# Piston Pressure and Unit Conversion

1. Jul 30, 2016

### Nim R

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

2. Jul 30, 2016

### TomHart

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.

3. Jul 30, 2016

### Nim R

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.