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)

Hint:

Turn the cylinder volume and pressure into an equivalent free air volume, then divide by the breathing rate.

Answer 1

Correct Answer: 200

Step 1: Apply Boyle's Law to expand the stored gas to normal pressure.
The oxygen inside the SCBA cylinder sits at a high pressure of 200 bar in a 2 liter space. Boyle's Law says that for a fixed amount of gas at constant temperature, $P_1 V_1 = P_2 V_2$. Take state 1 as the gas inside the cylinder and state 2 as the same gas released to atmospheric pressure, $P_2 = 1$ bar.
$P_1 V_1 = 200 \times 2 = 400$ (bar times liters)
So $V_2 = \dfrac{P_1 V_1}{P_2} = \dfrac{400}{1} = 400$ liters.
This confirms the cylinder really carries 400 liters worth of breathable oxygen once it drops to normal pressure.

Step 2: Divide by the rate of use to get the time available.
The miner uses this oxygen at a steady rate of 2 liters per minute. Time is simply the total quantity divided by the rate at which it gets used up.
$t = \dfrac{400 \text{ liters}}{2 \text{ liters/min}} = 200$ minutes.

Final Answer:
The apparatus lasts 200 minutes. \[ \boxed{200 \text{ min}} \]