5.1 The process shown in Figure P5.1 is a constant volume electric water heater. Ona particular day, as the tank water temperature reached the 80C mark, the heater broke down and stopped supplying heat. At this time, water was withdrawn from this 100 liter capacity tank at the rate of 10 liters/min; cold water at 30C automatically flowed into the tank at precisely the same rate. This exercise went on for exactly 5 min, and the water withdrawal was stopped. (Because of the heater design the cold water also stopped flowing in.) Cold Water Hot Water Heater Figure P5.1. The water heater. By developing an appropriate mathematical model for this process, show that it is reasonable to consider this a first-order process; and by solving the resulting 169 TAPS DYNAMICS OF LOW-ORDER SYSTEMS differential equation model, find the final tank water temperature at the end of this 5-minute period. State all your assumptions. 5.1 The process shown in Figure P5.1 is a constant volume electric water heater. Ona particular day, as the tank water temperature reached the 80C mark, the heater broke down and stopped supplying heat. At this time, water was withdrawn from this 100 liter capacity tank at the rate of 10 liters/min; cold water at 30C automatically flowed into the tank at precisely the same rate. This exercise went on for exactly 5 min, and the water withdrawal was stopped. (Because of the heater design the cold water also stopped flowing in.) Cold Water Hot Water Heater Figure P5.1. The water heater. By developing an appropriate mathematical model for this process, show that it is reasonable to consider this a first-order process; and by solving the resulting 169 TAPS DYNAMICS OF LOW-ORDER SYSTEMS differential equation model, find the final tank water temperature at the end of this 5-minute period. State all your assumptions