In a tank heater as shown in the figure a process stream is heated by using an electrical heater that has a power of Q keal/min and its temperature is tried to controlled at 90C with a P controller. The process flow enters to the tank at 20C with 2m3/min flow rate. The tank volume is 5m3. The density and heat capacity of the fluld are 800kg/m3 and 0.8kcal/kgC, respectively. It is known that there is a dead time of 4min in the system in case of disturbance change. It is known that the density and the heat capacity of the fluld do not change during the heating process. The transfer function of the thermocouple and final control element used in the system are as follows: G,(s)=(0.5s+1)16/100mA/C,G(s)=(2s+1)16mA50000kcal/min a) Find the optimum P controller parameters to control this system. b) If the temperature of feed increases to 40C, how much off set value is displayed in the system and What will be the value of the temperature? c) How much energy (per minute) is dellvered to the system at the measured temperature