical definitions==
In its most general form, emissivity can specified for a particular [[wavelength]], direction, and [[polarization (physics)|polarization]]. 

However, the most commonly used form of emissivity is the ''hemispherical total emissivity'', which considers emissions as totaled over all wavelengths, directions, and polarizations, given a particular temperature.<ref name="SH92">{{cite book |last1=Siegel |first1=Robert |last2=Howell |first2=John R. |title=Thermal Radiation Heat Transfer |date=1992 |publisher=Taylor & Francis |isbn=0-89116-271-2 |edition=3}}</ref>{{rp|60}}

Some specific forms of emissivity are detailed below.

===Hemispherical emissivity===
'''Hemispherical emissivity''' of a surface, denoted ''ε'', is defined as<ref name="ISO_9288-1989">{{cite web|url=https://www.iso.org/standard/82088.html|title=Thermal insulation — Heat transfer by radiation — Physical quantities and definitions|work=ISO 9288:2022|publisher=[[International Organization for Standardization|ISO]] catalogue|year=1989|access-date=2015-03-15}}</ref>
: <math>\varepsilon = \frac{M_\mathrm{e}}{M_\mathrm{e}^\circ},</math>

where
* ''M''<sub>e</sub> is the [[radiant exitance]] of that surface;
* ''M''<sub>e</sub>° is the radiant exitance of a black body at the same temperature as that surface.

===Spectral hemispherical emissivity===
'''Spectral hemispherical emissivity in frequency''' and '''spectral hemispherical emissivity in wavelength''' of a surface, denoted ''ε''<sub>ν</sub> and ''ε''<sub>λ</sub>, respectively, are defined as<ref name="ISO_9288-1989"/>
: <math>\begin{align}
      \varepsilon_\nu &= \frac{M_{\mathrm{e},\nu}}{M_{\mathrm{e},\nu}^\circ}, \\
  \varepsilon_\lambda &= \frac{M_{\mathrm{e},\lambda}}{M_{\mathrm{e},\lambda}^\circ},
\end{align}</math>

where
* ''M''<sub>e,ν</sub> is the spectral [[radiant exitance]] in frequency of that surface;
* ''M''<sub>e,ν</sub>° is the spectral radiant exitance in frequency of a black body at the same temperature as that surface;
* ''M''<sub>e,λ</sub> is the spectral radiant exitance in wavelength of that surface;
* ''M''<sub>e,λ</sub>° is the spectral radiant exitance in wavelength of a black body at the same temperature as that surface.

===Directional emissivity===
'''Directional emissivity''' of a surface, denoted ''ε''<sub>Ω</sub>, is defined as<ref name="ISO_9288-1989"/>
: <math>\varepsilon_\Omega = \frac{L_{\mathrm{e},\Omega}}{L_{\mathrm{e},\Omega}^\circ},</math>

where
* ''L''<sub>e,Ω</sub> is the [[radiance]] of that surface;
* ''L''<sub>e,Ω</sub>° is the radiance of a black body at the same temperature as that surface.

===Spectral directional emissivity===
'''Spectral directional emissivity in frequency''' and '''spectral directional emissivity in wavelength''' of a surface, denoted ''ε''<sub>ν,Ω</sub> and ''ε''<sub>λ,Ω</sub>, respectively, are defined as<ref name="ISO_9288-1989"/>
: <math>\begin{align}
      \varepsilon_{\nu,\Omega} &= \frac{L_{\mathrm{e},\Omega,\nu}}{L_{\mathrm{e},\Omega,\nu}^\circ}, \\
  \varepsilon_{\lambda,\Omega} &= \frac{L_{\mathrm{e},\Omega,\lambda}}{L_{\mathrm{e},\Omega,\lambda}^\circ},
\end{align}</math>

where
* ''L''<sub>e,Ω,ν</sub> is the spectral [[radiance]] in frequency of that surface;
* ''L''<sub>e,Ω,ν</sub>° is the spectral radiance in frequency of a black body at the same temperature as that surface;
* ''L''<sub>e,Ω,λ</sub> is the spectral radiance in wavelength of that surface;
* ''L''<sub>e,Ω,λ</sub>° is the spectral radiance in wavelength of a black body at the same temperature as that surface.

