Page 317 - Introduction to chemical reaction engineering and kinetics

298 Chapter 12: Batch Reactors (BR)
The rate of heat transfer, & whether it is an input or output, may be expressed as:

cj = lJA,(T, - T), (12.3-8)
where U = the overall heat transfer coefficient, J mP2 s-l K’ or W m-*
K- 1 , obtained experimentally or from an appropriate correlation;
A, = the area of the heating or cooling coil, m*;
T, = the temperature of the coil, K (not necessarily constant with re-
spect to position or time);
(T, - T), = the appropriate mean temperature difference AT,,, for heat trans-
fer (question: what is the interpretation of the form of AT,,, for a
BR?).

If 0 > 0 (T, > T), the heat transfer is an input (to the reacting system), and the converse
applies if cj < 0.
There may also be a significant input or output because of the energetics of the reac-
tion. An exothermic reaction implies a generation (an input) of energy. An endothermic
reaction implies a loss (an output) of energy. The rate of generation or loss is the prod-
uct of the energy of reaction and the (extensive) rate of reaction. The energy of reaction
is represented by the enthalpy of reaction (AH~) for a constant-pressure process, and
by the internal energy (AU,) for a constant-volume (or constant-density) process. For
a reaction represented by equation 12.3-1, with both the energy and rate of reaction in
terms of reactant A, then

rate of generation or loss of energy by reaction = (-AH,,)( -rA)V or (-AU&( -rA)V
(12.3-9)

Whether equation 12.3-9 represents an input or output depends on the sign of AHRA
(or AU,*). If AH,, > 0 (endothermic reaction), it is an output (negative; recall that
(-t-J is positive); if AH,, < 0 (exothermic reaction), it is an input.
Since equation 12.3-7 represents an enthalpy (or internal energy) balance, the rate
of accumulation of energy is the rate of change of enthalpy, H (or internal energy, U)
of the reacting system:

rate of accumulation = dHldt
= n,C,dTldt (12.3-10)
= m,cpdTldt (12.341)

where nt is the total number of moles, including moles of inert substances:

N
nt = 2 ni (12.3-12)
i = l
C, is the (total) molar heat capacity of the system at constant pressure, usually approx-
imated, as though for an ideal solution, by1

(12.3-13)
i=l
‘For a nonideal solution, Cpi is replaced by the partial molar heat capacity, c’pi, but such information may not
be available.