CODEL
OPS. 141 64
Issue : A
Revision : 1
Date : 14/06/18
Doc i/d : 0141/6
050028
Extinction Coefficient and Beer Lambert Relationship
The attenuation of light of a narrow waveband - such as visible or photopic light
by fine particulate matter is very specific and is expressed mathematically by
the Beer Lambert Relationship :
Transmittance T = exp (-k.n.a.l)
where : k is the extinction coefficient of the particles
n is the number of particles per unit volume
a is mean projected area of the particles
l is the path length through the gas
Thus Opacity = 100 [1 - exp ( -k.n.a.l)] %
The extinction coefficient k determines precisely how much light is attenuated
by the particles and depends totally on the physical and chemical nature of the
particles. For a given flue gas, the particulate type and size distribution should
be relatively constant so that the opacity measurement may, for a given path
length l, be related to the particulate concentration n.
Optical Density & Extinction
Optical density and Extinction are different names for the same parameter. This
parameter is useful in that assuming the nature and size distribution of the
particles are constant, for a given path length, it is directly proportional to the
particulate concentration n, and hence to particulate mass emission.
Optical density is expressed :
Optical Density = log
10
1/T
and, since T = exp (-k.n.a.l),
Optical density = k.n.a.l log
e
10
The following table provides a simple conversion from measurements in terms
of opacity or transmittance to optical density/extinction.
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