Page 566 - Elements of Chemical Reaction Engineering Ebook

536 Unsteady-State Nonisothermal Reactor Design Chap. 9

-_
dN, - -v, rAV+ Flo- F, (9-7)
dt
Using Equation (9-7) to substitute for dMildt, Equation (9-6) becomes

Q - Ws + C F,OH,o - C FJHl
dT
= CNICp, + C V,H,(-rAV) + C FloH, - C F,H,

Rearranging, we have
This form of the r I
energy balance
should be used (9-8)
when there is a
phase change

on a transient
CSTR or . dt (9-9)
semibatch n
reactor
i=l

Equation (9-9) applies to a semibatch reactor as well as unsteady operation of
a CSTR.
For liquid-phase reactions where ACp is small and can be neglected, the
following approximation is often made:
CNICp,~CNloCpJ =NAOC@JCpJ =N~oCpy
where Cps is the heat capacity of the solution. The units of NAoCps are (cal/K), 01
(Btu/ R) and
F~oCpI =
where the units of FAoCps are (cal/s. K) or (Btu/h.R) l. With this approxima-
tion and assuming that every species enters the reactor at temperature To, we have
- FA&, (T - TO) + [ - AHR~ (T )I ( - rA v)
dT - Q - (9-10)
--
dt NAOCPS

* We see that if heat capacity were given in terms of mass (Le,, Cp,, = cal/g.K) then
both FAo and NAo would have to be converted to mass:
mAOcpsm = NAOcps
and

mAOcpsm = FAOCps
but the units of the products would still be the same (cal/K) and (cal/s K), respectively.