Consider a tank where a hot stream whose volumetric flowrate is 9h and temperature is th is mixed with a cold stream with flowrate qe and temperature tc. the exit flowrate is q and temperature is t. (a) derive the dynamic model of the process, i. e. a set of differential equations describing the evolution of the height h and temperature t with time. assume a nonlinear resistance for the outlet flow, and constant density and heat capacity. (b) derive the linearized model in deviation variable form. use the following no- tation to conform to a standard state space model: xi = h, 12 = t, uj = 4c and u2 = 9h.