Page 465 - Elements of Chemical Reaction Engineering Ebook

436 Steady-State Nonisothermal Reactor Design Chap. 8

8.2.7 Variable Heat Capacities
We next want to arrive at a form of the energy balance for the case where
heat capacities are strong functions of temperature over a wide temperature range.
.Under these conditions the mean values used in Equation (8-30) may not be ade-
quate for the relationship between conversion and temperature. Combining Equa-
tion (8-23) with the quadratic form of the heat capacity, Equation (8-20),

c,, = cY.,+p,T+y,T2 (8-20)
we find that

T .
AHR,(T) = AHix(TR)+I (Aa+APT+AyT2) dT
TR
Integrating gives us

Heat capacity as a AP
2
function of AHRx(T) = AHix(TR)+A~(T-TR)+- 2 (T2-TR)+h (T3-Ti)
3
temperature
(8-3 1)
where

In a similar fashion, we can evaluate the heat capacity term in Equation (8-22):

.T

Substituting Equations (8-31) and (8-32) into Equation (8-22), the form of the
energy balance is

c P.0 c yjoi - 1
( T2 - Ti) + - Ti)
Energy balance for Q - Ws - FAo ai Oi (T - To ) + - 3 (T3
2
the case of highly
temperature-
sensitive heat
2 2 (.'-Ti)]
capacities AH& (TR) + Aa (T - TR) + - (T2 - TR) + - = 0
AP
2