Emissivity
The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that may include both visible radiation (light) and infrared radiation, which is not visible to human eyes. The thermal radiation from very hot objects (see photograph) is easily visible to the eye. Quantitatively, emissivity 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 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 (25 °C, 298.15 K); all real objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates.[1]
Emissivities are important in several 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.[2] In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window.[3]
- 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.[4]
- 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.[5] This facilitates radiative cooling and protection of the underlying structure and is an alternative to ablative coatings, used in single-use reentry capsules.
- 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.[6]
- 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.[7]
Mathematical definitions[edit]
Hemispherical emissivity[edit]
Hemispherical emissivity of a surface, denoted ε, is defined as[8]
where
- Me is the radiant exitance of that surface;
- Me° is the radiant exitance of a black body at the same temperature as that surface.
Spectral hemispherical emissivity[edit]
Spectral hemispherical emissivity in frequency and spectral hemispherical emissivity in wavelength of a surface, denoted εν and ελ, respectively, are defined as[8]
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[edit]
Directional emissivity of a surface, denoted εΩ, is defined as[8]
where
- Le,Ω is the radiance of that surface;
- Le,Ω° is the radiance of a black body at the same temperature as that surface.
Spectral directional emissivity[edit]
Spectral directional emissivity in frequency and spectral directional emissivity in wavelength of a surface, denoted εν,Ω and ελ,Ω, respectively, are defined as[8]
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.
Emissivities of common surfaces[edit]
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.[9] Visible light has a wavelength range of about 0.4 to 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.[10][11]
![](http://webcf.waybackmachine.org/web/20220402122711im_/http://upload.wikimedia.org/wikipedia/commons/thumb/7/7f/LesliesCube.png/220px-LesliesCube.png)
Material | Emissivity |
---|---|
Aluminium foil | 0.03 |
Aluminium, anodized | 0.9[12] |
Asphalt | 0.88 |
Brick | 0.90 |
Concrete, rough | 0.91 |
Copper, polished | 0.04 |
Copper, oxidized | 0.87 |
Glass, smooth (uncoated) | 0.95 |
Ice | 0.97 |
Limestone | 0.92 |
Marble (polished) | 0.89 to 0.92 |
Paint (including white) | 0.9 |
Paper, roofing or white | 0.88 to 0.86 |
Plaster, rough | 0.89 |
Silver, polished | 0.02 |
Silver, oxidized | 0.04 |
Skin, Human | 0.97 to 0.999 |
Snow | 0.8 to 0.9 |
Transition metal Disilicides (e.g. MoSi2 or WSi2) | 0.86 to 0.93[5] |
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 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.
Absorptivity[edit]
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 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.[7] 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.[13][14]
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. Thus white paint absorbs very little visible light. However, at an infrared wavelength of 10x10−6 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.
Directional spectral emissivity[edit]
In addition to the total hemispherical emissivities compiled in the table above, a more complex "directional spectral emissivity" can also be measured. This emissivity depends upon the wavelength and upon the angle of the outgoing thermal radiation. Kirchhoff's law actually applies exactly to this more complex emissivity: the emissivity for thermal radiation emerging in a particular direction and at a particular wavelength matches the absorptivity for incident light at the same wavelength and angle. The total hemispherical emissivity is a weighted average of this directional spectral emissivity; the average is described by textbooks on "radiative heat transfer".[7]
Emittance[edit]
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, will emit 97% of its energy at wavelengths below 14 μm.[5]
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.[15][16]
SI radiometry units[edit]
Quantity | Unit | Dimension | Notes | |||||
---|---|---|---|---|---|---|---|---|
Name | Symbol[nb 1] | Name | Symbol | Symbol | ||||
Radiant energy | Qe[nb 2] | joule | J | M⋅L2⋅T−2 | Energy of electromagnetic radiation. | |||
Radiant energy density | we | joule per cubic metre | J/m3 | M⋅L−1⋅T−2 | Radiant energy per unit volume. | |||
Radiant flux | Φe[nb 2] | watt | W = J/s | M⋅L2⋅T−3 | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy. | |||
Spectral flux | Φe,ν[nb 3] | watt per hertz | W/Hz | M⋅L2⋅T−2 | Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1. | |||
Φe,λ[nb 4] | watt per metre | W/m | M⋅L⋅T−3 | |||||
Radiant intensity | Ie,Ω[nb 5] | watt per steradian | W/sr | M⋅L2⋅T−3 | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. | |||
Spectral intensity | Ie,Ω,ν[nb 3] | watt per steradian per hertz | W⋅sr−1⋅Hz−1 | M⋅L2⋅T−2 | Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity. | |||
Ie,Ω,λ[nb 4] | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | |||||
Radiance | Le,Ω[nb 5] | watt per steradian per square metre | W⋅sr−1⋅m−2 | M⋅T−3 | Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity". | |||
Spectral radiance | Le,Ω,ν[nb 3] | watt per steradian per square metre per hertz | W⋅sr−1⋅m−2⋅Hz−1 | M⋅T−2 | Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". | |||
Le,Ω,λ[nb 4] | watt per steradian per square metre, per metre | W⋅sr−1⋅m−3 | M⋅L−1⋅T−3 | |||||
Irradiance Flux density |
Ee[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral irradiance Spectral flux density |
Ee,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy). | |||
Ee,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | |||||
