Please answer all the questions correctly providing necessary formulae, equations, expressions, diagrams, charts, graphs, plots and tables.

3. Consider a non-isothermal CSTR with jacket cooling where reactant A is converted to product by a first order reaction (A B). Assume constant volume system and constant density system. (i)Write the dynamic model equations (overall material balance, component balance and energy balance). For the parameter set given below show that 350K and 0.5 gmmole /it are the steady state temperature and concentration. Determine the number of steady state solutions and their stability characteristics. Generate a phase plane diagram. (ii) Consider the response to (+/)5K changes in the jacket temperature. For one direction you should find oscillatory behaviour, while the other direction is stable. This indicates that a Hopf bifurcation occurs for some value of Tj between 295K and 305K. Find the value of Tj where this occurs (a Hopf bifurcation occurs when the complex eigen values have zero real portion) Data: F (feed rate) =100 liters /min, V( volume )=100 liters, Tj( jacket temperature )=300K, ko(reaction rate constant )=7.21010min1,(H) (Heat of xreaction )=50000J/gmmole,E/R=8750K, Cp=239J/ liter K,Tr( feed temperature )=350K,CA( feed concentration )=10 kgmole/m3,UA=50000J/minK 3. Consider a non-isothermal CSTR with jacket cooling where reactant A is converted to product by a first order reaction (A B). Assume constant volume system and constant density system. (i)Write the dynamic model equations (overall material balance, component balance and energy balance). For the parameter set given below show that 350K and 0.5 gmmole /it are the steady state temperature and concentration. Determine the number of steady state solutions and their stability characteristics. Generate a phase plane diagram. (ii) Consider the response to (+/)5K changes in the jacket temperature. For one direction you should find oscillatory behaviour, while the other direction is stable. This indicates that a Hopf bifurcation occurs for some value of Tj between 295K and 305K. Find the value of Tj where this occurs (a Hopf bifurcation occurs when the complex eigen values have zero real portion) Data: F (feed rate) =100 liters /min, V( volume )=100 liters, Tj( jacket temperature )=300K, ko(reaction rate constant )=7.21010min1,(H) (Heat of xreaction )=50000J/gmmole,E/R=8750K, Cp=239J/ liter K,Tr( feed temperature )=350K,CA( feed concentration )=10 kgmole/m3,UA=50000J/minK