$1)$ Consider a well$-$mixed $2000$ L bioreactor operating at $37\backslash$deg C$.$ In order to maintain steady state

temperature due to heat loss through the vessel, a stainless$-$steel jacket is required and

operated at an inlet temperature of $60\backslash$deg C$,$ outlet at $52\backslash$deg C and flowrate of $10$ gpm $($gallons per

minute$).$ Assume no heat generated from cell growth. Answer the following questions based

on this information;

a$.$ How much heat $($KJ$)$ can this jacket remove from the bioreactor?

b$.$ A technician observes that the jacket pipping has a slight leak upstream of the bioreactor

$($leak is located on pipping that is before the actual bioreactor jacket$).$ A bucket is used to

identify a volumetric leak rate of $5$ LPM $($liters per minute$).$ If this is correct and there are no

further leaks, answer the following;

i$.$ Draw the process flow diagram required and define your system boundary

ii$.$ What is the new outlet temperature $(\backslash$deg C$)$ that we should observe on the outlet

of the jacket?

$2)$ Consider the well$-$mixed $2000$L bioreactor from Question $1.$ The bioreactor is operated in

perfusion mode with CHO cells at a density of $1$E$9$ cells$/$mL$.$ A small$-$scale experiment

shows that the glucose demand is $0\mathrm{.}02$ ng$/$cell$.$ For CHO cells, assume that the enthalpy of

reaction $($Hrxn$)$ due to cellular metabolism is ~ $-2760$ KJ$/$mol$-$glucose. Answer the

following questions:

a$.$ How much heat $($kJ$)$ will be generated from the reactor if it is well$-$insulated?

b$.$ Assume the bioreactor from Question $1$ is not insulated and does not have a leaking

jacket $($i$.$e$,$ heat loss similar to part $1$a$).$ The inlet of the jacket is still maintained at $60\backslash$deg C and

a flowrate of $10$ GPM$.$ What is the new outlet temperature $(\backslash$deg C$)$ from the jacket if we now

consider cellular growth heat generation and the heat loss from $1$a$?$