In a biofuels plant a shell-and-tube heat exchanger is used to cool a stream of 100% carbon dioxide off-gas from a beer column from 77°C to 27°C (350 to 300 K) at 1 atm total system pressure. The total molar flow rate of CO₂ gas is 36 kgmol/h (806.4 m³/h at STP). Liquid water will be used as the coolant. Cooling water is available at 20°C (293 K). CO₂ gas flows in the tube side, water in the shell side. 

a. Determine the cooling water flow rate required to provide a temperature of approach of 17°C on the shell side. 

b. What is the required area of the heat exchanger? 

c. How many tubes are needed to achieve a Reynolds number of 20,000 in each tube? What tube length would be required?