A cooling coil is integrated inside a stirred tank reactor to release heat generated during a reaction process. To maintain a constant reactor temperature, a proportional controller is utilized to control the flow rate of the coolant. The controller has been built in a manner that the regulated reactor displays common underdamped second-order temperature responses when it is disrupted by the flow rate of the feed or by the temperature changes of the coolant.
What is the gain of the transfer function (under feedback control) that relates the changes in the reactor temperature to that of the flow rate of the feed if the flow rate of the feed to the reactor changes from 0.4 kg/s to 0.5 kg/s and the reactor temperature changes from 100 ⁰C to 102 ⁰C?