In
radiometry
Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as opposed to phot ...
, radiant energy density is the
radiant energy
Radiant may refer to:
Computers, software, and video games
* Radiant (software), a content management system
* GtkRadiant, a level editor created by id Software for their games
* Radiant AI, a technology developed by Bethesda Softworks for ''The ...
per unit
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
.
The
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
of radiant
energy density
In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or .
Often only the ''useful'' or extract ...
is the
joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
per
cubic metre
The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is m ...
(J/m
3).
Mathematical definition
Radiant energy density, denoted ''w''
e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as
[Karel Rusňák]
Přenos energie elektromagnetickým vlněním
Department of Physics, Faculty of Applied Sciences, University of West Bohemia
The University of West Bohemia ( cs, Západočeská univerzita v Plzni, ZČU) is a university in Plzeň, Czech Republic. It was founded in 1991 and consists of nine faculties.
History
The university was formed by the merger of the ''College of Me ...
. 2005-11. Visited 2013-10-06
:
where
*∂ is the
partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Part ...
symbol;
*''Q''
e 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 In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
:
:
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
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...
, then the energy transmission is best described by
radiance
In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiatio ...
:
:
Radiant exitance
In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether ...
through a small opening from such a cavity is:
[Max Planck]
The Theory of Heat Radiation
Equation 7. 1914.
:
These relations can be used for example in the
black-body radiation
Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spect ...
equation's derivation.
SI radiometry units
References
{{reflist
Physical quantities
Radiometry