Hemispherical emissivity can also be expressed as a weighted average of the directional spectral emissivities as described in textbooks on "radiative heat transfer".<ref name=Siegel/>

==Emissivities of common surfaces==
Emissivities ''ε'' can be measured using simple devices such as [[Leslie's cube]] in conjunction with a thermal radiation detector such as a [[thermopile]] or a [[bolometer]]. The apparatus compares the thermal radiation from a surface to be tested with the thermal radiation from a nearly ideal, black sample. The detectors are essentially black absorbers with very sensitive thermometers that record the detector's temperature rise when exposed to thermal radiation. For measuring room temperature emissivities, the detectors must absorb thermal radiation completely at infrared [[wavelength]]s near 10×10<sup>−6</sup> metre.<ref>For a truly black object, the spectrum of its thermal radiation peaks at the wavelength given by [[Wien's displacement law|Wien's Law]]: ''λ''<sub>max</sub> = ''b''/''T'', where the temperature ''T'' is in kelvins and the constant ''b'' ≈ 2.90×10<sup>−3</sup> metre-kelvins. Room temperature is about 293 kelvins. Sunlight itself is thermal radiation originating from the hot surface of the Sun. The Sun's surface temperature of about 5800 kelvins corresponds well to the peak wavelength of sunlight, which is at the green wavelength of about 0.5×10<sup>−6</sup> metres. See {{cite book |title=The Earth's Atmosphere: Its Physics and Dynamics |first=Kshudiram |last=Saha |publisher=[[Springer Science & Business Media]] |date=2008 |isbn=9783540784272 |page=84 |url=https://books.google.com/books?id=Jlb5PtwpkI8C&pg=PA84 }}</ref> Visible light has a wavelength range of about 0.4–0.7×10<sup>−6</sup> metre from violet to deep red.

Emissivity measurements for many surfaces are compiled in many handbooks and texts. Some of these are listed in the following table.<ref>{{cite book |title=Thermal Radiative Transfer and Properties |first=M. Quinn |last=Brewster
|publisher=[[John Wiley & Sons]] |date=1992 |isbn=9780471539827 |page=56 |url=https://books.google.com/books?id=z_anVNTmQLUC&pg=PA56}}</ref><ref>{{cite book |title=2009 ASHRAE Handbook: Fundamentals - IP Edition |publisher=American Society of Heating, Refrigerating and Air-Conditioning Engineers |date=2009 |location=Atlanta |pages=<!--page numbers needed--> |isbn=978-1-933742-56-4}} "IP" refers to inch and pound units; a version of the handbook with metric units is also available. Emissivity is a simple number, and doesn't depend on the system of units.</ref>

