Wien's Displacement Law - FLIR EX series User Manual

17
Theory of thermography
W
λb
c
h
k
T
λ
NOTE
-6
The factor 10 is used since spectral emittance in the curves is expressed in 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
proaches zero again at very long wavelengths. The higher the temperature, the shorter
the wavelength at which maximum occurs.
Figure 17.4 Blackbody spectral radiant emittance according to Planck's law, plotted for various absolute
temperatures. 1: Spectral radiant emittance (W/cm

17.3.2 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 mathemati-
cally the common observation that colors vary from red to orange or yellow as the tem-
perature of a thermal radiator increases. The wavelength of the color is the same as the
wavelength calculated for λ
blackbody temperature is obtained by applying the rule-of-thumb 3 000/T μm. 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 wave-
length 0.27 μm.
#T559828; r.18043/22369; en-US
Blackbody spectral radiant emittance at wavelength λ.
Velocity of light = 3 × 10 8 m/s
Planck's constant = 6.6 × 10
Boltzmann's constant = 1.4 × 10
Absolute temperature (K) of a blackbody.
Wavelength (μm).
2 × 10 3 (μm)); 2: Wavelength (μm)
. A good approximation of the value of λ
max
-34 Joule sec.
-23 Joule/K.
2
, μm.
and after passing it ap-
max
for a given
max
60