Capacity of an object to radiate electromagnetic energy
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
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/m2) at a room temperature of 25 °C (298 K; 77 °F).
Objects generally have emissivities less than 1.0, and emit radiation at correspondingly lower rates.[1]
However, wavelength- and subwavelength-scale particles,[2]metamaterials,[3] and other nanostructures[4] may have an emissivity greater than 1.
Practical applications
Emissivities are important in a variety of contexts:
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.[5] In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window.[6]
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.[7]
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.[8] This facilitates
radiative cooling and protection of the underlying structure and is an alternative to ablative coatings, used in single-use
reentry capsules.
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.[9] These surfaces minimize the absorption of
solar radiation to lessen heat gain in order to maximize the emission of LWIR thermal radiation.[10] It has been proposed as a solution to global warming.[11]
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.[12]
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.[13]
Mathematical definitions
In its most general form, emissivity can be specified for a particular
wavelength, 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.[14]: 60
Some specific forms of emissivity are detailed below.
Hemispherical emissivity
Hemispherical emissivity of a surface, denoted ε, is defined as[15]
Me° 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 εν and ελ, respectively, are defined as[15]
where
Me,ν is the spectral
radiant exitance in frequency of that surface;
Me,ν° is the spectral radiant exitance in frequency of a black body at the same temperature as that surface;
Me,λ is the spectral radiant exitance in wavelength of that surface;
Me,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 εΩ, is defined as[15]
Le,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 εν,Ω and ελ,Ω, respectively, are defined as[15]
where
Le,Ω,ν is the spectral
radiance in frequency of that surface;
Le,Ω,ν° is the spectral radiance in frequency of a black body at the same temperature as that surface;
Le,Ω,λ is the spectral radiance in wavelength of that surface;
Le,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".[13]
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
wavelengths near 10×10−6 metre.[16] 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.[17][18]
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 (27 °C; 80 °F).
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 "
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.[13] 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.[22][23]
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 1,273 K (1,000 °C; 1,832 °F), will emit 97% of its energy at wavelengths below 14
μm.[8]
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.[24][25][26]
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).[27] 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
two-color pyrometry.[28]
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.[29]
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.[30] 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 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 through a less obstructed
atmospheric window spanning 8-13 μm.[31] 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.[32]
Atmosphere
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.[33] Nitrogen (N 2) and oxygen (O 2) - the primary atmospheric components - interact less significantly with thermal radiation in the infrared band.[21] 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.[34] 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).[35] Carbon dioxide (CO 2) and other greenhouse gases contribute about ε=0.2 to εa when atmospheric humidity is low.[36] Researchers have also evaluated the contribution of differing cloud types to atmospheric absorptivity and emissivity.[37][38][39]
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.[40]
The
IPCC reports an outgoing thermal radiation flux (OLR) of 239 (237-242) W m-2 and a surface thermal radiation flux (SLR) of 398 (395-400) W m-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 where is the effective emissivity of Earth as viewed from space and 289 K (16 °C; 61 °F) is the
effective temperature of the surface.[41]: 934
Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "
spectral absorbance".
^For a truly black object, the spectrum of its thermal radiation peaks at the wavelength given by
Wien's Law: λmax = b/T, where the temperature T is in kelvins and the constant b ≈ 2.90×10−3 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 0.5×10−6 metres. See Saha, Kshudiram (2008).
The Earth's Atmosphere: Its Physics and Dynamics.
Springer Science & Business Media. p. 84.
ISBN9783540784272.
^2009 ASHRAE Handbook: Fundamentals - IP Edition. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers. 2009.
ISBN978-1-933742-56-4. "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.
^The visible color of an anodized aluminum surface does not strongly affect its emissivity. See
"Emissivity of Materials". Electro Optical Industries, Inc.
Archived from the original on 2012-09-19.
^"Table of Total Emissivity"(PDF). Archived from
the original(PDF) on 2009-07-11. Table of emissivities provided by a company; no source for these data is provided.
^"Influencing factors". evitherm Society - Virtual Institute for Thermal Metrology. Archived from
the original on 2014-01-12. Retrieved 2014-07-19.
"Spectral emissivity and emittance". Southampton, PA: Temperatures.com, Inc. Archived from
the original on 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).
"Emissivity Coefficients of some common Materials". 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.