1. Physical Basics
Radiation principles (1/2)
Radiation principles are important for the understanding of thermal radiation which is emitted by any object depending on its temperature and also its material properties. Efficiencies of absorbance and emission of radiation are material properties which need consideration here and their dependence on each other is given by Kirchhoff’s law.
The temperature dependence of emitted radiation follows the Stefan-Boltzmann law. Radiation is emitted in the form of electromagnetic waves, their intensity being a function of the wavelength. The emission maximum of thermal radiation is explained by Wien’s displacement law, while the shape of the entire emission spectrum is given by Planck’s law.
Kirchhoff’s law
The emission efficiency ε denotes the efficiency of an object to emit thermal radiation, a quantity varying between 0 (no emission at all) and 1 (highest possible emission). The absorption efficiency α of an object denotes its efficiency to absorb incident radiation. It is defined as
and varies between 0 and 1, whereby 1 corresponds to total absorption and 0 to total reflection or transmission.
Kirchhoff’s law, found in 1859, states:
the efficiencies of absorption and emission of an object are the same. Therefore, objects which absorb all incident radiation (α=1) have highest thermal emission efficiency (ε=1). They are denoted as black body emitters, where the term black indicates that there is no reflected radiation. Objects which absorb a fraction of the incident radiation only (α<1) are denoted as grey body emitters.
Absorption and emission efficiencies are wavelength dependent in case of a selective emitter. High or low absorption efficiencies of an object in different spectral ranges go along with high or low emission efficiencies in the same spectral ranges. Therefore, a generalised Kirchhoff'’s law can be written as:
Source: Beckel 2007
Stefan-Boltzmann law
This law theoretically found by Josef Stefan in 1879 and experimentally confirmed by Ludwig Boltzmann in 1884 explains the temperature dependence of the intensity of thermal radiation emitted by an object. It increases strongly with increasing absolute temperature T given in Kelvin (K). The radiant exitance M, which is the radiative power emitted by the surface of an object and given in units of W/(m2) is:
with the Stefan-Boltzmann constant σ=5.7·10-8 W/(m2K). For example, increasing the absolute temperature of an object by a factor of two results in a 16 times stronger emission of thermal radiation.
This temperature change is also connected with a changing emission spectrum, which is explained by Planck’s law (see on the following page).
