Consider a continuous stirred tank reactor, CSTR. Given that c_Ai and c_A represent molar concentrations of A (in mol/m³) at inlet and outlet streams, respectively. T_i and T denote the inlet and outlet temperatures (in ⁰C) whereas F_i and F denote the inlet and outlet volumetric flowrates (in m³/min), respectively.

1. If a first order endothermic reaction AB takes place in the CSTR, and the volume is not constant, discuss the relevant conservation equations that are required in order to derive the unsteady-state models relating the system variables V, c_A and T. Sketch the schematic diagram. Derive the unsteady-state models and state your assumptions clearly.

2. If the endothermic reaction now is second order with respect to c_A, and assuming constant holdup (V=constant), derive the unsteady-state (dynamic) models and find the transfer functions for C_A(s)/C_Ai(s). Discuss how your dynamic models would differ from those obtained in part (a).

3. If the reaction is now isothermal, discuss how your dynamic models would differ from those obtained in parts (a) and (b)?