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
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)