Section 3
3-8
Theory of Operation
3.5 Pressure Broadening Due to Water Vapor
Water vapor can influence infrared detection of CO
2
in three ways:
1) direct absorption in the CO
2
waveband of interest, 2) dilution, and 3)
pressure broadening. Direct infrared absorption by water vapor can be
virtually eliminated by judicious choice of wavebands and filters, and
methods to correct for dilution are well known (Section 3.6); however,
pressure broadening is more of a problem.
Gas phase absorption of infrared radiation is due to energy-induced changes
in vibrational and rotational energy states. Such energy states are altered by
intermolecular collisions which increase in number as pressure increases.
The kinetic theory of gases and quantum mechanics predicts that absorption
band widths increase with pressure, and it is observed that broad band
infrared absorption increases as pressure increases at constant absorber
concentration.
Not all gases are equally effective in causing pressure-induced line
broadening. Gases that are similar are more effective than dissimilar gases.
This effect is embodied in the concept of equivalent pressure, or effective
pressure, P
e
. Total pressure P is equal to the sum of partial pressures of
component gases, while equivalent pressure is defined as
P
e
= a
1
p
1
+ a
2
p
2
+ ...
where a
i
are weighting factors representing the pressure broadening
effectiveness of each gas species relative to nitrogen (a
N
2
= 1). For CO
2
in
nitrogen P
e
= p
N
2
+ 1.3 p
CO
2
(2).
Consider a simple atmosphere made up of H
2
O vapor with pressure e, plus
dry gases with pressure P
d
, so that
P = P
d
+ e,
or, in mole fraction units,
1 = X
d
+ X
w
3-18
where X
d
is the mole fraction of all dry gases and X
w
is the water vapor
mole fraction (e/P).
The equivalent pressure will be P
e
=
Σ
a
i
p
i
+ a
w
e. In principle, P
e
will vary
with CO
2
partial pressure, but the CO
2
partial pressure is so small that it can
