P$12-15$ The first$-$order, irreversible, exothermic liquid$-$phase

reaction

A $->$ B

is to be carried out in a jacketed CSTR$.$ Species A and

an inert I are fed to the reactor in equimolar amounts. The

molar feed rate of A is $80$ mol$/$min$.$

Additional information:

Heat capacity of the inert: $30$ cal$/$mol$$ C $\backslash$tau $=100$ min

Heat capacity of A and B: $20$ cal$/$mol$$ C $\backslash$Delta H$$Rx $=7500$ cal$/$mol

UA: $8000$ cal$/$min$$

$$ C k $=6\mathrm{.}6\backslash$times $103$min

$1$at $350$ K

Ambient temperature, Ta

: $300$ K E $=40000$ cal$/$mol $$ K

$($a$)$ What is the reactor temperature for a feed temperature

of $450$ K$?$

$($b$)$ Plot and then analyze the reactor temperature as a

function of the feed temperature.

$($c$)$ To what inlet temperature must the fluid be preheated

for the reactor to operate at a high conversion? What are

the corresponding temperature and conversion of the fluid

in the CSTR at this inlet temperature?

$($d$)$ Suppose that the fluid inlet temperature is now heated

$5\backslash$deg C above the reactor temperature in part $($c$)$ and then

cooled $20\backslash$deg C$,$ where it remains. What will be the

conversion?

$($e$)$ What is the inlet extinction temperature for this

reaction system? $($Ans: T $=87\backslash$deg C$)$