It actually does. Think of it this way. If you filled a balloon with a 9L tank filled to 310 bar it would expand to 88 cubic feet of volume. A 6.8L tank would fill a balloon to 66 cubic feet of volume.
I think you're conflating "breathable" vs "total" air.
Grok sexplains it pretty concisely:
To calculate the breathable versus total air volume in cubic feet (cu ft) for a 9L tank compressed to 4500 psi, we need to determine the total air volume when decompressed to atmospheric pressure and estimate the breathable (usable) volume, accounting for practical diving limitations.Step 1: Total Air VolumeA 9L tank refers to its water capacity, or internal volume, which is 9 liters. To find the total air volume when the compressed air is released to atmospheric pressure (approximately 14.7 psi at sea level), we use the ideal gas law, assuming constant temperature (isothermal expansion).
- Convert units:
- 9 liters = 9 × 0.0353147 cu ft = 0.3178323 cu ft (internal tank volume).
- 4500 psi is the absolute pressure. Gauge pressure is given, so absolute pressure = 4500 psi + 14.7 psi ≈ 4514.7 psi.
- Atmospheric pressure = 14.7 psi.
- Calculate compression ratio:The ratio of compressed pressure to atmospheric pressure gives the factor by which the air expands:
Compression ratio=4514.714.7≈307.1224\text{Compression ratio} = \frac{4514.7}{14.7} \approx 307.1224\text{Compression ratio} = \frac{4514.7}{14.7} \approx 307.1224 - Total free air volume:Multiply the tank’s internal volume by the compression ratio:
Total volume=0.3178323 cu ft×307.1224≈97.648 cu ft\text{Total volume} = 0.3178323 \, \text{cu ft} \times 307.1224 \approx 97.648 \, \text{cu ft}\text{Total volume} = 0.3178323 \, \text{cu ft} \times 307.1224 \approx 97.648 \, \text{cu ft}
So, the total air volume when decompressed is approximately 97.65 cu ft.
Step 2: Breathable (Usable) Air VolumeIn scuba diving, not all the air in a tank is considered "breathable" because tanks are not emptied completely. A reserve pressure is typically left to ensure safety (e.g., to avoid regulator failure or to account for emergencies). Common reserve pressures are 500–700 psi, but let’s assume a conservative reserve of 500 psi for this calculation.
- Usable pressure:
Usable pressure=4500 psi−500 psi=4000 psi\text{Usable pressure} = 4500 \, \text{psi} - 500 \, \text{psi} = 4000 \, \text{psi}\text{Usable pressure} = 4500 \, \text{psi} - 500 \, \text{psi} = 4000 \, \text{psi} - Usable pressure ratio:
Usable pressure ratio=4000+14.714.7≈4014.714.7≈273.041\text{Usable pressure ratio} = \frac{4000 + 14.7}{14.7} \approx \frac{4014.7}{14.7} \approx 273.041\text{Usable pressure ratio} = \frac{4000 + 14.7}{14.7} \approx \frac{4014.7}{14.7} \approx 273.041 - Breathable air volume:Multiply the tank’s internal volume by the usable pressure ratio:
Breathable volume=0.3178323 cu ft×273.041≈86.759 cu ft\text{Breathable volume} = 0.3178323 \, \text{cu ft} \times 273.041 \approx 86.759 \, \text{cu ft}\text{Breathable volume} = 0.3178323 \, \text{cu ft} \times 273.041 \approx 86.759 \, \text{cu ft}
So, the breathable air volume is approximately 86.76 cu ft.
Step 3: VerificationA 9L tank at 4500 psi is less common in scuba diving (where 3000–3300 psi is typical for high-pressure tanks), but the calculations align with standard dive tank formulas. For reference, a standard 80 cu ft aluminum tank (11L at 3000 psi) holds about 77–80 cu ft of free air, so 97.65 cu ft for a 9L tank at 4500 psi is reasonable given the higher pressure.Final Answer
- Total air volume: 97.65 cu ft
- Breathable air volume (assuming 500 psi reserve): 86.76 cu ft
Not that anyone using PCP is ever going to deal with those 12-13 cu ft differences. Just throwing it out there for the masses to understand. Your initial chart is close enough for gubmint work.
