Page 295 - Instrumentation Reference Book 3E

Measurement techniques: radiation thermometers 279
In practice a sighting hole in a furnace will portional to the fourth power of the tempera-
radiate as a blackbody if the furnace and its ture Kelvin of the radiator.
contents are in thermal equilibrium and provided
it does not contain a gas or flame which absorbs
or radiates preferentially in any wavelength band. 14.6.1.2 The distribution of energy in the
However, the radiation from the sighting hole spectizan: Wien 's laws
will only be blackbody radiation provided every- When a body is heated it appears to change color.
thing in the furnace is at the same temperature. This is because the total energy and distribution
When all objects in the furnace are at the same of radiant energy between the different wave-
temperature all lines of demarcation between lengths is changing as the temperature rises.
them will disappear. If a cold object is introduced When the temperature is about 500°C the body
to the furnace it will be absorbing more energy is just visibly red. As the temperature rises, the
than it is radiating; the rest of the furnace will be body becomes dull red at 700"C, cherry red at
losing more radiation than it receives. Under 900°C. orange at 1100°C. and finally white hot
these conditions the radiation will no longer be at temperatures above 1400 "C. The body appears
blackbody radiation but will be dependent upon white hot because it radiates all colors in the
the emissivity of the furnace walls. visible spectrum.
It is found that the wavelength of the radiation
Prevost's theory of exchanges Two bodies A and of the maximum intensity gets shorter as the
B in a peirfectly heat-insulated space will both be temperature rises. This is expressed in Wien's
radiating and both be absorbing radiation. IfA is displacement law:
hotter than B it will radiate more energy than B.
Therefore B will receive more energy than it radi- A,T = constant
ates and consequently its temperature will rise. By =2898ym.K (14.26)
contrast body A will lose more energy by radi-
ation than it receives so its temperature will fall. where A, is the wavelength corresponding to the
This process will continue until both bodies reach radiation of maximum intensity. and T is the
the same temperature. At that stage the heat temperature Kelvin. The actual value of the spec-
exchanged from A to B will be equal to that tral radiance at the wavelength A, is given by
exchanged from B to A. Wien's second law:
A therimometer placed in a vessel to measure
gas temperature in that vessel will; if the vessel LA, = constant x T5 (14.27)
walls are cooler than the gas, indicate a tem-
perature than the gas temperature because where LA, is the maximum value of the spectrai
it will radiate more heat to the vessel walls than radiance at any wavelength, Le., the value of the
it receive:; from them. radiance at A,, and Tis the temperature Kelvin.
The constant does not have the same value as the
Blackbo~+ radiation: Stefan-Boltzmann lw constant in equation (14.26). It is important to
The total power of radiant flux of all wavelengths realize that it is only the maximum radiance at
R emitted into the frontal hemisphere by a unit one particular wavelength which is proportional
area of a perfectly black body is proportional to to T'; the total radiance for all wavelengths is
the fourth power of the temperature Kelvin: given by the Stefan-Boltzmann law, Le.. it is pro-
portional to T4.
R = GrP (14.25) Wien deduced that the spectral concentration
of radiance, that is, the radiation emitted per unit
where CT is the Stefan-Boltzmann constant, having solid angle per unit area of a small aperture in a
an accepted value of 5.670 32 x lo-' W m-? K-4, uniform temperature enclosure in a direction nor-
and 7 is the temperature Kelvin. mal to the area in the range of wavelengths
This law is very important, as most total between A and A + SA is LA. SA where
radiation thermometers are based upon it. If a
receiving element at a temperature TI is (14.28)
arranged so that radiation from a source at a
temperature T2 falls upon it. then it will receive
heat at the rate of aT;> and emit it at a rate of where Tis the temperature Kelvin, and C1 and C,
UT;. It will, therefore, gain heat at the rate of are constants. This formula is more convenient to
G~(T: - Tf). the temperature of the receiver is use and applies with less than 1 percent deviation
If
small in comparison with that of the source, from the more refined Planck's radiation law
then Tf may be neglected in comparison with used to define IPTS-68 provided AT < 3 x
T;> and the radiant energy gained will be pro- 103rn. K.