Cell growth gives off energy which must be removed, or else the temperature will

Question

Cell growth gives off energy which must be removed, or else the temperature will rise so much that the cells may be killed. A continuous fermenter is utilized for the production of Penicillium Chrysogenum, where the cells generate 27.6 kJ/L per hour, and the volume of the well insulated fermenter is 2L. Feed temperature is 25 F and the exit temperature is equal to the temperature in the fermenter (assume it is well-mixed). Penicillium Chrysogenum cannot grow above 42 C. Will the cells survive?

Assume the inlet and outlet streams have a heat capacity of 4 J/g C and that the mass flow rates are constant at 1025 g/hr.

Explanation / Answer

power generated in fermenter in 1 hour in 2 litre volume(Q)= 27.6*2= 55.2 kJ/h

let exit temp is Te.

therefore energy balance,

m*cp*(Te-Ti)=Q

1025*4*(Te-Ti)=55.2*103

Te-25=13.46

Te=38.46 degree celcius.

since exit temperature =38.46 degree celcius which is less then 42 degree celcius ..therefore cells will survive.

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