2) The equation for a well-mixed tank with a steady flow rate F=100L/min and constant heat input (Q) is given below mCpdtdT=FCpTiFCpT+Q ( Cp and is the heat capacity and density of the fluid, respectively) a)Show that the transfer function of the system Ti(s)T(s)=ps+1Kp. b) Determine the value of the time constant if the volume of the tank (V) is 500L. c) Hence sketch the graphs of the output water temperatures and compare the results given that V1=500L and V2=750L and input temperature (Ti) is a step change from 50C to 60C if the system is at steady state with the outlet water temperature of 80C. d) Find the value of the output for the two situation after a long time has elapsed and immediately after the step is input (part c). (Hint: Densities and heat capacities of inlet/outlet streams and mixture in the tank can be considered constant) (50 points)