View source for Radiant energy density

In [[radiometry]], '''radiant energy density''' is the [[radiant energy]] per unit [[volume]].<ref name=GoldBook>{{GoldBookRef|title=Radiant energy density|file= goldbook.R05040|accessdate=2015-03-15}}</ref> The [[International System of Units|SI unit]] of radiant [[energy density]] is the [[joule]] per [[cubic metre]] (J/m<sup>3</sup>).

==Mathematical definition==
'''Radiant energy density''', denoted ''w''<sub>e</sub> ("e" for "energetic", to avoid confusion with photometric quantities), is defined as<ref name="Rusňák">Karel 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</ref>
:<math>w_\mathrm{e} = \frac{\partial Q_\mathrm{e}}{\partial V},</math>
where
*∂ is the [[partial derivative]] symbol;
*''Q''<sub>e</sub> is the radiant energy;
*''V'' is the volume.

==Relation to other radiometric quantities==
Because radiation always ''transmits'' the energy,<ref name="Rusňák" /> 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]]:<ref name="Rusňák" />
:<math>E_\mathrm{e} = c w_\mathrm{e},</math>
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]]:<ref>Max Planck. [https://openlibrary.org/books/OL7154661M The Theory of Heat Radiation]. Equation 21. 1914.</ref>
:<math>L_\mathrm{e} = \frac{c}{4\pi} w_\mathrm{e}.</math>

[[Radiant exitance]] through a small opening from such a cavity is:<ref>Max Planck. [https://openlibrary.org/books/OL7154661M The Theory of Heat Radiation]. Equation 7. 1914.</ref>
:<math>M_\mathrm{e} = \pi L_\mathrm{e} = \frac{c}{4} w_\mathrm{e}.</math>
These relations can be used for example in the [[black-body radiation]] equation's derivation.

==SI radiometry units==
{{SI radiometry units}}

==References==
{{reflist}}

[[Category:Physical quantities]]
[[Category:Radiometry]]