LI-COR LI-8100A - Page 65

4-10
Theory of Operation
the chamber atmosphere and ambient atmosphere are small. But when the
gradient is not small, leaks cannot be neglected and it can be shown that the
parameters in equation (4-10) are altered to become,
a = (k + gs/v) and c
x
' = [(gs/v)c
s
' + kc
a
'] (gs/v + k)
-1
, 4-17
where k and c
a
' are the leak rate time constant and water-corrected ambient CO
2
concentration, respectively, and the expression for c
x
' replaces c
s
' in equation (4-
10). Thus, when chamber CO
2
concentrations are high, the rate constant and
asymptote will reflect leaks from the system.
Table 4-1. Definitions of the variables used in the derivations and implemented in
the LI-8100A.
Variable Description (units) LI-8100A Data File Column
v
Total Volume (m
3
)
V
Total Volume (cm
3
)
"Vtotal"
s
Total Surface Area (m
2
)
S
Total Surface Area (cm
2
)
"Area"
f
w
Water Evaporation rate (mol
m
-2
s
-1
)
p
Pressure (Pa)
P
Pressure (kPa) "Pressure"
P
o
Initial value of P Type 1 "Pressure"
T
K
Absolute temperature ((K)
T
Temperature (°C) "Tcham"
T
o
Initial value of T (°C) Type 1 "T
cham
"
R
Gas Constant (8.314 Pa m
3
(K
-1
mol
-1
)
f
c
CO
2
Flux (mol m
-2
s
-1
)
Type 2 Exponential Fit "Flux"
Type 3 Linear Fit "Flux"
F
c
CO
2
Flux (μmol m
-2
s
-1
)
C'/t
Rate of change in water
corrected CO
2
(μmol mol
-1
s
-1
or
ppm s
-1
)
Type 2 Exponential Fit
"Cdry/t"
Type 3 Linear Fit "Cdry/t"
RH
Relative Humidity (%) "RH"
w
c
Water Vapor Mole Fraction (mol
mol
-1
)
W
Water Vapor Mole Fraction
(mmol mol
-1
)
"H2O"