[9.3.2 — Wien’s displacement law]
ThermaCAM™ PM575/595 Operator’s Manual
54
9.3.2 Wien’s displacement law
By differentiating Planck’s formula with respect to
λ, and finding the maximum, we
have:
This is Wien’s formula, which expresses mathematically the common observation
that colours vary from red to orange or yellow as the temperature of a thermal radi-
ator increases. The wavelength of the colour is the same as the wavelength calcu-
lated for
λ
max
. A good approximation of the value of λ
max
for a given blackbody
temperature is obtained by applying the rule-of-thumb (3 000 K). Thus, a very hot
star such as Sirius (11 000 K), emitting bluish-white light, radiates with the peak
of spectral radiant emittance occurring within the invisible ultraviolet spectrum, at
wavelength 0.27 µm.
The sun (approx. 6 000 K) emits yellow light, peaking at about 0.5 µm in the mid-
dle of the visible light spectrum.
At room temperature (300 K) the peak of radiant emittance lies at 9.7 µm, in the
far infrared, while at the temperature of liquid nitrogen (77 K) the maximum of the
almost insignificant amount of radiant emittance occurs at 38 µm, in the extreme
infrared wavelengths.
λ
max
2898
------------µm[]=
Figure 9.3 Planckian curves plotted
on semi-log scales from 100 K to
1000 K. The dotted line represents
the locus of maximum radiant emit-
tance at each temperature as
described by Wien's displacement
law.
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