Absorptance

Last updated May 05, 2023

In the study of heat transfer, absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power.^[1]

Mathematical definitions

Hemispherical absorptance

Hemispherical absorptance of a surface, denoted $A$ is defined as^[2]

A=\mathrm {\frac {\Phi _{e}^{a}}{\Phi _{e}^{i}}} ,

where

$\mathrm {\Phi _{e}^{a}}$ is the radiant flux absorbed by that surface;
$\mathrm {\Phi _{e}^{i}}$ is the radiant flux received by that surface.

Spectral hemispherical absorptance

Spectral hemispherical absorptance in frequency and spectral hemispherical absorptance in wavelength of a surface, denoted $A ν$ and $A λ$ respectively, are defined as^[2]

{\begin{aligned}A_{\nu }&=\mathrm {\frac {\Phi _{e,\nu }^{a}}{\Phi _{e,\nu }^{i}}} ,\\A_{\lambda }&=\mathrm {\frac {\Phi _{e,\lambda }^{a}}{\Phi _{e,\lambda }^{i}}} ,\end{aligned}}

where

$\mathrm {\Phi _{e,\nu }^{a}}$ is the spectral radiant flux in frequency absorbed by that surface;
$\mathrm {\Phi _{e,\nu }^{i}}$ is the spectral radiant flux in frequency received by that surface;
$\mathrm {\Phi _{e,\lambda }^{a}}$ is the spectral radiant flux in wavelength absorbed by that surface;
$\mathrm {\Phi _{e,\lambda }^{i}}$ is the spectral radiant flux in wavelength received by that surface.

Directional absorptance

Directional absorptance of a surface, denoted $A Ω$ , is defined as^[2]

A_{\Omega }={\frac {L_{\mathrm {\mathrm {e} ,\Omega } }^{\mathrm {a} }}{L_{\mathrm {e} ,\Omega }^{\mathrm {i} }}},

where

$L\mathrm {_{e,\Omega }^{a}}$ is the radiance absorbed by that surface;
$L\mathrm {_{e,\Omega }^{i}}$ is the radiance received by that surface.

Spectral directional absorptance

Spectral directional absorptance in frequency and spectral directional absorptance in wavelength of a surface, denoted $A ν,Ω$ and $A λ,Ω$ respectively, are defined as^[2]

{\begin{aligned}A_{\nu ,\Omega }&={\frac {L\mathrm {_{e,\Omega ,\nu }^{a}} }{L\mathrm {_{e,\Omega ,\nu }^{i}} }},\\[4pt]A_{\lambda ,\Omega }&={\frac {L\mathrm {_{e,\Omega ,\lambda }^{a}} }{L\mathrm {_{e,\Omega ,\lambda }^{i}} }},\end{aligned}}

where

$L\mathrm {_{e,\Omega ,\nu }^{a}}$ is the spectral radiance in frequency absorbed by that surface;
$L\mathrm {_{e,\Omega ,\nu }^{i}}$ is the spectral radiance received by that surface;
$L\mathrm {_{e,\Omega ,\lambda }^{a}}$ is the spectral radiance in wavelength absorbed by that surface;
$L\mathrm {_{e,\Omega ,\lambda }^{i}}$ is the spectral radiance in wavelength received by that surface.

Other radiometric coefficients

Radiometry coefficients
v
t
e
Quantity		SI units	Notes
Name	Sym.	SI units	Notes
Hemispherical emissivity	$ε$	—	Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface.
Spectral hemispherical emissivity	$ε ν$ $ε λ$	—	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	$ε Ω$	—	Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface.
Spectral directional emissivity	$ε Ω, ν$ $ε Ω, λ$	—	Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.
Hemispherical absorptance	$A$	—	Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance".
Spectral hemispherical absorptance	$A ν$ $A λ$	—	Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance	$A Ω$	—	Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".
Spectral directional absorptance	$A Ω, ν$ $A Ω, λ$	—	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	$R$	—	Radiant flux reflected by a surface, divided by that received by that surface.
Spectral hemispherical reflectance	$R ν$ $R λ$	—	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	$R Ω$	—	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	$R Ω, ν$ $R Ω, λ$	—	Spectral radiance reflected by a surface, divided by that received by that surface.
Hemispherical transmittance	$T$	—	Radiant flux transmitted by a surface, divided by that received by that surface.
Spectral hemispherical transmittance	$T ν$ $T λ$	—	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	$T Ω$	—	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	$T Ω,ν$ $T Ω, λ$	—	Spectral radiance transmitted by a surface, divided by that received by that surface.
Hemispherical attenuation coefficient	$μ$	m⁻¹	Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral hemispherical attenuation coefficient	$μ ν$ $μ λ$	m⁻¹	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Directional attenuation coefficient	$μ Ω$	m⁻¹	Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient	$μ Ω, ν$ $μ Ω, λ$	m⁻¹	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.

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Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.

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In radiometry, radiosity is the radiant flux leaving a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiosity is the watt per square metre, while that of spectral radiosity in frequency is the watt per square metre per hertz (W·m⁻²·Hz⁻¹) and that of spectral radiosity in wavelength is the watt per square metre per metre (W·m⁻³)—commonly the watt per square metre per nanometre. The CGS unit erg per square centimeter per second is often used in astronomy. Radiosity is often called intensity in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.

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The Elliott formula describes analytically, or with few adjustable parameters such as the dephasing constant, the light absorption or emission spectra of solids. It was originally derived by Roger James Elliott to describe linear absorption based on properties of a single electron–hole pair. The analysis can be extended to a many-body investigation with full predictive powers when all parameters are computed microscopically using, e.g., the semiconductor Bloch equations or the semiconductor luminescence equations.

References

↑ IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " Absorptance ". doi : 10.1351/goldbook.A00035
1 2 3 4 "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.

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[GoldBook-1] IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " Absorptance ". doi : 10.1351/goldbook.A00035

[ISO_9288-1989-2] 1 2 3 4 "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.

[1]

[2]

Absorptance

Contents

Mathematical definitions

Hemispherical absorptance

Spectral hemispherical absorptance

Directional absorptance

Spectral directional absorptance

Other radiometric coefficients

Related Research Articles

References