Campbell Scientific IRGASON IRGASON Integrated CO2/H2O Open-Path Gas Analyzer - Page 59

Appendix B. Equations

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Appendix B. Equations TABLE B-1 lists variables and constants used in the following equations. TABLE B-1. Table of Equation Variables and Constants Variable or Constant ρ c ρ v ρ d X c X v M c M d M v P R T e f T d Td _ tmp Description CO2 Mass Density H2O Mass Density Mass Density of Dry Air CO2 Molar Mixing Ratio (concentration relative to dry air) H2O Molar Mixing Ratio (concentration relative to dry air) Molecular Weight of CO2 Molecular weight of dry air Molecular weight of H2O Ambient Pressure Universal Gas Constant Ambient Temperature Vapor Pressure Enhancement Factor Dew Point Temperature Temporary variable for dew point calculation Units mg·m-3 g·m-3 g·m-3 µmol·mol-1 mmol·mol-1 44 mg·mmol-1 0.029 g·mmol-1 0.018 g·mmol-1 kPa 8.3143×10-6 kPa·m3·K-1·mmol-1 oC kPa Arbitrary oC Arbitrary Mass Density from Molar Mixing Ratios ρc = XcMc 106  R(T + P 273.15) − ρv Mv  ρ v = R(T + X v PM v 273.15)(1000 + Xv) ρ d = (P − e)M d R(T + 273.15) ρ d =  P − XvP 1000 + X v M d R(T + 273.15) (B-11) (B-21) (B-3) (B-4) B-1

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Appendix B. Equations
TABLE B-1 lists variables and constants used in the following equations.
TABLE B-1.
Table of Equation Variables and Constants
Variable or Constant
Description
Units
c
ρ
CO
2
Mass Density
mg
·
m
-3
v
ρ
H
2
O Mass Density
g
·
m
-3
d
ρ
Mass Density of Dry Air
g
·
m
-3
c
X
CO
2
Molar Mixing Ratio
(concentration relative to dry air)
µmol
·
mol
-1
v
X
H
2
O Molar Mixing Ratio
(concentration relative to dry air)
mmol
·
mol
-1
c
M
Molecular Weight of CO
2
44 mg
·
mmol
-1
d
M
Molecular weight of dry air
0.029 g
·
mmol
-1
v
M
Molecular weight of H
2
O
0.018 g
·
mmol
-1
P
Ambient Pressure
kPa
R
Universal Gas Constant
8.3143×10
–6
kPa·m
3
·K
-1
·mmol
-1
T
Ambient Temperature
o
C
e
Vapor Pressure
kPa
f
Enhancement Factor
Arbitrary
d
T
Dew Point Temperature
o
C
tmp
d
T
_
Temporary variable for dew point
calculation
Arbitrary
Mass Density from Molar Mixing Ratios
(
)
+
=
v
v
c
c
c
M
T
R
P
M
X
ρ
ρ
15
.
273
10
6
(B-1
1
)
(
)(
)
v
v
v
v
X
T
R
PM
X
+
+
=
1000
15
.
273
ρ
(B-2
1
)
(
)
(
)
15
.
273
+
=
T
R
M
e
P
d
d
ρ
(B-3)
(
)
15
.
273
1000
+
+
=
T
R
M
X
P
X
P
d
v
v
d
ρ
(B-4)
B-1