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Radiant energy density
Radiant energy per unit volume From Wikipedia, the free encyclopedia
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In radiometry, radiant energy density is the radiant energy per unit volume.[1] The SI unit of radiant energy density is the joule per cubic metre (J/m3).
Mathematical definition
Radiant energy density, denoted we ("e" for "energetic", to avoid confusion with photometric quantities), is defined as[2]
where
- ∂ is the partial derivative symbol;
- Qe is the radiant energy;
- V is the volume.
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Relation to other radiometric quantities
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Perspective
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 given by the irradiance:[2]
where c is the radiation propagation speed.
Contrarily if the radiation intensity is equal in all directions, like in a cavity in a thermodynamic equilibrium, then the energy transmission is best described by radiance:[3]
Radiant exitance through a small opening from such a cavity is:[4]
These relations can be used for example in the black-body radiation equation's derivation.
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SI radiometry units
- Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- Spectral quantities given per unit wavelength are denoted with suffix "λ".
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References
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