Environmental Engineering Reference
In-Depth Information
where
M
H2O
and
M
CO2
are the molecular masses of H
2
O and CO
2
. The diffusion coef-
ficients ratio was estimated by Jørgensen and Svirezhev (2004) as
D
H2O
/
D
CO2
≈
1.32
and according to Budyko (1977):
z
CO
2
0
−
0
.
1
z
CO
2
0
.
It is also assumed that the concentration of water vapor within the leaf corre-
sponds to the saturation pressure
p
s
,
T
at temperature
T
:
z
H2OL
z
CO
2
L
≈
=
p
s
,
T
/p
0
. Thus equation
(2.4.101) can be written as:
5
.
4
p
sT
−
ϕ
0
p
s
0
p
0
z
CO
2
0
r
=
(2.4.102)
The ratio
r
is determined by the diffusion processes which control the rate of
reaction (2.4.96), accordingly to assumption (
xi
).
Energy conservation equation
for the system at instant steady state shown schemat-
ically in Figure 2.4.19 includes the energy delivered of absorbed solar radiation and
the enthalpies of carbon dioxide and liquid water. The energy increase of the system
is determined by the rates of the sugar substance and liquid water in the produced
biomass. The extracted energy consists of the enthalpies of oxygen and water vapor
as well as convective heat and emission exchanged by the leaf surface:
γ
[
α
V
j
V
+
α
L
(
j
S
−
j
V
)]
+
n
CO
2
h
CO
2
+
n
w
h
w
=
n
SU
h
SU
+
n
wL
h
w
+
n
O
2
h
O
2
+
n
H
2
O
h
H
2
O
+
q
k
+
e
L
(2.4.103)
where
α
V
and
α
L
are the absorptivities of the leaf within and beyond the PAR
wavelength range, respectively.
According to assumption (vii), the biomass is an ideal solution of sugar and water
and the total enthalpy of biomass is the sum of the respective components;
n
SU
·
h
SU
·
and
n
wL
h
w
.
The heat transferred by convection from the leaf surface to the environment is:
q
k
T
0
), where
k
is the convective heat transfer coefficient. Equation (2.4.103)
is used to calculate the unknown rate
n
SU
. The leaf temperature
T
is higher than the
environment temperature
T
0
by the difference
T, i.e.
T
=
k
·
(
T
−
=
T
0
+
T, according to
assumption (ix).
Exergy balance equation
according to the scheme (Fig. 2.4.19) is:
γ
[
α
V
b
V
+
α
L
(
b
S
−
b
V
)]
+
n
CO
2
b
CO
2
+
n
w
b
w
=
n
SU
b
SU
+
n
wL
b
w
+
n
O
2
b
O
2
+
n
H
2
O
b
H
2
O
+
b
qk
+
b
eL
+
δb
(2.4.104)
where
δb
is the total exergy loss due to the sum of every irreversibility occurring within
the system and is determined by formula (2.2.10). Again as for enthalpy, the total
exergy of biomass is the sum of the respective components;
n
SU
·
b
w
.
Perfection degrees of photosynthesis
are calculated based on the assumption that
the produced sugar represents the useful product and the feed is determined by radia-
tion, CO
2
and liquid water. Other components of the balance equations are categorized
b
SU
and
n
wL
·
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