Q1. (30 P) In a heat exchanger, it is desired to heat a process stream to 90C with saturated vapour at 100C and control the temperature with P controller by manipulating the flow rate of saturated vapour (M,kg/min). Process stream enters the heat exchanger at 20C with 2m3/min flow rate. In the heat exchanger, the total volume of the pipes through which the process fluid passes is 5m3. The density and heat capacity of fluid are 1000kg/m3 and 0.8kcal/kgC, respectively. The density and heat capacity values of the process stream are constant during the heating process. On the other hand, in the case of disturbance effect a 4 minutes dead time is observed in the system. The condensation enthalpy of saturated vapour (Hb) is 640kcal/kg. The transfer function of the thermocouple and the pneumatic valve used in the process are as follows; Gs(s)=(0.5s+1)16/100mA/C,Gv(s)=(2s+1)12psia50m3/min a) Derive the transfer function of the system. b) Find the P controller parameters. c) If the inlet temperature of the process stream increases to 50C(att=0) what will be the value of the temperature? How much energy is delivered to the system per minute at this measured temperature