An emphysema patient is breathing pure O2 through a face mask. The cylinder of O2 contains 0.20 ft3 of O2 gas at a pressure of 2200 lb/in2.
(a) What volume would the oxygen occupy at atmospheric pressure (and the same temperature)?
ft3
(b) If the patient takes in 8.0 L/min of O2 at atmospheric pressure, how long will the cylinder last?
To find the volume of oxygen at atmospheric pressure, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant. The formula is:
P1V1 = P2V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
(a) To find the volume of oxygen at atmospheric pressure, we can plug the values into the equation:
P1 = 2200 lb/in^2
V1 = 0.20 ft^3
P2 = atmospheric pressure (let's assume it's 14.7 lb/in^2, which is close to the average atmospheric pressure at sea level)
V2 = volume at atmospheric pressure (what we want to find)
Using the equation:
P1V1 = P2V2
(2200 lb/in^2)(0.20 ft^3) = (14.7 lb/in^2)(V2)
Now we can solve for V2:
V2 = (2200 lb/in^2)(0.20 ft^3) / (14.7 lb/in^2)
V2 = 29.93 ft^3
Therefore, the volume of oxygen at atmospheric pressure would be 29.93 ft^3.
(b) To find how long the cylinder will last, we need to convert the oxygen intake rate from liters per minute to ft^3 per minute. There are 28.3168 liters in 1 ft^3, so the conversion factor is:
1 ft^3 / 28.3168 L
Now we can use the conversion factor:
8.0 L/min * (1 ft^3 / 28.3168 L) = 0.282 ft^3/min
So, the patient takes in 0.282 ft^3 of oxygen per minute. To find how long the cylinder will last, we divide the cylinder volume by the oxygen intake rate:
29.93 ft^3 / 0.282 ft^3/min = 106.15 minutes
Therefore, the cylinder will last approximately 106.15 minutes, or about 1 hour and 46 minutes.