Thermodynamics of Bioreactions
105
the system due to the bioreaction
A ff= 2 X ( - A» * ) - Z 1'„(-A ffs )
(4.io)
'
J
The heat delivered to the surroundings, the heat of reaction
Q,
is given by:
e=Z y
.,
) - 2X (-^.,)=IX etf
(4.ii)
i
'
i
'
where
QC1
is the heat of combustion of reactant i. When the approximation
- A H ci= Qqi=
115 K *
is introduced we find:
Q =
Z
Y.,K‘
i
- Z
v
L
J
<
115 kJ (C-mole)
(4.12)
If the relation between
Qai
and K* had been exactly true (4.12) would be identical to (4.11). The
small errors introduced with (4.12) are of no importance in engineering calculations leading for
example to the design of a heat exchanger in a bioreactor - and (4.11) is not either exact: active
biomass may have a degree of reduction K from just over 4 to perhaps 4.40 and still the heat of
combustion of all biomass is set to 560 kJ (C-mole
)'1
in Table 4.3.
Since the reference level for
Qc
as well as for the degree of reduction of an element is arbitrary one
may just as well apply
instead of K, in (4.
1
2). Thus (4.12) and (4.13) gives identical values for
Q
Q =
•115 kJ (C-mole
)*1
(4.13)
It is perhaps convenient to work with only one set of degrees of reduction and (4.13) may be
mnemotechnically easier to apply than (4.12).
If
Yw
is determined by a degree of reduction balance
H
W
. - Z ^ . - Z ^
(4.14)
i
then (4.13) is identical to (4.15), which is very easy to use for aerobic processes when
YK
is a
calculated quantity:
Q = 4
• 115
Y„ =
460
Yio
kJ (C-mole
) 1
(4.15)
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