Wien's Displacement Law; Figure 18.4 Blackbody Spectral Radiant Emittance According To Planck's Law, Plotted For Various Absolute Temperatures. 1: Spectral Radiant Emittance - FLIR ThermaCAM P20 Operator's Manual

18.3 – Blackbody radiation
λ
NOTE: The factor 10
factor is excluded, the dimension will be Watt/m
Planck's formula, when plotted graphically for various temperatures, produces a
family of curves. Following any particular Planck curve, the spectral emittance is
zero at λ = 0, then increases rapidly to a maximum at a wavelength λ
passing it approaches zero again at very long wavelengths. The higher the tem-
perature, the shorter the wavelength at which maximum occurs.
10327103;3
Figure 18.4 Blackbody spectral radiant emittance according to Planck's law, plotted for various absolute
temperatures. 1: Spectral radiant emittance (W/cm
18.3.2

Wien's displacement law

By differentiating Planck's formula with respect to λ, and finding the maximum,
we have:
This is Wien's formula (after Wilhelm Wien, 1864–1928), which expresses mathe-
matically the common observation that colors vary from red to orange or yellow
as the temperature of a thermal radiator increases. The wavelength of the color
is the same as the wavelength calculated for λ
value of λ
for a given blackbody temperature is obtained by applying the rule-
max
90
Wavelength (μm).
-6
is used since spectral emittance in the curves is expressed in Watt/m
2
μm.
2 3
× 10 (μm)); 2: Wavelength (μm)
. A good approximation of the
max
Publ. No. 1 557 536 Rev. a35 – ENGLISH (EN) – January 20, 2004
2
m. If the
and after
max