2. (3 points) A continuous stirred thermal mixing tank (shown below with two inlet streams and an outlet stream at temperature T) is operated at constant flowrate (Fi=F2=5 kg/min) so that the mass of liquid in the mixer is constant (100 kg). The inlet temperatures of stream 2 is fixed (T2 = 75 C). The inlet temperature of stream 1 is initially T1 = 25C, but can vary with time. The system is initially at steady state. The temperature of the liquid in the tank (T) is measured using a temperature sensor that can be described by the following model: T2 dTm dt - (T - Tm) where I'm represents the measured temperature and T2 = 2 min. F F T T, T a. Find the transfer function for the effect of changes in T, on the measured temperature of the stream Ts'(S)/T'(s). Write the function in terms of the process variables. What is the order of the transfer function? b. What is the gain of this transfer function (with units)