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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 emitted by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electro ...
. Thermal radiation is
electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
that most commonly includes both visible radiation (light) and
infrared Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...
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, also known as ''Stefan's law'', describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Lu ...
. (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) at a room temperature of . Objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates. However, wavelength- and subwavelength-scale particles, metamaterials, and other nanostructures 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. 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 surfaces 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 that is designed spaceflight, to fly and operate in outer space. Spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth observation, Weather s ...
or hypersonic 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 has b ...
and protection of the underlying structure and is an alternative to ablative coatings, used in single-use reentry capsules. ;
Passive daytime radiative cooling Passive daytime radiative cooling (PDRC) (also passive radiative cooling, daytime passive radiative cooling, radiative sky cooling, photonic radiative cooling, and terrestrial radiative cooling) is the use of unpowered, reflective/Emissivity, ther ...
: 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 Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible light perceptible to the human eye as well as invisible infrared (typically p ...
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: Pyrometers and 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.


Mathematical definitions

In its most general form, emissivity can be specified for a particular
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
, direction, and 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. Some specific forms of emissivity are detailed below.


Hemispherical emissivity

Hemispherical emissivity of a surface, denoted ''ε'', is defined as : \varepsilon = \frac, where * ''M''e is the radiant exitance 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 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 radiati ...
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 radiati ...
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 in conjunction with a thermal radiation detector such as a thermopile 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 and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
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, .


Closely related properties


Absorptance

There is a fundamental relationship (
Gustav Kirchhoff Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German chemist, mathematician, physicist, and spectroscopist who contributed to the fundamental understanding of electrical circuits, spectroscopy and the emission of black-body ...
'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, 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 , 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.


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). 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 o
two-color pyrometry


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 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, 260±50 K (-13±50 °C, 8±90 °F). The most energetic emissions are thus within a band spanning about 4-50 μm as governed by Planck's law. 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 parametrizations within some simpler meteorlogic and climatologic models.


Surface

Earth's surface emissivities (εs) have been inferred with satellite-based instruments by directly observing surface thermal emissions at
nadir The nadir 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 direction opposite of the nadir is the zenith. Et ...
through a less obstructed atmospheric window 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.


Atmosphere

Water also dominates the planet's atmospheric emissivity and absorptivity in the form of
water vapor Water vapor, water vapour, or aqueous vapor is the gaseous phase of Properties of water, water. It is one Phase (matter), state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from th ...
. 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 by general circulation models using radiation transport codes and databases such as MODTRAN/ HITRAN. Emission, absorption, and
scattering In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...
are thereby simulated through both space and time. For many practical applications it may not be possible, economical 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 observations (from the ground or outer space) or defined according to the simplifications utilized by a particular model. For example, an effective global value of εa≈0.78 has been estimated from application of an idealized single-layer-atmosphere energy-balance model to Earth.


Effective emissivity due to atmosphere

The
IPCC The Intergovernmental Panel on Climate Change (IPCC) is an intergovernmental body of the United Nations. Its job is to "provide governments at all levels with scientific information that they can use to develop climate policies". The World M ...
reports an outgoing thermal radiation flux (OLR) of 239 (237–242) W m and a surface thermal radiation flux (SLR) of 398 (395–400) W m, 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 \mathrm = \epsilon_\mathrm\,\sigma\,T_^4 where \epsilon_\mathrm \approx 0.6 is the effective emissivity of Earth as viewed from space and T_\mathrm \equiv \left mathrm/\sigma\right \approx is the
effective temperature The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature ...
of the surface.


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 and others. In 1860,
Gustav Kirchhoff Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German chemist, mathematician, physicist, and spectroscopist who contributed to the fundamental understanding of electrical circuits, spectroscopy and the emission of black-body ...
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 t ...
(i.e. Kirchhoff's law of thermal radiation). 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 Ludwig Eduard Boltzmann ( ; ; 20 February 1844 – 5 September 1906) was an Austrian mathematician and Theoretical physics, theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical ex ...
from fundamental statistical principles. 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 Svante August Arrhenius ( , ; 19 February 1859 – 2 October 1927) was a Swedish scientist. Originally a physicist, but often referred to as a chemist, Arrhenius was one of the founders of the science of physical chemistry. In 1903, he received ...
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. By 1900
Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
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 fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...
*
Black-body radiation Black-body radiation is the thermal radiation, 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 ...
*
Passive daytime radiative cooling Passive daytime radiative cooling (PDRC) (also passive radiative cooling, daytime passive radiative cooling, radiative sky cooling, photonic radiative cooling, and terrestrial radiative cooling) is the use of unpowered, reflective/Emissivity, ther ...
* Radiant barrier * Reflectance *
Sakuma–Hattori equation In physics, 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 ...
*
Stefan–Boltzmann law The Stefan–Boltzmann law, also known as ''Stefan's law'', describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Lu ...
* View factor *
Wien's displacement law In physics, 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 ...


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