Please solve the process control problem accurately and I'll rate you based on accuracy! Thank you for your time!

Exercise 2 (30 points) Often liquid surge tanks (particularly those containing hydrocarbons) will have a gas "blanket" of nitrogen or carbon dioxide to prevent the accumulation of explosive vapors above the liquid, as depicted below. 94 gas liquid F F, Let qs and q represent the inlet and outlet gas molar flow rates, Fy and F the inlet and outlet liquid volumetric flow rates, V the constant (total) volume, Vi the liquid volume, V, the gas volume and P the gas pressure. Assume the ideal gas law. Show that the modeling equations are the ones given below (i.e. show how they are derived). 9 gas F liquid F Let qr and q represent the inlet and outlet gas molar flow rates, Frand F the inlet and outlet liquid volumetric flow rates, V the constant (total) volume, V the liquid volume, V, the gas volume and P the gas pressure. Assume the ideal gas law. Show that the modeling equations are the ones given below (i.e. show how they are derived). dV = F,-F dt dP dt P RT v v; (,-F)+ -F (4-9) V-V + V-V