S4. A 500L steam jacketed tank is full of water. The water in the tank is initially at 72F with no steam entering/leaving the jacket. Suddenly the inlet and exit valves are opened and water enters the tank at 5C and 15LPM. Water exits the tank at the same mass flow rate as it enters. At the same time that the valves are opened, the steam valve to the jacket is also opened. The jacket fluid is estimated to provide energy at a constant rate of 45kW. a) Put the energy balance in terms of temperature. Use U-substitution to solve the resulting differential equation. Explicitly solve for the functional form of the system temperature for any time (Tsys(t)). b) Use the result from a) to calculate the temperature of the water in the tank after 20 minutes. c) Use Excel to plot the resulting expression from part a). Graphically determine the steady state temperature. Approximately how long does it take the system to reach steady state