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## Homework Statement

A pneumatic lift system is being demonstrated at a sales show. The total load is 70 kg, and the lift piston is 15.2 cm in diameter and has a 20.2 cm stroke. A portable air bottle with an initial pressure of 20 MPa and a temperature of 23 Celsius degrees is to be used as the pneumatic supply. A regulator reduces the pressure from the bottle to the lift system. Neglecting all volume in the lines from the bottle to the piston, determine the number of times the piston can operate per air bottle if the air in the bottle remains at 23 celsius degrees and the volume of the bottle is 0.05 m3

## Homework Equations

P = F/A

PV = mRT

M = ρ v

V = πr

^{2}h

A = 2πrh + 2πr

^{2}

## The Attempt at a Solution

V = π (0.076)

^{2}x 0.202

V = 0.0036m

^{3}

A = 2 π 0.076 x 0.202 + 2π(0.076)

^{2}

A = 0.13m

^{2}

P = 70 x 9.81 / 0.13 + P

_{atm}

P

_{cyl}= 106607.61 Pa

m

_{air}= 1.225 x 0.0036

m

_{air}= 0.0049 kg

Finding mass of air in bottle

PV = mRT

2000x10

^{3}x 0.05 = m x 0.287x10

^{3}x 296

m

_{bot}= 1.18kg

m

_{bot}/ m

_{air}= 240 lifts.

I am unsure if that is the correct step to take, I feel as though i am missing something obvious.