Piston Pressure and Unit Conversion

AI Thread Summary
The discussion revolves around calculating the area of a piston containing CO2 at a pressure of 30 atm. The calculations involve converting barometric pressure and applying relevant equations to determine the force exerted by the piston. The final calculated area of the piston is approximately 0.1347 in², which raises concerns about its size relative to the force applied. Participants express confusion over the small area and its implications for practical applications. The conversation highlights the importance of understanding the relationship between pressure, force, and area in such scenarios.
Nim R
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Problem:
CO2 is contained in a vertical cylinder at a pressure of 30 atm by a piston with a mass of 57 lbm. If g is 32.4 ft/sec2 and the barometric pressure is 29.7 in. Hg what is the area of the piston?

Relevant equations
F = Ma/gc
W = Mg/gc
P= F/A
gc = 32.174 lbm ft / (lbf sec2)
1 atm = 29.9 in. Hg
1 atm = 2116.217 lbf / ft2

Attempt (4 sig figs)
1)
29.7 in. Hg * 1 atm / (29.9 in. Hg) = 0.9933 atm
2) 30 atm - 0.9933 atm = 29.01 atm * 2116.217 lbf / ft2 / (1 atm) = 61,380 lbf / ft2
3) 61,380 lbf / ft2 = (57 lbm) * (32.4 ft / sec2) / (A * (32.174 lbm ft / (lbf sec2))
4) A = 9.352 x 10-4 ft2 = 0.1347 in2

I feel like this number is way too small. Was the assumption that the force of the piston was only its weight on the gas wrong?

Thanks
 
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I'm pretty rusty on these types of problems, but if I take 60 lb and apply it to an area of 0.001 ft2 (which is 0.144 in2), I get a pressure of 60000 lb/ft2. Your number certainly appears to be in the ballpark.
 
Well good to know my answer numerically makes sense. Intuitively though I don't have a clue what something with those dimensions and strength would look like.

Thanks for the reply!
 
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