A 7.35 million gallon tank used for storing liquefied natural gas (LNG, which may be taken to be pure methane) must be taken out of service and inspected. All the liquid that can be pumped from the tank is first removed, and the tank is allowed to warm from its service temperature of about -260°F to 80°F at 1 atm. The gas remaining in the tank is then purged in two steps: (1) Liquid nitrogen is sprayed gently onto the tank floor, where it vaporizes. As the cold nitrogen vapor is formed, it displaces the methane in a piston-like flow until the tank is completely filled with nitrogen. Once all the methane has been displaced, the nitrogen is allowed to warm to ambient temperature. (2) Air is blown into the tank where it rapidly and completely mixes with the nitrogen until the composition of the gas leaving the tank is very close to that of air.

(a) Use the ideal-gas equation of state to estimate the densities of methane at 80°F and 1 atm and of nitrogen at -260°F and 1 atm. How confident are you about the accuracy of each estimate? Explain.

(b) If the density of liquid nitrogen is 50 lb_m/ft³, how many gallons will be required to displace all the methane from the tank?

(c) Howmany cubic feet of air will be required to increase the oxygen concentration to 20%by volume?

(d) Explain the logic behind vaporizing nitrogen in the manner described. Why purge with nitrogen first as opposed to purging with air?