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 Title: Radiant energy density Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

In radiometry, radiant energy density is the measure of the amount of radiant energy per unit volume at a given location and time. Its SI unit is joule per cubic metre (J/m3).

It is defined by

w = \frac{\mathrm{d}W}{\mathrm{d}V},

where

w is the radiant energy density,
W is the amount of radiant energy in some volume,
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 expressed by radiant flux density, whose value is

I_\mathrm{e} = c w,

where

I_\mathrm{e} is the radiant flux density (i.e. radiant flux per unit area),
c is the speed of light (generally radiation propagation speed),
w 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

L_\mathrm{e} = \frac{c}{4\pi} w.

Radiant exitance through a small opening from such cavity is M_\mathrm{e} = \pi L_\mathrm{e}. These relations can be used for example in the black body radiation equations derivation.