[[Image:LesliesCube.png|thumb|right|Photographs of an aluminium [[Leslie's cube]]. The color photographs are taken using an infrared camera; the black and white photographs underneath are taken with an ordinary camera. All faces of the cube are at the same temperature of about {{Cvt|55|C}}. The face of the cube that has been painted (black or white paint has negligible impact) has a large emissivity, which is indicated by the reddish color in the infrared photograph. The polished face of the cube has a low emissivity indicated by the blue color, and the reflected image of the warm hand is clear.]]
{| class="wikitable sortable"
|-
! Material
! data-sort-type="number" | Emissivity
|-
| [[Aluminium foil]]
| 0.03 
|-
| [[Aluminium]], [[anodized]]
| 0.9<ref>The visible color of an anodized aluminum surface does not strongly affect its emissivity. See {{cite web |title=Emissivity of Materials |url=http://www.electro-optical.com/eoi_page.asp?h=Emissivity%20of%20Materials |publisher=Electro Optical Industries, Inc. |archive-url=https://web.archive.org/web/20120919150451/http://www.electro-optical.com/eoi_page.asp?h=Emissivity%20of%20Materials |archive-date=2012-09-19 |url-status=live}}</ref>
|-
|Aluminium, smooth, polished
|0.04
|-
|Aluminium, rough, oxidized
|0.2
|-
| [[Asphalt concrete|Asphalt]]
| 0.88
|-
| [[Brick]]
| 0.90 
|-
| [[Concrete]], rough
| 0.91 
|-
| [[Copper]], polished
| 0.04
|-
| [[Copper]], oxidized
| 0.87
|-
| [[Glass#Silicate|Glass]], smooth uncoated
| 0.95
|-
| [[Ice]]
| 0.97-0.99
|-
|[[Iron]], polished
|0.06
|-
| [[Limestone]]
| 0.92 
|-
| [[Marble]], polished
| 0.89–0.92
|-
| Nitrogen or Oxygen gas layer, pure
| ~0<ref name="togler95">{{Cite journal |last1=Trogler |first1=William C. |title=The Environmental Chemistry of Trace Atmospheric Gases |journal=Journal of Chemical Education |volume=72 |issue=11 |pages=973 |year=1995 |doi=10.1021/ed072p973 |bibcode=1995JChEd..72..973T }}</ref><ref name="hopfner"/>
|-
| Paint, including white
| 0.9 
|-
| Paper, roofing or white
| 0.88–0.86 
|-
| [[Plaster]], rough
| 0.89
|-
| [[Silver]], polished
| 0.02
|- 
| Silver, oxidized
| 0.04
|- 
| Skin, human
| 0.97–0.999
|- 
| [[Snow]]
| 0.8–0.9 
|-
|[[Polytetrafluoroethylene]] (Teflon)
|0.85
|-
| [[Transition metal]] [[disilicide]]s (e.g. [[molybdenum disilicide|MoSi<sub>2</sub>]] or [[tungsten disilicide|WSi<sub>2</sub>]])
| 0.86–0.93<ref name="rtps"/>
|-
|Vegetation
|0.92-0.96
|-
| [[Water]], pure
| 0.96
|}

Notes:
# These emissivities are the total hemispherical emissivities from the surfaces.
# The values of the emissivities apply to materials that are [[optical depth|optically thick]]. This means that the absorptivity at the wavelengths typical of thermal radiation doesn't depend on the thickness of the material. Very thin materials emit less thermal radiation than thicker materials.
# Most emissitivies in the chart above were recorded at room temperature, {{convert|300|K}}.

==Closely related properties==

===Absorptance===
{{Main|Kirchhoff's law of thermal radiation}}
There is a fundamental relationship ([[Gustav Kirchhoff]]'s 1859 law of thermal radiation) that equates the emissivity of a surface with its absorption of incident radiation (the "[[Absorptance#absorptance|absorptivity]]" of a surface). Kirchhoff's law is rigorously applicable with regard to the spectral directional definitions of emissivity and absorptivity. The relationship explains why emissivities cannot exceed 1, since the largest absorptivity—corresponding to complete absorption of all incident light by a truly black object—is also 1.<ref name=Siegel>{{cite book |title=Thermal Radiation Heat Transfer, Fourth Edition |last=Siegel |first=Robert |publisher=[[CRC Press]] |date=2001 |isbn=9781560328391 |url=https://books.google.com/books?id=O389yQ0-fecC&pg=PA41 |page=41 }}</ref> Mirror-like, metallic surfaces that reflect light will thus have low emissivities, since the reflected light isn't absorbed. A polished silver surface has an emissivity of about 0.02 near room temperature. Black soot absorbs thermal radiation very well; it has an emissivity as large as 0.97, and hence soot is a fair approximation to an ideal black body.<ref name=table>{{cite web |url=http://www.monarchserver.com/TableofEmissivity.pdf |title=Table of Total Emissivity |url-status=dead |archive-url=https://web.archive.org/web/20090711135115/http://www.monarchserver.com/TableofEmissivity.pdf |archive-date=2009-07-11 }} Table of emissivities provided by a company; no source for these data is provided.</ref><ref>{{cite web|url=http://www.evitherm.org/default.asp?ID=216 |title=Influencing factors |publisher=evitherm Society - Virtual Institute for Thermal Metrology |access-date=2014-07-19 |url-status=dead |archive-url=https://web.archive.org/web/20140112002045/http://www.evitherm.org/default.asp?ID=216 |archive-date=2014-01-12 }}</ref>

With the exception of bare, polished metals, the appearance of a surface to the eye is not a good guide to emissivities near room temperature. For example, white paint absorbs very little visible light. However, at an infrared wavelength of 10×10<sup>−6</sup> metre, paint absorbs light very well, and has a high emissivity. Similarly, pure water absorbs very little visible light, but water is nonetheless a strong infrared absorber and has a correspondingly high emissivity.

