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The emissivity of the surface of a material is its effectiveness in emitting energy as
thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
. Thermal radiation is
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
that most commonly includes both visible radiation (light) and
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
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 ideal black surface at the same temperature as given by the
Stefan–Boltzmann law The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths ...
. 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 at room temperature (, ). All real objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates. Emissivities are important in several contexts: ;
Insulated windows Insulating glass (IG) consists of two or more glass window panes separated by a space to reduce heat transfer across a part of the building envelope. A window with insulating glass is commonly known as double glazing or a double-paned window, ...
: 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 Low emissivity (low ''e'' or low thermal emissivity) refers to a surface condition that emits low levels of radiant thermal (heat) energy. All materials absorb, reflect, and emit radiant energy according to Planck's law but here, the primary conc ...
coatings emit less thermal radiation than ordinary windows. In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window. ; Solar heat collectors: Similarly, solar heat collectors lose heat by emitting thermal radiation. Advanced solar collectors incorporate
selective surface In solar thermal collectors, a selective surface or selective absorber is a means of increasing its operation temperature and/or efficiency. The selectivity is defined as the ratio of solar radiation absorption (αsol) to thermal infrared radia ...
s that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation. ; Thermal shielding: For the protection of structures from high surface temperatures, such as reusable
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
or
hypersonic In aerodynamics, a hypersonic speed is one that exceeds 5 times the speed of sound, often stated as starting at speeds of Mach 5 and above. The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since in ...
aircraft, high-emissivity coatings (HECs), with emissivity values near 0.9, are applied on the surface of insulating ceramics. This facilitates
radiative cooling In the study of heat transfer, radiative cooling is the process by which a body loses heat by thermal radiation. As Planck's law describes, every physical body spontaneously and continuously emits electromagnetic radiation. Radiative cooling ha ...
and protection of the underlying structure and is an alternative to ablative coatings, used in single-use
reentry capsule A reentry capsule is the portion of a space capsule which returns to Earth following a spaceflight. The shape is determined partly by aerodynamics; a capsule is aerodynamically stable falling blunt end first, which allows only the blunt end to re ...
s. ;
Passive daytime radiative cooling Passive daytime radiative cooling (PDRC) is a renewable cooling method proposed as a solution to global warming of enhancing terrestrial heat flow to outer space through the installation of thermally-emissive surfaces on Earth that require zero ...
: 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. These surfaces minimize the absorption of
solar radiation Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre (W/m ...
to lessen heat gain in order to maximize the emission of LWIR thermal radiation. It has been proposed as a solution to global warming. ; 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. Emissivity of a planet is determined by the nature of its surface and atmosphere. ; Temperature measurements:
Pyrometer A pyrometer is a type of remote-sensing thermometer used to measure the temperature of distant objects. Various forms of pyrometers have historically existed. In the modern usage, it is a device that from a distance determines the temperature of ...
s and
infrared cameras Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
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.


Mathematical definitions


Hemispherical emissivity

Hemispherical emissivity of a surface, denoted ''ε'', is defined as : \varepsilon = \frac, where * ''M''e is the
radiant exitance In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether ...
of that surface; * ''M''e° 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''ν and ''ε''λ, respectively, are defined as : \begin \varepsilon_\nu &= \frac, \\ \varepsilon_\lambda &= \frac, \end where * ''M''e,ν is the spectral
radiant exitance In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether ...
in frequency of that surface; * ''M''e,ν° is the spectral radiant exitance in frequency of a black body at the same temperature as that surface; * ''M''e,λ is the spectral radiant exitance in wavelength of that surface; * ''M''e,λ° 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''Ω, is defined as : \varepsilon_\Omega = \frac, where * ''L''e,Ω is the
radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiatio ...
of that surface; * ''L''e,Ω° 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''ν,Ω and ''ε''λ,Ω, respectively, are defined as : \begin \varepsilon_ &= \frac, \\ \varepsilon_ &= \frac, \end where * ''L''e,Ω,ν is the spectral
radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiatio ...
in frequency of that surface; * ''L''e,Ω,ν° is the spectral radiance in frequency of a black body at the same temperature as that surface; * ''L''e,Ω,λ is the spectral radiance in wavelength of that surface; * ''L''e,Ω,λ° 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".


