Component A is fed into the tank at a volumetric flow rate of vo, a concentration of CAO and a temperature of T_{0}. The initial volume of the tank is V_{l}. The solution comes out of the tank with a volumetric flow rate of v proportional to the square root of the liquid level of the tank. The first order A -> B exothermic reaction takes place in the tank. The tank is cooled by a fluid that enters at a temperature of T_{a1} (^ C) and exits at a temperature of T_{a2} (C) and has a mass flow rate of m (kg / s).

a) Write the model equations that describe the system. (Specify the assumptions you made when writing the equations.)

b) Classify the models you have created (macroscopic-microscopic, linear-nonlinear, sedentary-non-sedentary, homogeneous parameterized-distribution parameterized)