X* [***** A batch reactor is used to carry out the consecutive first order reaction ABC Where B is the desired product. Since the reaction sequence is endothermic, steam at pressure Ps is available to control the reactor contents to a desired operating temperature (TP) by varying the flow rate (Fs) of steam to the heating jacket. Heat transfer only occurs through the jacket into the reaction mixture. Condensate is quickly withdraw from the heating jacket, however the dynamics of the of the steam jacket are considered to be important. The reactor is shown in Figure 1. Significant input power is expended in order to stir the reactor contents. As well the reactor wall has a significant heat capacity and its energy holdup cannot be ignored. Amongst the system variables are: ma, ma, mc = reactor species molar holdups. Tw= The reactor wall temperature, Mw = The reactor wall mass T=The reactor contents temperature, Tsj= Steam jacket temperature- Ps= Steam supply pressure, Ps= Steam pressure in jacket Ws agitator power, V = Reactor volume, V- Jacket volume The reaction rates are first order with constants k = k, e- k = koe -ke-r Your tasks are to: a) State clearly the underlying mechanisms relevant to the system and show the balance boundaries. (3 marks) b) State the assumptions relevant to the modeling. (3 marks) c) Develop in a systematic manner the equations which describe the system dynamics needed for control studies to be carried out. Clearly state any extra variables you define (13 marks) d) Carry out a degree of freedom analysis of your system equations and state how the degree of freedom are to be consumed. State all variables, constants and parameters (4 marks) e) Sketch the general trends for the compositions of the 3 species with time marks) TSP TC Ta TE 1.Batch Reactor with Controls (3