A liquid is continuously fed into a tank as shown in Figure 3 . The tank has an external cooling jacket to cool the liquid contents to a required temperature. It is assumed that the tank is well mixed so that the temperature of the outlet stream is the same as the tank temperature. The tank can be described using the following equations: Mass balance FinFout=Adtdz Heat balance Cp,lFinTinCp,lFoutT+Cp,ccFc(TcT)=Cp,lAdtd(zT) Where, and c are the densities of liquid and coolant respectively Fin and Foutarethetheflowratesoftheliquidinandoutofthetankrectively A is the area of the tank base z is the height of liquid in the tank t is time Cp,l and Cp,c are the heat capacities of the liquid and coolant respectively Tin is the temperature of the feed T is the liquid temperature in both the tank and outlet Tc and Fc are the coolant temperature and flowrate respectively (i). Assuming that feed flowrate Fin and temperature Tin as well as the coolant temperature Tc are determined by preceding processes and that densities and heat capacities of both liquid and coolant do not vary with temperature, determine the degrees of freedom in the system described above. [4 marks] (ii). Use the degrees of freedom to specify a control system capable of controlling against disturbances in feed flowrate Fin and temperature Tin. Give reasons for your choice of controlled and manipulated variables and control loops and include a diagram of the control system. (c) The equation for proportional and integral control is shown below: JJ0=Kc(+I10tdt) Show that this can be represented by the following transfer function: Gc(s)=(s)J(s)=Kc(1+ls1) A table of Laplace transforms is given in Table 3. Tahle .3 Tahle of I anlace Transforms