1. A completely enclosed stirred-tank heating process is used to heat an incoming stream whose flow rate varies. The heating rate from this coil and the volume are both constant. (a) Develop a mathematical model (differential and algebraic equations) that describes the exit temperature if heat losses to the ambient occur and if the ambient temperature (Ta) and the incoming stream's temperature (Ti) both can vary. (b) Discuss qualitatively what to expect to happen as Ti and w increase (or decrease). Justify by reference to your model. Assumptions: - P and Cp are constants. - U, the overall heat transfer coefficient, is constant. - As, the surface area for heat losses to ambient. - Ti>Ta (inlet temperature is higher that ambient temperature)