In a chemical reactor, an increase in the steam flow rate of 1,000 lb/h produces an increase of 5°F in the reactor outlet temperature. A step input change in the steam flow rate takes approximately 40 minutes to affect 98% of the outlet temperature rise to the new steady-state value. Using this information develop a transfer function model for the process between the outlet reactor temperature and inlet steam flow rate. (10 points)

The mixing tank shown here initially contains 50 kg of water at 25 degree C. Suddenly the two inlet valves and the single outlet valve are opened, so that two water streams, each at flow rate of 5 kg/min, flow into the tank, and a single exit stream with a flow rate of 10 kg/min leaves the tank. The temperature of one inlet stream is 80 degree C and the other is 50 degree C. The tank is well-mixed, so that the temperature of the outlet stream us always same as the temperature in the tank. Compute the stead-state temperature that will finally be obtained in the tank. Develop an expression for the temperature of the fluid in the tank at any time.