Radiant energy density
In radiometry, radiant energy density is the measure of the amount of radiant energy per unit volume at a given location and time.^{[1]} Its SI unit is joule per cubic metre (J/m^{3}).
It is defined by
where
Relation to other radiometric quantities
Because radiation always transmits the energy,^{[2]} it is useful to wonder what the speed of the transmission is. If all the radiation at given location propagates in the same direction, then the radiant flux through a unit area perpendicular to the propagation direction is expressed by radiant flux density, whose value is
where
- is the radiant flux density (i.e. radiant flux per unit area),
- is the speed of light (generally radiation propagation speed),
- is the radiant energy density.
Contrarily if the radiation intensity is equal in all directions, like in a cavity in a thermodynamic equilibrium, then the energy transmition is best described by radiance (i.e. radiant flux per unit area and unit solid angle), whose value is
Radiant exitance through a small opening from such cavity is .^{[4]} These relations can be used for example in the black body radiation equations derivation.
References
- ↑ IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Radiant energy density. Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.R05040. Last update: 2012-08-19; version: 2.3.2. Visited 2013-10-07.
- ↑ ^{2.0} ^{2.1} ^{2.2} Karel Rusňák. Přenos energie elektromagnetickým vlněním. Department of Physics, Faculty of Applied Sciences, University of West Bohemia. 2005-11. Visited 2013-10-06
- ↑ Max Plack. The Theory of Heat Radiation. Equation 21. 1914.
- ↑ Max Plack. The Theory of Heat Radiation. Equation 7. 1914.
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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 | |||
Radiant flux | Φ_{e}^{[nb 2]} | watt | W or J/s | M⋅L^{2}⋅T^{−3} | radiant energy per unit time, also called radiant power. | |||
Spectral power | Φ_{eλ}^{[nb 2]}^{[nb 3]} | watt per metre | W⋅m^{−1} | M⋅L⋅T^{−3} | radiant power per wavelength. | |||
Radiant intensity | I_{e} | watt per steradian | W⋅sr^{−1} | M⋅L^{2}⋅T^{−3} | power per unit solid angle. | |||
Spectral intensity | I_{eλ}^{[nb 3]} | watt per steradian per metre | W⋅sr^{−1}⋅m^{−1} | M⋅L⋅T^{−3} | radiant intensity per wavelength. | |||
Radiance | L_{e} | watt per steradian per square metre | W⋅sr^{−1}⋅m^{−2} | M⋅T^{−3} | power per unit solid angle per unit projected source area. confusingly called "intensity" in some other fields of study. | |||
Spectral radiance | L_{eλ}^{[nb 3]} or L_{eν}^{[nb 4]} |
watt per steradian per metre^{3} or watt per steradian per square |
W⋅sr^{−1}⋅m^{−3} or W⋅sr^{−1}⋅m^{−2}⋅Hz^{−1} |
M⋅L^{−1}⋅T^{−3} or M⋅T^{−2} |
commonly measured in W⋅sr^{−1}⋅m^{−2}⋅nm^{−1} with surface area and either wavelength or frequency. | |||
Irradiance | E_{e}^{[nb 2]} | watt per square metre | W⋅m^{−2} | M⋅T^{−3} | power incident on a surface, also called radiant flux density. sometimes confusingly called "intensity" as well. | |||
Spectral irradiance | E_{eλ}^{[nb 3]} or E_{eν}^{[nb 4]} |
watt per metre^{3} or watt per square metre per hertz |
W⋅m^{−3} or W⋅m^{−2}⋅Hz^{−1} |
M⋅L^{−1}⋅T^{−3} or M⋅T^{−2} |
commonly measured in W⋅m^{−2}⋅nm^{−1} or 10^{−22} W⋅m^{−2}⋅Hz^{−1}, known as solar flux unit.^{[nb 5]} | |||
Radiant exitance / Radiant emittance |
M_{e}^{[nb 2]} | watt per square metre | W⋅m^{−2} | M⋅T^{−3} | power emitted from a surface. | |||
Spectral radiant exitance / Spectral radiant emittance |
M_{eλ}^{[nb 3]} or M_{eν}^{[nb 4]} |
watt per metre^{3} or watt per square |
W⋅m^{−3} or W⋅m^{−2}⋅Hz^{−1} |
M⋅L^{−1}⋅T^{−3} or M⋅T^{−2} |
power emitted from a surface per unit wavelength or frequency. | |||
Radiosity | J_{e} | watt per square metre | W⋅m^{−2} | M⋅T^{−3} | emitted plus reflected power leaving a surface. | |||
Spectral radiosity | J_{eλ}^{[nb 3]} | watt per metre^{3} | W⋅m^{−3} | M⋅L^{−1}⋅T^{−3} | emitted plus reflected power leaving a surface per unit wavelength | |||
Radiant exposure | H_{e} | joule per square metre | J⋅m^{−2} | M⋅T^{−2} | also referred to as fluence | |||
Radiant energy density | ω_{e} | joule per metre^{3} | J⋅m^{−3} | M⋅L^{−1}⋅T^{−2} | ||||
See also: SITemplate:· RadiometryTemplate:· Photometry |
- ↑ Standards organizations recommend that radiometric quantities should be denoted with a suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} ^{2.4} Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant emittance.
- ↑ ^{3.0} ^{3.1} ^{3.2} ^{3.3} ^{3.4} ^{3.5} Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
- ↑ ^{4.0} ^{4.1} ^{4.2} Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
- ↑ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).