Radiosity | Je[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral radiosity | Je,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity". | |||
Je,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | |||||
Radiant exitance | Me[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity". | |||
Spectral exitance | Me,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity". | |||
Me,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | |||||
Radiant exposure | He | joule per square metre | J/m2 | M⋅T−2 | Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence". | |||
Spectral exposure | He,ν[nb 3] | joule per square metre per hertz | J⋅m−2⋅Hz−1 | M⋅T−1 | Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence". | |||
He,λ[nb 4] | joule per square metre, per metre | J/m3 | M⋅L−1⋅T−2 | |||||
Hemispherical emissivity | ε | N/A | 1 | Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
Spectral hemispherical emissivity | εν or ελ |
N/A | 1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
Directional emissivity | εΩ | N/A | 1 | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. | ||||
Spectral directional emissivity | εΩ,ν or εΩ,λ |
N/A | 1 | Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. | ||||
Hemispherical absorptance | A | N/A | 1 | Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance". | ||||
Spectral hemispherical absorptance | Aν or Aλ |
N/A | 1 | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". | ||||
Directional absorptance | AΩ | N/A | 1 | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". | ||||
Spectral directional absorptance | AΩ,ν or AΩ,λ |
N/A | 1 | Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance". | ||||
Hemispherical reflectance | R | N/A | 1 | Radiant flux reflected by a surface, divided by that received by that surface. | ||||
Spectral hemispherical reflectance | Rν or Rλ |
N/A | 1 | Spectral flux reflected by a surface, divided by that received by that surface. | ||||
Directional reflectance | RΩ | N/A | 1 | Radiance reflected by a surface, divided by that received by that surface. | ||||
Spectral directional reflectance | RΩ,ν or RΩ,λ |
N/A | 1 | Spectral radiance reflected by a surface, divided by that received by that surface. | ||||
Hemispherical transmittance | T | N/A | 1 | Radiant flux transmitted by a surface, divided by that received by that surface. | ||||
Spectral hemispherical transmittance | Tν or Tλ |
N/A | 1 | Spectral flux transmitted by a surface, divided by that received by that surface. | ||||
Directional transmittance | TΩ | N/A | 1 | Radiance transmitted by a surface, divided by that received by that surface. | ||||
Spectral directional transmittance | TΩ,ν or TΩ,λ |
N/A | 1 | Spectral radiance transmitted by a surface, divided by that received by that surface. | ||||
Hemispherical attenuation coefficient | μ | reciprocal metre | m−1 | L−1 | Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Spectral hemispherical attenuation coefficient | μν or μλ |
reciprocal metre | m−1 | L−1 | Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Directional attenuation coefficient | μΩ | reciprocal metre | m−1 | L−1 | Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Spectral directional attenuation coefficient | μΩ,ν or μΩ,λ |
reciprocal metre | m−1 | L−1 | Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
See also: SI · Radiometry · Photometry |
- ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- ^ a b c d e f g Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.
- ^ a b c d e f g Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).
- ^ a b Directional quantities are denoted with suffix "Ω" (Greek).
See also[edit]
- Albedo
- Black-body radiation
- Radiant barrier
- Reflectance
- Sakuma–Hattori equation
- Stefan–Boltzmann law
- View factor
- Wien's displacement law
References[edit]
- ^ The Stefan–Boltzmann law is that the rate of emission of thermal radiation is σT4, where σ=5.67×10−8 W/m2/K4, and the temperature T is in Kelvins. See Trefil, James S. (2003). The Nature of Science: An A-Z Guide to the Laws and Principles Governing Our Universe. Houghton Mifflin Harcourt. p. 377. ISBN 9780618319381.
- ^ "The Low-E Window R&D Success Story" (PDF). Windows and Building Envelope Research and Development: Roadmap for Emerging Technologies. U.S. Department of Energy. February 2014. p. 5.
- ^ Fricke, Jochen; Borst, Walter L. (2013). Essentials of Energy Technology. Wiley-VCH. p. 37. ISBN 978-3527334162.
- ^ Fricke, Jochen; Borst, Walter L. (2013). "9. Solar Space and Hot Water Heating". Essentials of Energy Technology. Wiley-VCH. p. 249. ISBN 978-3527334162.
- ^ a b c Shao, Gaofeng; et al. (2019). "Improved oxidation resistance of high emissivity coatings on fibrous ceramic for reusable space systems". Corrosion Science. 146: 233–246. arXiv:1902.03943. doi:10.1016/j.corsci.2018.11.006. S2CID 118927116.
- ^ "Climate Sensitivity". American Chemical Society. Retrieved 2014-07-21.
- ^ a b c Siegel, Robert (2001). Thermal Radiation Heat Transfer, Fourth Edition. CRC Press. p. 41. ISBN 9781560328391.
- ^ a b c d "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.
- ^ 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. ISBN 9783540784272.
- ^ Brewster, M. Quinn (1992). Thermal Radiative Transfer and Properties. John Wiley & Sons. p. 56. ISBN 9780471539827.
- ^ 2009 ASHRAE Handbook: Fundamentals - IP Edition. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers. 2009. 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.
- ^ 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.
- ^ "ASTM C835 - 06(2013)e1: Standard Test Method for Total Hemispherical Emittance of Surfaces up to 1400°C". ASTM International. Retrieved 2014-08-09.
- ^ Kruger, Abe; Seville, Carl (2012). Green Building: Principles and Practices in Residential Construction. Cengage Learning. p. 198. ISBN 9781111135959.
Further reading[edit]
- "Spectral emissivity and emittance". Southampton, PA: Temperatures.com, Inc. Archived from the original on 4 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.