During cell growth processes, the temperature might increase due to the anabolism $($synthesis of complex biomolecules$).$ This energy must be released out of the system. Otherwise, the cell cycle will be terminated by the temperature rise.

Consider a continuous fermenter reactor to produce of Penicillium chrysogenum. The enthalpy of reaction for the cells $(H_r)$ is $-27\mathrm{.}6k\frac{J}{L}h.$ The volume of the well$-$insulated $($adiabatic$)$ fermenter reactor is $2\mathrm{.}4L.$ The inlet stream temperature is at ambient temperature $(25C).$ The cells of Penicillium chrysogenum are not able to grow above $42C.$

Figure: Summary for the process to produce Penicillium chrysogenum. Adapted from: Barreiro, C$.,$ et al$.,2019.,$ J$.$ Proteomics, $198,119-131.$

Draw and label the flowchart for this process. Write the related energy balance and choose the reference temperature to calculate the exit temperature. Will the cells be able to survive at the temperature that you would determine? $($Assume that the inlet and outlet streams have a heat capacity of $3\mathrm{.}8\frac{J}{g}C$ and the mass flow rate of $1575\frac{g}{h}$ are constants.$)$