A stirred-tank reactor has an internal cooling coil to remove heat liberated in the reaction. A proportional controller is used to regulate coolant flow rate so as to keep the reactor temperature reasonably constant. The controller has been designed so that the controlled reactor exhibits typical underdamped second-order temperature response characteristics when it is disturbed, either by feed flow rate or by coolant temperature changes. The feed flow rate to the reactor changes suddenly from 0.4 to 0.5 kg/s, and the temperature of the reactor contents, initially at 100C, changes eventually to 102C. What is the gain of the transfer function (under feedback control) that relates changes in reactor temperature to changes in feed flow rate? b. The operator notes that the resulting response is slightly oscillatory with maxima estimated to be 102.5 and 102.0 C occurring at times 1000 and 3060 s after the change is initiated. What is the complete process transfer function? The operator failed to note the rise time. Predict te based on the results in (a) and (b)