===Emittance===
Emittance (or emissive power) is the total amount of thermal energy emitted per unit area per unit time for all possible wavelengths. Emissivity of a body at a given temperature is the ratio of the total emissive power of a body to the total emissive power of a perfectly black body at that temperature. Following [[Planck's law]], the total energy radiated increases with temperature while the peak of the emission spectrum shifts to shorter wavelengths. The energy emitted at shorter wavelengths increases more rapidly with temperature.  For example, an ideal [[blackbody]] in thermal equilibrium at {{convert|1273|K}}, will emit 97% of its energy at wavelengths below {{Val|14|ul=μm}}.<ref name="rtps"/>

The term emissivity is generally used to describe a simple, homogeneous surface such as silver. Similar terms, '''emittance''' and '''thermal emittance''', are used to describe thermal radiation measurements on complex surfaces such as insulation products.<ref>{{cite web |title=ASTM C835 - 06(2013)e1: Standard Test Method for Total Hemispherical Emittance of Surfaces up to 1400°C |url=http://www.astm.org/Standards/C835.htm |access-date=2014-08-09 |publisher=[[ASTM International]]}}</ref><ref>{{cite book |title=Green Building: Principles and Practices in Residential Construction |first1=Abe |last1=Kruger |first2=Carl |last2=Seville |publisher=[[Cengage Learning]] |date=2012 |isbn=9781111135959 |page=198 |url=https://books.google.com/books?id=_YM6TOKEEwgC&pg=PA198}}</ref><ref>{{Cite journal |last1=Saad |first1=Abdullah A. |last2=Martinez |first2=Carlos |last3=Trice |first3=Rodney W. |date=2023-02-13 |title=Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra-high temperature ceramics |journal=International Journal of Ceramic Engineering & Science |volume=5 |issue=2 |language=en |doi=10.1002/ces2.10171 |issn=2578-3270|doi-access=free }}</ref>

=== Measurement of Emittance ===
Emittance of a surface can be measured directly or indirectly from the emitted energy from that surface. In the direct radiometric method, the emitted energy from the sample is measured directly using a spectroscope such as Fourier transform infrared spectroscopy (FTIR).<ref>{{Cite journal |last1=Saad |first1=Abdullah A. |last2=Martinez |first2=Carlos |last3=Trice |first3=Rodney W. |date=2023-02-13 |title=Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra-high temperature ceramics |journal=International Journal of Ceramic Engineering & Science |volume=5 |issue=2 |language=en |doi=10.1002/ces2.10171 |issn=2578-3270|doi-access=free }}</ref> In the indirect calorimetric method, the emitted energy from the sample is measured indirectly using a calorimeter. In addition to these two commonly applied methods, inexpensive emission measurement technique based on the principle of [https://ceramics.onlinelibrary.wiley.com/doi/full/10.1002/ces2.10171 two-color pyrometry].<ref>{{Cite journal |last1=Saad |first1=Abdullah A. |last2=Martinez |first2=Carlos |last3=Trice |first3=Rodney W. |date=2023-02-13 |title=Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra-high temperature ceramics |journal=International Journal of Ceramic Engineering & Science |volume=5 |issue=2 |language=en |doi=10.1002/ces2.10171 |issn=2578-3270|doi-access=free }}</ref>

==Emissivities of planet Earth==
[[File:IR emission in current greenhouse levels.png|thumb|right|A typical spectrum of Earth's total outgoing (upwelling) thermal radiation flux under clear-sky conditions, as simulated with [[MODTRAN]].  [[Planck curve]]s are also shown for a range of Earth temperatures.]]

