Radiant energy density
{{Short description|Radiant energy per unit volume}}
In radiometry, radiant energy density is the radiant energy per unit volume.{{GoldBookRef|title=Radiant energy density|file= goldbook.R05040|accessdate=2015-03-15}} 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 asKarel Rusňák. [http://www.kfy.zcu.cz/dokumenty/FYA2/prenos.en.elmg.vln.pdf Přenos energie elektromagnetickým vlněním]. Department of Physics, Faculty of Applied Sciences, University of West Bohemia. 2005-11. Visited 2013-10-06
:
where
- ∂ is the partial derivative symbol;
- Qe is the radiant energy;
- V is the volume.
Relation to other radiometric quantities
Because radiation always transmits the energy, 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:
:
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:Max Planck. [https://openlibrary.org/books/OL7154661M The Theory of Heat Radiation]. Equation 21. 1914.
:
Radiant exitance through a small opening from such a cavity is:Max Planck. [https://openlibrary.org/books/OL7154661M The Theory of Heat Radiation]. Equation 7. 1914.
:
These relations can be used for example in the black-body radiation equation's derivation.
SI radiometry units
{{SI radiometry units}}