Emissivities of common surfaces

Emissivities ''ε'' can be measured using simple devices such as
Leslie's cube Leslie's cube is a device used in the measurement or demonstration of the variations in thermal radiation emitted from different surfaces at the same temperature. Device It was devised in 1804 by John Leslie (1766–1832), a Scottish mathematicia ...
in conjunction with a thermal radiation detector such as a
thermopile A thermopile is an electronic device that converts thermal energy into electrical energy. It is composed of several thermocouples connected usually in series or, less commonly, in parallel. Such a device works on the principle of the thermoelect ...
or a
bolometer A bolometer is a device for measuring radiant heat by means of a material having a temperature-dependent electrical resistance. It was invented in 1878 by the American astronomer Samuel Pierpont Langley. Principle of operation 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 In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
s near 10×10−6 metre. Visible light has a wavelength range of about 0.4–0.7×10−6 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. Notes: # These emissivities are the total hemispherical emissivities from the surfaces. # The values of the emissivities apply to materials that are 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 (300 K).


Closely related properties


Absorptivity

There is a fundamental relationship (
Gustav Kirchhoff Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coine ...
's 1859 law of thermal radiation) that equates the emissivity of a surface with its absorption of incident radiation (the " 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. 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. Table of emissivities provided by a company; no source for these data is provided. 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 10×10−6 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 In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. At ...
, 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 A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body ...
in thermal equilibrium at 1,273 K, will emit 97% of its energy at wavelengths below . 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.


Emissivities of planet Earth

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 radiative emissions to space typically function as the primary cooling mechanism for these otherwise isolated bodies. The
balance Balance or balancing may refer to: Common meanings * Balance (ability) in biomechanics * Balance (accounting) * Balance or weighing scale * Balance as in equality or equilibrium Arts and entertainment Film * ''Balance'' (1983 film), a Bulgarian ...
between all other incoming plus internal sources of energy versus the outgoing flow regulates planetary temperatures. For Earth, equilibrium skin temperatures range near the freezing point of water (260K±50K). The most energetic emissions are thus within a band spanning about 4-50 μm as governed by
Planck's law In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. At ...
. 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. Earth's surface emissivities (εs) have been inferred with satellite-based instruments by directly observing surface thermal emissions at
nadir The nadir (, ; ar, نظير, naẓīr, counterpart) is the direction pointing directly ''below'' a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface. The direc ...
through a less obstructed
atmospheric window An atmospheric window is a range of wavelengths of the electromagnetic spectrum that can pass through the atmosphere of Earth. The optical, infrared and radio windows comprise the three main atmospheric windows. The windows provide direct channels ...
spanning 8-13 μm. Values range about εs=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 εs=0.95. Water also dominates the planet's atmospheric emissivity and absorptivity in the form of
water vapor (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vapor, water vapour or aqueous vapor is the gaseous pha ...
. Clouds, carbon dioxide, and other components make substantial additional contributions, especially where there are gaps in the water vapor absorption spectrum. Nitrogen () and oxygen () - the primary atmospheric components - interact less significantly with thermal radiation in the infrared band. Direct measurement of Earths atmospheric emissivities (εa) 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 εa 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 εa≈1. At a lower limit, clear sky (cloud-free) conditions promote the largest opening of transmission windows. The more uniform concentration of long-lived trace greenhouse gases in combination with water vapor pressures of 0.25-20 mbar then yield minimum values in the range of εa=0.55-0.8 (with ε=0.35-0.75 for a simulated water-vapor-only atmosphere). Carbon dioxide () and other greenhouse gases contribute about ε=0.2 to εa when atmospheric humidity is low. Researchers have also evaluated the contribution of differing cloud types to atmospheric absorptivity and emissivity. These days, the detailed processes and complex properties of radiation transport through the atmosphere are evaluated with radiation transport codes and databases such as
MODTRAN MODTRAN (MODerate resolution atmospheric TRANsmission) is a computer program designed to model atmospheric propagation of electromagnetic radiation for the 100-50,000 cm−1 (0.2 to 100 µm) spectral range. This covers the spectrum from ...
/
HITRAN HITRAN (an acronym for High Resolution Transmission) molecular spectroscopic database is a compilation of spectroscopic parameters used to simulate and analyze the transmission and emission of light in gaseous media, with an emphasis on planetary a ...
. "Effective" atmospheric emissivites for downwelling and upwelling thermal radiation are thereby simulated, and compared to similar results obtained from ground and satellite observations. An effective global value of εa≈0.78 has been estimated from application of an idealized energy-balance model to the planet.


