A reactor with a capacity of 10 tons was filled with 5 tons of reactant. The reaction is exothermic and the reactor is cooled by the cooling water passing through the jacket of the reactor. Cooling water enters the reactor at 20C and leaves at 30C. The temperature inside the reactor is desired to be 75C. The control valve is open 50% in steady state conditions and its offset value is zero at that time. At t=0, a catalyst is added to the reaction medium and an extra 30000 kcal of heat is given to the reactor. In this case, the difference between the inlet and outlet coolant temperature is constant. What would be the proportional gain of the control valve, provided the offset is kept at 0.2C?

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