You decided that you wanted to have hot baths and due to MCO you can only build a continuous heater using your variable kitchen pipe water supply and water kettle. You run the water through the kettle with the heater turned on and collect the water that flows out. Assume that you have a constant volume kettle, V (Volume), with a constant heating rate, Q (Power) and variable water flow of F (mass/time). a) What is i) Your process objective? ii) Your Process Variable iii) Your Manipulated Variable? (10 Marks) b) Derive a mathematical model (An Ordinary Differential Equation) for your process. Draw the process diagram and label the process control variables. State your assumptions and define your variables clearly. (15 Marks) c) Use deviation variables and Laplace Transforms to derive your Transfer Function Block for your Process. Draw your Transfer Function block with it's related input and output. (10 Marks) d) Sketch the expected process response if your manipulated variable decreased by 50% suddenly. (5 Marks) e) Bonus: Your water supply suddenly stops. Derive your new process model, Transfer Function, and sketch expected process response (10 Marks)