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6000 K Industrial Sensors and Contr ol 335
10 4 3 2 4000 K
Radiation intensity (W/cm 2 · mm) 10 –1 1 1 2000 K 1000 K 500 K
10
10
10

–2
10
10
–4
10 –3 300 K
0.4 0.6 0.8 1 2 4 6 8 10 20 30
Wavelength (mm)
FIGURE 7.7 Spectral distribution of blackbody radiation.

energy from a blackbody is proportional to the fourth power of abso-
lute temperature and is expressed as:

W = σ T 4 (7.2)
t
where σ is the Stefan-Boltzmann constant and has the value of
–8
5.6697 × 10 W/m ?K .
4
2
The wavelength at which the radiated energy has its highest value
is given by Wien’s displacement law,
×
.
−3
h
λ T = 2 8978 10 m K (7.3)
m
Thus, the absolute temperature can be measured by analyzing
the intensity of the spectrum of the radiated energy from a blackbody.
A source of measurement error is the emissivity of the object, which
depends on the material and its surface condition. Other causes of error
are deviation from the required measurement distance and the pres-
ence of any absorbing medium between the object and the detector.
Use of optical fibers as signal transmission lines in pyrometers
allows remote sensing over long distances, easy installation, and
accurate determination of the position to be measured by observation
of a focused beam of visible light from the fiber end to the object. The
sensing head consists of a flexible bundle with a large number of sin-
gle fibers and lens optics to pick up the radiated energy (Fig. 7.8).
The use of a single silica fiber instead of a bundle is advantageous
for measuring small objects and longer distance transmission of the
picked-up radiated light. The lowest measurable temperature is
500°C, because of the unavoidable optical loss in silica fibers at wave-
lengths longer than 2 μm. Air cooling of the sensing head is usually
necessary when the temperature exceeds 1000°C.