LumaSense Technologies BoilerSpection-SD - Manual (Page 45)

BoilerSpection HD/SD Manual Principles of Thermal Imaging 45
6.3 Blackbody Radiation
Note: A blackbody is a theoretical surface, which radiates energy according to Planck's
law, and absorbs all the radiative energy it receives. It does not reflect or transmit any IR
energy. Perfect blackbody surfaces do not exist in nature.
The emissivity of a body is defined formally by the equation below as the ratio of the radiant
energy emitted by the body to the radiation, which would be emitted by a blackbody at the same
temperature.
Where,
Wo = total radiant energy emitted by a body at a given temperature T.
Wbb = total radiant energy emitted by a blackbody at the same temperature T.
If all energy falling on an object were absorbed (no transmission or reflection), the absorptivity
would equal to 1. At thermal equilibrium, all the energy absorbed could be re-radiated (emitted) so
that the emissivity of such a body would equal 1. Therefore in a blackbody,
absorptivity = emissivity = 1
Practical real life objects do not behave exactly as this ideal, but as described with transmissivity and
reflectivity,
absorptivity + transmissivity + reflectivity = 1
Planck’s Law (1)
Energy radiated from the blackbody is described as follows [“Planck’s Law”.]
Stefan Bolzmann’s equation (2)
In order to obtain total radiant emittance of the blackbody, integrate the equation (1) through all
wavelengths (0 to infinity). The result is as follows and is called “Stefan-Bolzmann equation.”
Wien’s displacement law (3)
The temperature of blackbody can be obtained directly from the radiant energy of the blackbody
by this equation. In order to find out the wavelength on the maximum spectral radiant emittance,
differentiate Planck’s law and take the value to 0. The equation is called “Wien’s displacement
law”.
Where in (1) to (3)