Oxygen therapy uses various devices to provide oxygen to patients having difficulty getting sufficient amounts from air through normal breathing. Among the devices is a nasal cannula, which transports oxygen through small plastic tubes from a supply tank to prongs placed in the nostril. Consider a specific configuration in which the supply tank, whose volume is 6.0 ft3, is filled to a pressure of 2100 psig at a temperature of 85°F. The patient is in an environment where the ambient temperature is 40°F. When the cannula is put into use, the pressure in the tank begins to decrease as oxygen flows at 10-15 L/min through a tube and the cannula into the nostrils.

(a) Estimate the original mass of oxygen in the tank using the compressibility-factor equation of state.

(b) What is the initial pressure when the temperature is 40°F? How much oxygen remains in the tank when application of the ideal-gas equation of state produces a result that is within 3% of that predicted by the compressibility-factor equation of state (i.e., when 0.97 ≤ z ≤ 1.03)?

(c) How long will it take for the gauge on the tank to read 50 psig, assuming an average flow rate of 12.5 L/min?