A closed stirred-tank (see the figure 1 below) is used to heat an incoming stream with temperature Ti, whose flowrate, w, changes. The heating rate from the heating coil and the tank volume are both constant. Notes: Pressure P and specific heat capacity Cp are constants. U, the overall heat transfer coefficient, is constant. This is for heat transfer through the outer walls of the tank to the surroundings. As is the surface area for heat losses to the ambient surroundings. T> T. (inlet temperature is higher than ambient temperature). T; Ta Heating coil -T Figure 1 1.1. Develop a mathematical model (differential and algebraic equations) that describes the exit temperature if heat losses to the ambient occur and the incoming stream's temperature (T) can vary.