The emissivity of a planet or other astronomical body is determined by the composition and structure of its outer skin.  In this context, the "skin" of a planet generally includes both its semi-transparent atmosphere and its non-gaseous surface.  The resulting [[Outgoing longwave radiation|radiative emissions]] to space typically function as the primary cooling mechanism for these otherwise isolated bodies.  The [[Earth's energy balance|balance]] between all other incoming plus internal sources of energy versus the outgoing flow regulates planetary temperatures.<ref>{{cite web |url=https://earthobservatory.nasa.gov/features/EnergyBalance |title=Climate and Earth's Energy Budget |date=14 January 2009 |publisher=NASA Earth Observatory |accessdate=10 October 2022}}</ref>

For Earth, equilibrium skin temperatures range near the freezing point of water, 260±50 K (-13±50 °C, 8±90 °F).  The most energetic emissions are thus within a band spanning about 4-50&nbsp;μm as governed by [[Planck's law]].<ref>{{cite book |last1=Petty |first1=Grant W. |title=A first course in atmospheric radiation |date=2006 |publisher=Sundog Publ. |location=Madison, Wisc.|isbn=978-0972903318 |page=68 |edition=2 }}</ref>  Emissivities for the atmosphere and surface components are often quantified separately,  and validated against satellite- and terrestrial-based observations as well as laboratory measurements.  These emissivities serve as input parameters within some meteorlogic and climatologic models.

===Surface===
Earth's surface emissivities (ε<sub>s</sub>) have been inferred with satellite-based instruments by directly observing surface thermal emissions at [[nadir]] through a less obstructed [[atmospheric window]] spanning 8-13&nbsp;μm.<ref>{{cite web |url=https://terra.nasa.gov/news/aster-global-emissivity-database-100-times-more-detailed-than-its-predecessors |title=ASTER global emissivity database: 100 times more detailed than its predecessor |date=17 November 2014 |publisher=NASA Earth Observatory |accessdate=10 October 2022}}</ref>  Values range about ε<sub>s</sub>=0.65-0.99, with lowest values typically limited to the most barren desert areas.  Emissivities of most surface regions are above 0.9 due to the dominant influence of water;  including oceans, land vegetation, and snow/ice.  Globally averaged estimates for the hemispheric emissivity of Earth's surface are in the vicinity of ε<sub>s</sub>=0.95.<ref>{{cite web |url=https://emissivity.jpl.nasa.gov/ |title=Joint Emissivity Database Initiative |publisher=NASA Jet Propulsion Laboratory |accessdate=10 October 2022}}</ref>

===Atmosphere===
[[File:Atmosfaerisk spredning.png|thumb|left|A typical spectrum of infrared radiation transmittance through Earth's atmosphere. A 'window' can be seen between 8 and 14&nbsp;μm that enables direct transmission of the most intense thermal emissions from Earth's surface.  The remaining portion of the upwelling energy, as well as downwelling radiation back to the surface, undergoes absorption and emission by the various atmospheric components as indicated.]]

Water also dominates the planet's atmospheric emissivity and absorptivity in the form of [[water vapor]].  Clouds, carbon dioxide, and other components make substantial additional contributions, especially where there are gaps in the water vapor absorption spectrum.<ref>{{cite web |url=https://www.earthobservatory.nasa.gov/features/RemoteSensing/remote_04.php |title=Remote Sensing: Absorption Bands and Atmospheric Windows |publisher=[[NASA Earth Observatory]] |date=17 September 1999 |accessdate=28 October 2022}}</ref>  Nitrogen ({{chem|N|2}}) and oxygen ({{chem|O|2}}) - the primary atmospheric components - interact less significantly with thermal radiation in the infrared band.<ref name="hopfner">{{Cite journal |last1=Höpfner |first1=M. |last2=Milz |first2=M. |last3=Buehler |first3=S. |last4=Orphall |first4=J. |last5=Stiller |first5=G. |date=24 May 2012 |title=The natural greenhouse effect of atmospheric oxygen (O<sub>2</sub>) and nitrogen (N<sub>2</sub>) |journal=Geophysical Research Letters |language=en |volume=39 |issue=L10706 |doi=10.1029/2012GL051409 |bibcode=2012GeoRL..3910706H |s2cid=128823108 |issn=1944-8007}}</ref>  Direct measurement of Earths atmospheric emissivities (ε<sub>a</sub>) are more challenging than for land surfaces due in part to the atmosphere's multi-layered and more dynamic structure.