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, John Leslie,
Balfour Stewart Balfour Stewart (1 November 182819 December 1887) was a Scottish physicist and meteorologist. His studies in the field of radiant heat led to him receiving the Rumford Medal of the Royal Society in 1868. In 1859 he was appointed director of K ...
and others. In 1860,
Gustav Kirchhoff Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coine ...
published a mathematical description of their relationship under conditions of
thermal equilibrium Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
(i.e.
Kirchoff's law of thermal radiation In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsage ...
). By 1884 the emissive power of a perfect blackbody was inferred by
Josef Stefan Josef Stefan ( sl, Jožef Štefan; 24 March 1835 – 7 January 1893) was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire. Life and work Stefan was born in an outskirt village of St. Peter (Slovene: ; to ...
using
John Tyndall John Tyndall FRS (; 2 August 1820 – 4 December 1893) was a prominent 19th-century Irish physicist. His scientific fame arose in the 1850s from his study of diamagnetism. Later he made discoveries in the realms of infrared radiation and the p ...
's experimental measurements, and derived by
Ludwig Boltzmann Ludwig Eduard Boltzmann (; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodyn ...
from fundamental statistical principles. Emissivity, defined as a further
proportionality factor In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a Constant (mathematics), constant ratio, which is called the coefficient of proportionality or p ...
to the Stefan-Boltzmann law, was thus implied and utilized in subsequent evaluations of the radiative behavior of grey bodies. For example,
Svante Arrhenius Svante August Arrhenius ( , ; 19 February 1859 – 2 October 1927) was a Swedes, Swedish scientist. Originally a physicist, but often referred to as a chemist, Arrhenius was one of the founders of the science of physical chemistry. He received ...
applied the recent theoretical developments to his 1896 investigation of Earth's surface temperatures as calculated from the planet's
radiative equilibrium Radiative equilibrium is the condition where the total thermal radiation leaving an object is equal to the total thermal radiation entering it. It is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of t ...
with all of space. By 1900
Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...
empirically derived a generalized law of blackbody radiation, thus clarifying the emissivity and absorptivity concepts at individual wavelengths.


Other radiometric coefficients


See also

*
Albedo Albedo (; ) is the measure of the diffuse reflection of sunlight, solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body ...
*
Black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spect ...
*
Passive daytime radiative cooling Passive daytime radiative cooling (PDRC) is a renewable cooling method proposed as a solution to global warming of enhancing terrestrial heat flow to outer space through the installation of thermally-emissive surfaces on Earth that require zero ...
*
Radiant barrier A radiant barrier is a type of building material that reflects thermal radiation and reduces heat transfer. Because thermal energy is also transferred by conduction and convection, in addition radiation, radiant barriers are often supplemented wit ...
*
Reflectance The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...
*
Sakuma–Hattori equation The Sakuma–Hattori equation is a mathematical model for predicting the amount of thermal radiation, radiometric flux or radiometric power emitted from a perfect blackbody or received by a thermal radiation detector. History The Sakuma–Hattori ...
*
Stefan–Boltzmann law The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths ...
*
View factor In radiative heat transfer, a view factor, F_, is the proportion of the radiation which leaves surface A that strikes surface B. In a complex 'scene' there can be any number of different objects, which can be divided in turn into even more surfaces ...
*
Wien's displacement law Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck r ...


References


Further reading

* 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). * 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 Physical quantities Radiometry Heat transfer