2. Exercise (Laplace Method in Process Control) The stirred tank heating and mixing process is operating with a liquid inlet 1 flow rate is wu = 30kg/min, and liquid inlet 2 flow rate is w2 = 20kg/min. Assuming the two inlet streams has the same liquid that has a density (p = 25kg/m3) and same specific heat capacity (0.32 kg m /kgC), and the tank has liquid volume that is constant at 2m3. Assume The sum of inlets and outlet flow rates are equal (wi +w2 = w3); thus, the liquid holdup V is constant, the density p and heat capacity c of the liquid are assumed to be constant; and heat losses are negligible. Assuming the differential equation describing the system is pVTz(t) = w1T1(t)+w2T2(t) W3T3(t) Where Ti(t) = e-24 and Tu(t) = 1 (a) (0.5 points) Apply Initial value theorem for the given system for both sided ? (b) (0.5 points) Apply Final value theorem for the given system for both sided