Upper and lower limits have been measured and calculated for ε<sub>a</sub> in accordance with extreme yet realistic local conditions.  At the upper limit, dense low cloud structures (consisting of liquid/ice aerosols and saturated  water vapor) close the infrared transmission windows, yielding near to black body conditions with ε<sub>a</sub>≈1.<ref>{{cite journal |last1=Liu |first1=Lei |last2=Zhang |first2=Ting |last3=Wu |first3=Yi |last4=Niu |first4=Zhencong |last5=Wang |first5=Qi |year=2018 |title=Cloud Effective Emissivity Retrievals Using Combined Ground-Based Infrared Cloud Measuring Instrument and Ceilometer Observations |journal=Remote Sensing |volume=10 |issue=2033 |page=2033 |doi=10.3390/rs10122033 |bibcode=2018RemS...10.2033L |doi-access=free }}</ref>  At a lower limit, clear sky  (cloud-free) conditions promote the largest opening of transmission windows.  The more uniform concentration of [[list of greenhouse gases|long-lived trace greenhouse gases]] in combination with water vapor pressures of 0.25-20&nbsp;mbar then yield minimum values in the range of ε<sub>a</sub>=0.55-0.8 (with ε=0.35-0.75 for a simulated water-vapor-only atmosphere).<ref name=hitran>{{cite journal |last1=Mendoza |first1=Victor M.. |last2=Vallanueva |first2=Elba E. |last3=Garduno |first3=Rene |last4=Sanchez-Meneses |first4=Oscar 
|title=Atmospheric emissivity with clear sky computed by E-Trans/HITRAN |journal=Atmospheric Environment |date=31 January 2017 |volume=155 |pages=174–188 |doi=10.1016/j.atmosenv.2017.01.048 |bibcode=2017AtmEn.155..174M |issn=1352-2310 |doi-access= }}</ref> Carbon dioxide ({{chem|link=carbon dioxide|CO|2|}}) and other greenhouse gases contribute about ε=0.2 to ε<sub>a</sub> when atmospheric humidity is low.<ref>{{cite journal |last1=Staley |first1=D.O. |last2=Jurica |first2=G.M. |title=Effective atmospheric emissivity under clear skies |journal=Applied Meteorology and Climatology |date=1 March 1972 |volume=11 |issue=2 |pages=349–356 |doi=10.1175/1520-0450(1972)011<0349:EAEUCS>2.0.CO;2 |bibcode=1972JApMe..11..349S |doi-access=free}}</ref>  Researchers have also evaluated the contribution of differing cloud types to atmospheric absorptivity and emissivity.<ref>{{cite web |url=https://earthobservatory.nasa.gov/features/Clouds |title=Clouds and Radiation |publisher=[[NASA Earth Observatory]] |date=1 March 1999 |author=Graham, Steve |accessdate=28 October 2022}}</ref><ref>{{cite journal |last1=Cox |first1=Stephen K. |title=Observations of cloud infrared effective emissivity |journal=Atmospheric Sciences |date=1 February 1976 |volume=33 |issue=2 |pages=287–289 |doi=10.1175/1520-0469(1976)033<0287:OOCIEE>2.0.CO;2 |bibcode=1976JAtS...33..287C |doi-access=free}}</ref><ref>{{cite journal |last1=Chylek |first1=Petr |last2=Ramaswamy |first2=V. |title=Simple approximation of infrared emissivity of water clouds |journal=Atmospheric Sciences |date=1 January 1982 |volume=39 |issue=1 |pages=171–177 |doi=10.1175/1520-0469(1982)039<0171:SAFIEO>2.0.CO;2 |bibcode=1982JAtS...39..171C |doi-access=free}}</ref>  

These days, the detailed processes and complex properties of radiation transport through the atmosphere are evaluated with [[atmospheric radiative transfer codes|radiation transport codes]] and databases such as [[MODTRAN]]/[[HITRAN]].<ref name=hitran />

