Section 3
3-10
Theory of Operation
where A is total band absorption, P is total pressure (kPa), u is absorber
amount (mol m
-2
) =
ρ
L;
ρ
is mol density (mol m
-3
), and L is pathlength (m);
g is a general unspecified function.
From the ideal gas law, the absorber mole density
ρ
can be expressed as
ρ =
p
RT
=
XP
RT
3-24
where
ρ
is absorber partial pressure and X is absorber mole fraction (mol
absorber/mol air). Therefore,
u
P
XL
RT
=
3-25
Substituting equation 3-25 into 3-23 and incorporating the constants L and R
into a new function h gives
A
P
h
X
T
=
3-26
In principle, equation 3-26 can be solved for mole fraction, giving
X
h
A
P
T
=
−
1
3-27
Since LI-COR gas analyzers produce an output voltage that is proportional
to absorptance,
V=KA
3-28
substituting 3-28 into 3-27 yields
C
F V
P
P
T
T
o
o
=
3-29
where C is the CO
2
mole fraction in
µ
mol mol
-1
, and the constants K, P
o
and
T
o
are included in the general function F; P
o
= 101.3 kPa, and T
o
is the
calibration temperature in degrees Kelvin. Equation 3-29 is the fundamental
LI-COR gas analyzer calibration function, where F(x) is a polynomial. By
