Two well-insulated stirred tanks of constant fluid volume V and V respectively are connected in series via a pipe with constant flowrate F as shown in Figure 1 below. Initially the system is at steady state, with the temperature in both tanks and the inlet stream (To(t), Ti(t) and T2(t)) at 20C. The system parameters are given below. Identify the system parameters, state variables and input variables for each tank Derive an ODE for the fluid temperature in each tank Derive an ODE for the deviation of the fluid temperature in each tank Derive the transfer functions that relate the following disturbances: T:'(t) to To'(t), Tz (t) to T1'(t) Draw the block diagram for this system Derive the second order transfer function that relates Tz (t) to To (t) Calculate the gain, time constant and damping coefficient of this function Comment on whether the system is under-, over- or critically damped Derive an expression for T(t) when To(t) steps from 20C to 100C F = 2 m/hr p = 1000 kg/m F, To(t) V, T(t) V= 5 m C = 4200 J/(kg C) F, T(t) V2, T2(t) Figure 1: Stirred Tanks in Series V = 10 m To = T = T = 20 C F, T(t)