For many practical applications it may not be possible, cost-effective or necessary to know all emissivity values locally.  "Effective" or "bulk" values for an atmosphere or an entire planet may be used.  These can be based upon [[remote sensing|remote]] observations (from the ground or outer space) or defined according to the [[all models are wrong|simplifications]] utilized by a particular model.  For example, an effective global value of ε<sub>a</sub>≈0.78 has been estimated from application of an idealized [[idealized greenhouse model|single-layer-atmosphere energy-balance model]] to Earth.<ref>{{cite web |url=https://www.acs.org/content/acs/en/climatescience/atmosphericwarming/singlelayermodel.html |title=ACS Climate Science Toolkit - Atmospheric Warming - A Single-Layer Atmosphere Model |publisher=[[American Chemical Society]] |accessdate=1 December 2022}}</ref>

===Effective emissivity due to atmosphere===
{{See also|Climate model#Zero-dimensional models}}
The [[IPCC]] reports an outgoing thermal radiation flux (OLR) of 239 (237-242)&nbsp;W m{{sup|-2}} and a surface thermal radiation flux (SLR) of 398 (395-400)&nbsp;W m{{sup|-2}}, where the parenthesized amounts indicate the 5-95% confidence intervals as of 2015. These values indicate that the atmosphere (with clouds included) reduces Earth's overall emissivity, relative to its surface emissions, by a factor of 239/398 ≈ 0.60.  In other words, emissions to space are given by <math>\mathrm{OLR} = \epsilon_\mathrm{eff}\,\sigma\,T_{se}^4</math> where <math>\epsilon_\mathrm{eff} \approx 0.6</math> is the effective emissivity of Earth as viewed from space and <math> T_\mathrm{se} \equiv \left[\mathrm{SLR}/\sigma\right]^{1/4} \approx</math> {{convert|289|K}}  is the [[effective temperature]] of the surface.<ref name="ipccAR6WG1">{{Cite book  |ref= {{harvid|IPCC AR6 WG1|2021}}
 |author= IPCC |author-link= IPCC
 |year= 2021
 |title= Climate Change 2021: The Physical Science Basis
 |series= Contribution of Working Group I to the [[IPCC Sixth Assessment Report|Sixth Assessment Report]] of the Intergovernmental Panel on Climate Change
 |display-editors= 4
 |editor1-first= V.     |editor1-last= Masson-Delmotte
 |editor2-first= P.     |editor2-last= Zhai
 |editor3-first= A.	|editor3-last= Pirani
 |editor4-first= S. L.  |editor4-last= Connors
 |editor5-first= C.     |editor5-last= Péan
 |editor6-first= S.     |editor6-last= Berger
 |editor7-first= N.     |editor7-last= Caud
 |editor8-first= Y.     |editor8-last= Chen
 |editor9-first= L.     |editor9-last= Goldfarb
 |editor10-first= M. I. |editor10-last= Gomis
 |publisher= Cambridge University Press (In Press)
 |place= 
 |isbn= 
 |url= https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Full_Report.pdf
}}</ref>{{rp|934}}

