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:
Hemispherical emissivity of a surface, denoted ?, is defined as^{[8]}
where
Spectral hemispherical emissivity in frequency and spectral hemispherical emissivity in wavelength of a surface, denoted ?_{?} and ?_{?} respectively, are defined as^{[8]}
where
Directional emissivity of a surface, denoted ?_{?}, is defined as^{[8]}
where
Spectral directional emissivity in frequency and spectral directional emissivity in wavelength of a surface, denoted ?_{?,?} and ?_{?,?} respectively, are defined as^{[8]}
where
Emissivities ? 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} metres.^{[9]} Visible light has a wavelength range of about 0.4 to 0.7×10^{-6} metres 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]}
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. MoSi_{2} or WSi_{2}) | 0.86 to 0.93 |
Water, pure | 0.96 |
Notes:
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} metres, 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.
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 (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 Plancks 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 1273 K, will emit 97% of its energy at wavelengths below 14 ?m.^{[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]}
Quantity | Unit | Dimension | Notes | |||||
---|---|---|---|---|---|---|---|---|
Name | Symbol^{[nb 1]} | Name | Symbol | Symbol | ||||
Radiant energy | Q_{e}^{[nb 2]} | joule | J | M?L^{2}?T^{-2} | Energy of electromagnetic radiation. | |||
Radiant energy density | w_{e} | joule per cubic metre | J/m^{3} | M?L^{-1}?T^{-2} | Radiant energy per unit volume. | |||
Radiant flux | ?_{e}^{[nb 2]} | watt | W = J/s | M?L^{2}?T^{-3} | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power". | |||
Spectral flux | ?_{e,?}^{[nb 3]} | watt per hertz | W/Hz | M?L^{2}?T^{-2} | Radiant flux per unit frequency or wavelength. The latter is commonly measured in W?nm^{-1}. | |||
?_{e,?}^{[nb 4]} | watt per metre | W/m | M?L?T^{-3} | |||||
Radiant intensity | I_{e,?}^{[nb 5]} | watt per steradian | W/sr | M?L^{2}?T^{-3} | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. | |||
Spectral intensity | I_{e,?,?}^{[nb 3]} | watt per steradian per hertz | W?sr^{-1}?Hz^{-1} | M?L^{2}?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. | |||
I_{e,?,?}^{[nb 4]} | watt per steradian per metre | W?sr^{-1}?m^{-1} | M?L?T^{-3} | |||||
Radiance | L_{e,?}^{[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 | L_{e,?,?}^{[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". | |||
L_{e,?,?}^{[nb 4]} | watt per steradian per square metre, per metre | W?sr^{-1}?m^{-3} | M?L^{-1}?T^{-3} | |||||
Irradiance Flux density |
E_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M?T^{-3} | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral irradiance Spectral flux density |
E_{e,?}^{[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} = 10^{4} Jy). | |||
E_{e,?}^{[nb 4]} | watt per square metre, per metre | W/m^{3} | M?L^{-1}?T^{-3} | |||||
Radiosity | J_{e}^{[nb 2]} | watt per square metre | W/m^{2} | 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 | J_{e,?}^{[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". | |||
J_{e,?}^{[nb 4]} | watt per square metre, per metre | W/m^{3} | M?L^{-1}?T^{-3} | |||||
Radiant exitance | M_{e}^{[nb 2]} | watt per square metre | W/m^{2} | 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 | M_{e,?}^{[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". | |||
M_{e,?}^{[nb 4]} | watt per square metre, per metre | W/m^{3} | M?L^{-1}?T^{-3} | |||||
Radiant exposure | H_{e} | joule per square metre | J/m^{2} | 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 | H_{e,?}^{[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". | |||
H_{e,?}^{[nb 4]} | joule per square metre, per metre | J/m^{3} | M?L^{-1}?T^{-2} | |||||
Hemispherical emissivity | ? | 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 | ?_{?} or ?_{?} |
N/A | 1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
Directional emissivity | ?_{?} | 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 | ?_{?,?} or ?_{?,?} |
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 | A_{?} or A_{?} |
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 | A_{?} | 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 | A_{?,?} or A_{?,?} |
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 | R_{?} or R_{?} |
N/A | 1 | Spectral flux reflected by a surface, divided by that received by that surface. | ||||
Directional reflectance | R_{?} | N/A | 1 | Radiance reflected by a surface, divided by that received by that surface. | ||||
Spectral directional reflectance | R_{?,?} or R_{?,?} |
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 | T_{?} or T_{?} |
N/A | 1 | Spectral flux transmitted by a surface, divided by that received by that surface. | ||||
Directional transmittance | T_{?} | N/A | 1 | Radiance transmitted by a surface, divided by that received by that surface. | ||||
Spectral directional transmittance | T_{?,?} or T_{?,?} |
N/A | 1 | Spectral radiance transmitted by a surface, divided by that received by that surface. | ||||
Hemispherical attenuation coefficient | ? | 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 | ?_{?} or ?_{?} |
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 | ?_{?} | 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 | ?_{?,?} or ?_{?,?} |
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 |