Question:
A closed-circuit self-contained breathing apparatus (SCBA) contains 2 liters of \(O_2\) at 200 bar. If a miner uses \(O_2\) at a rate of 2 liters \(\text{min}^{-1}\), the maximum duration that the apparatus can supply \(O_2\), in min, is . (answer in integer)
A closed-circuit self-contained breathing apparatus (SCBA) contains 2 liters of \(O_2\) at 200 bar. If a miner uses \(O_2\) at a rate of 2 liters \(\text{min}^{-1}\), the maximum duration that the apparatus can supply \(O_2\), in min, is . (answer in integer)
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Turn the cylinder volume and pressure into an equivalent free air volume, then divide by the breathing rate.
Updated On: Jul 27, 2026
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Correct Answer: 200
Solution and Explanation
Step 1: Find the free air volume stored in the cylinder.
The SCBA cylinder holds 2 liters of oxygen, but that oxygen is packed in at 200 bar. To find how much oxygen this really is once it expands to normal breathing pressure of 1 bar, multiply the stored volume by the pressure.
\[ V_{free} = V_{cylinder} \times P = 2 \times 200 = 400 \text{ liters} \]
So the apparatus effectively carries 400 liters of oxygen measured at normal atmospheric pressure.
Step 2: Divide the free air volume by the breathing rate.
The miner uses oxygen at 2 liters per minute, and this rate is already stated at normal pressure, so it can be compared directly with the free air volume found in Step 1.
\[ t = \frac{V_{free}}{\text{rate}} = \frac{400}{2} = 200 \text{ min} \]
Final Answer:
The SCBA can supply oxygen for 200 minutes before it runs out. \[ \boxed{200 \text{ min}} \]
The SCBA cylinder holds 2 liters of oxygen, but that oxygen is packed in at 200 bar. To find how much oxygen this really is once it expands to normal breathing pressure of 1 bar, multiply the stored volume by the pressure.
\[ V_{free} = V_{cylinder} \times P = 2 \times 200 = 400 \text{ liters} \]
So the apparatus effectively carries 400 liters of oxygen measured at normal atmospheric pressure.
Step 2: Divide the free air volume by the breathing rate.
The miner uses oxygen at 2 liters per minute, and this rate is already stated at normal pressure, so it can be compared directly with the free air volume found in Step 1.
\[ t = \frac{V_{free}}{\text{rate}} = \frac{400}{2} = 200 \text{ min} \]
Final Answer:
The SCBA can supply oxygen for 200 minutes before it runs out. \[ \boxed{200 \text{ min}} \]
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