==History==
The concepts of emissivity and absorptivity, as properties of matter and radiation, appeared in the late-eighteenth thru mid-nineteenth century writings of [[Pierre Prévost (physicist)|Pierre Prévost]], [[John Leslie (physicist)|John Leslie]], [[Balfour Stewart]] and others.<ref>{{Cite journal|last=Prévost|first=Pierre|date=April 1791|title=Mémoire sur l'équilibre du feu|url=https://books.google.com/books?id=7ZLOAAAAMAAJ&pg=PA314|journal=Observations Sur la Physique|language=fr|volume=XXXVIII|issue=1|pages=314–323}}</ref><ref>{{cite book |last=Leslie |first=John |title= An Experimental Inquiry into the Nature and Propagation of Heat |date= 1804 |publisher= J. Mawman |location= Edinburgh |url= https://archive.org/details/bub_gb_Cz4IAAAAIAAJ}}</ref><ref>{{Cite book|last=Stewart|first=Balfour |year=1866 |title=An Elementary Treatise on Heat |publisher=Oxford, Clarendon Press |url=https://archive.org/details/elementarytreati00stewuoft/page/n5/mode/2up}}</ref> In 1860, [[Gustav Kirchhoff]] published a mathematical description of their relationship under conditions of [[thermal equilibrium]] (i.e. [[Kirchoff's law of thermal radiation]]).<ref>{{cite journal |last1=Kirchhoff |first1=Gustav |year=1860 |title=Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht |journal=[[Annalen der Physik und Chemie]]
|volume=109 |pages=275–301 |doi=10.1002/andp.18601850205 |doi-access=free |bibcode = 1860AnP...185..275K |issue=2 }}</ref>  By 1884 the emissive power of a perfect blackbody was inferred by [[Josef Stefan]] using [[John Tyndall]]'s experimental measurements, and derived by [[Ludwig Boltzmann]] from fundamental statistical principles.<ref>{{cite journal|last1=Boltzmann|first1=Ludwig|title=Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie|journal=Annalen der Physik und Chemie|date=1884|volume=258|issue=6|pages=291–294|doi=10.1002/andp.18842580616|url=https://babel.hathitrust.org/cgi/pt?id=uc1.a0002763670;view=1up;seq=305|trans-title=Derivation of Stefan's law, concerning the dependency of heat radiation on temperature, from the electromagnetic theory of light|language=de|bibcode=1884AnP...258..291B|doi-access=free}}</ref>   Emissivity, defined as a further [[proportionality factor]] to the [[Stefan-Boltzmann law]], was thus implied and utilized in subsequent evaluations of the radiative behavior of grey bodies.  For example, [[Svante Arrhenius]] applied the recent theoretical developments to his 1896 investigation of Earth's surface temperatures as calculated from the planet's [[radiative equilibrium]] with all of space.<ref>{{Cite journal | author=Svante Arrhenius | year=1896 | title=On the influence of carbonic acid in the air upon the temperature of the ground | journal=Philosophical Magazine and Journal of Science | volume=41 | issue=251 | pages=237–276 | language=en| doi=10.1080/14786449608620846 | url=https://zenodo.org/record/1431217 |doi-access=free}}</ref>  By 1900 [[Max Planck]] empirically derived a [[Planck's law|generalized law of blackbody radiation]], thus clarifying the emissivity and absorptivity concepts at individual wavelengths.<ref>{{cite journal |last1=Planck |first1=Max |author1-link=Max Planck |year=1901 |title=Über das Gesetz der Energieverteilung im Normalspektrum |journal=[[Annalen der Physik]] |volume=4 |issue=3 |pages=553–563 |bibcode=1901AnP...309..553P |doi=10.1002/andp.19013090310 |doi-access=free}}</ref>

==Other radiometric coefficients==
{{Radiometry coefficients}}

==See also==
* [[Albedo]]
* [[Black-body radiation]]
* [[Passive daytime radiative cooling]]
* [[Radiant barrier]]
* [[Reflectance]]
* [[Sakuma–Hattori equation]]
* [[Stefan–Boltzmann law]]
* [[View factor]]
* [[Wien's displacement law]]

==References==
{{Reflist}}

==Further reading==
* {{cite web |url=http://www.spectralemissivity.com |title=Spectral emissivity and emittance |publisher=Temperatures.com, Inc. |location=Southampton, PA |archive-url=https://web.archive.org/web/20170424062858/http://www.spectralemissivity.com/ |archive-date=24 April 2017}} An open community-focused website & directory with resources related to spectral emissivity and emittance. On this site, the focus is on available data, references and links to resources related to spectral emissivity as it is measured & used in thermal radiation thermometry and thermography (thermal imaging).
* {{cite web |url=http://www.engineeringtoolbox.com/emissivity-coefficients-d_447.html |title=Emissivity Coefficients of some common Materials |publisher=engineeringtoolbox.com }} Resources, Tools and Basic Information for Engineering and Design of Technical Applications. This site offers an extensive list of other material not covered above.

{{Authority control}}

[[Category:Physical quantities]]
[[Category:Radiometry]]
[[Category:Heat transfer]]