Please answer part ii.) and iii.)

A cubic storage tank is used to cool a solvent. The sohent in the tank is cooled by water passing through the cooling jacket, as shown below. Solvent fows in the tank at a temperature and with constant flowrate, initially Ti==30C and the flowrute is F=0.01m3/min. Given the following data initial values of T4=Tc=50C size of additional step decrease in Tc=20C volume of solvent =1.0m3m V density of solvent =703kgm3= specific heat of solvent =2.22kJkg1+C1=Cvv tank height =1m=H heat transfer coefficicat of wall between tank and heating jacket =216.8.Wm21=h flow rate =F=0.01m3/min (i) Starting from first priaciples derive a differential equation which models the dynamic response of solvent temperature, Tn, to changes in the heating water temperature, Tc (suppose Tr= constant. F=0.0m1/min) (3 marks) (ii) Starting from first principles derive a differcntial equation which models the dynamic response of solvent temperafure, Tk, to changes in the input water temperature. TN. (suppose Tc= constant, and flow cooling water =0.0m3/min ) (3 marks) (iii) Starting from first princlples derive a differential equation which models the dynamic response of solvent temperature, Tn to changes in the input water temperature, Trv and changes in heating water temperature (2 marks) (iv) Using the equation from (f) derive an algebraic etpression which relates T,tototimeforastep the change in Tc. Define cleatly all of the parameters used in your derivations. (4 marks) (v) At the new steady state ( Ts=Tcc=30C). Suppose a steam leak has occurred somewhere in the process which makes the cooling water heat up at a rate of 1.0C/min. Give the differential and algebraic equations to deseribe this problem. Calculate values for Ts at 10 minutes and 60 minutes and calculate how long will it take before the solvent inside the tank reaches 100C ? (4 marks) A cubic storage tank is used to cool a solvent. The sohent in the tank is cooled by water passing through the cooling jacket, as shown below. Solvent fows in the tank at a temperature and with constant flowrate, initially Ti==30C and the flowrute is F=0.01m3/min. Given the following data initial values of T4=Tc=50C size of additional step decrease in Tc=20C volume of solvent =1.0m3m V density of solvent =703kgm3= specific heat of solvent =2.22kJkg1+C1=Cvv tank height =1m=H heat transfer coefficicat of wall between tank and heating jacket =216.8.Wm21=h flow rate =F=0.01m3/min (i) Starting from first priaciples derive a differential equation which models the dynamic response of solvent temperature, Tn, to changes in the heating water temperature, Tc (suppose Tr= constant. F=0.0m1/min) (3 marks) (ii) Starting from first principles derive a differcntial equation which models the dynamic response of solvent temperafure, Tk, to changes in the input water temperature. TN. (suppose Tc= constant, and flow cooling water =0.0m3/min ) (3 marks) (iii) Starting from first princlples derive a differential equation which models the dynamic response of solvent temperature, Tn to changes in the input water temperature, Trv and changes in heating water temperature (2 marks) (iv) Using the equation from (f) derive an algebraic etpression which relates T,tototimeforastep the change in Tc. Define cleatly all of the parameters used in your derivations. (4 marks) (v) At the new steady state ( Ts=Tcc=30C). Suppose a steam leak has occurred somewhere in the process which makes the cooling water heat up at a rate of 1.0C/min. Give the differential and algebraic equations to deseribe this problem. Calculate values for Ts at 10 minutes and 60 minutes and calculate how long will it take before the solvent inside the tank reaches 100C ? (4 marks)