Emissivity

Blacksmiths 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 light, but for objects near room temperature this light is infrared and 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 black object emits thermal radiation at the rate of approximately 448 watts per square meter at room temperature (25°C, 298.15 K); real objects with emissivities less than 1.0 emit radiation at correspondingly lower rates.

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. In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window.

Solar water heating system based on 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 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.
• 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

Hemispherical emissivity

Hemispherical emissivity of a surface, denoted ε, is defined as

$\varepsilon = \frac{M_\mathrm{e}}{M_\mathrm{e}^\circ},$

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

$\varepsilon_\nu = \frac{M_{\mathrm{e},\nu}}{M_{\mathrm{e},\nu}^\circ},$

$\varepsilon_\lambda = \frac{M_{\mathrm{e},\lambda}}{M_{\mathrm{e},\lambda}^\circ},$

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

$\varepsilon_\Omega = \frac{L_{\mathrm{e},\Omega}}{L_{\mathrm{e},\Omega}^\circ},$

where

• L_e,Ω is the radiance 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

$\varepsilon_{\nu,\Omega} = \frac{L_{\mathrm{e},\Omega,\nu}}{L_{\mathrm{e},\Omega,\nu}^\circ},$

$\varepsilon_{\lambda,\Omega} = \frac{L_{\mathrm{e},\Omega,\lambda}}{L_{\mathrm{e},\Omega,\lambda}^\circ},$

where

• L_e,Ω,ν is the spectral radiance 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.

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 meters. Visible light has a wavelength range of about 0.4 to 0.7×10⁻⁶ meters 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.

Photographs of 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 55 °C (131 °F). The face of the cube that has been painted black has a large emissivity, which is indicated by the reddish color in the infrared photograph. The polished face of the aluminum cube has a low emissivity indicated by the blue color, and the reflected image of the warm hand is clear.

Material	Emissivity
Aluminum foil	0.03
Aluminum, anodized	0.9
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
Snow	0.8 to 0.9
Water, pure	0.96

Notes:

1. These emissivities are the "total hemispherical emissivities" from the surfaces. The term emissivity is also used for "directional spectral emissivities" that describe thermal radiation emitted near specific wavelengths and at specific angles to the surface.
2. 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.
3. Snow will vary a lot depending on if it is fresh fallen or old dirty snow.

Emissivity and absorptivity

Main article: Kirchoff'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 "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. Mirror-like, metallic surfaces that reflect light well 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.

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 meters, 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

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".

Emissivity and emittance

Emittance (or emissive power) is the total amount of thermal energy emitter 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.

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.

SI radiometry units

SI radiometry units

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol	Symbol
Radiant energy	Qe	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	watt	W or J/s	M⋅L2⋅T−3	Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power".
Spectral flux	Φe,ν or Φe,λ	watt per hertz or watt per metre	W/Hz or W/m	M⋅L2⋅T−2 or M⋅L⋅T−3	Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1.
Radiant intensity	Ie,Ω	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 or Ie,Ω,λ	watt per steradian per hertz or watt per steradian per metre	W⋅sr−1⋅Hz−1 or W⋅sr−1⋅m−1	M⋅L2⋅T−2 or M⋅L⋅T−3	Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity.
Radiance	Le,Ω	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 or Le,Ω,λ	watt per steradian per square metre per hertz or watt per steradian per square metre, per metre	W⋅sr−1⋅m−2⋅Hz−1 or W⋅sr−1⋅m−3	M⋅T−2 or M⋅L−1⋅T−3	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".
Irradiance	Ee	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	Ee,ν or Ee,λ	watt per square metre per hertz or watt per square metre, per metre	W⋅m−2⋅Hz−1 or W/m3	M⋅T−2 or M⋅L−1⋅T−3	Irradiance of a surface per unit frequency or wavelength. The terms spectral flux density or more confusingly "spectral intensity" are also used. Non-SI units of spectral irradiance include Jansky = 10−26 W⋅m−2⋅Hz−1 and solar flux unit (1SFU = 10−22 W⋅m−2⋅Hz−1).
Radiosity	Je	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 or Je,λ	watt per square metre per hertz or watt per square metre, per metre	W⋅m−2⋅Hz−1 or W/m3	M⋅T−2 or M⋅L−1⋅T−3	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".
Radiant exitance	Me	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 or Me,λ	watt per square metre per hertz or watt per square metre, per metre	W⋅m−2⋅Hz−1 or W/m3	M⋅T−2 or M⋅L−1⋅T−3	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".
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 or He,λ	joule per square metre per hertz or joule per square metre, per metre	J⋅m−2⋅Hz−1 or J/m3	M⋅T−1 or M⋅L−1⋅T−2	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".
Hemispherical emissivity	ε			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			1	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	εΩ			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			1	Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.
Hemispherical absorptance	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			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			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			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			1	Radiant flux reflected by a surface, divided by that received by that surface.
Spectral hemispherical reflectance	Rν or Rλ			1	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	RΩ			1	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	RΩ,ν or RΩ,λ			1	Spectral radiance reflected by a surface, divided by that received by that surface.
Hemispherical transmittance	T			1	Radiant flux transmitted by a surface, divided by that received by that surface.
Spectral hemispherical transmittance	Tν or Tλ			1	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	TΩ			1	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	TΩ,ν or TΩ,λ			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

See also

• Albedo
• Stefan–Boltzmann law
• Radiant barrier
• Reflectivity
• Form factor (radiative transfer)
• Sakuma–Hattori equation
• Wien's displacement law

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).