A bicycle floor pump has a cylindrical tube with an inside diameter of 1.0 inche

Question

A bicycle floor pump has a cylindrical tube with an inside diameter of 1.0 inches. On the pump's upstroke, a diaphragm check valve opens and brings air in at 13.0 psia. The air is then transferred to the tire during the down stroke. The stroke length is 18 inches. Determine how many down strokes will be required to inflate a mountain bike tire to 40 psia.

I'm short on time. I don't know what to do about how much air is leaving... it supposed to be simple because we haven't done anything more than PV=nRT

Explanation / Answer

1 psi = 6894.7573 Pa

13 psi = 89631.845 Pa

40 psi = 275790.3 Pa

1 inch = 0.0254 m

18 inches = 0.4572 m

So Pressure, P = 89631.845 Pa

Volume = pi*r^2*h = pi*(0.0254/2)^2*0.4572 = 2.3167 x 10^-4 m^3

PV = nRT

PV = constant since n,T are constant

Given,

P1 = 89631.845 Pa

V1 = 2.3167 x 10^-4 m^3

P2 = 275790.3 Pa

V2 = ?

V2 = (P1V1)/P2 = (89631.845*2.3167x10^-4)/(275790.3) = 7.53 x 10^-5 m^3

So number of down strokes required = V1/V2 = (2.3167 x 10^-4)/(7.53 x 10^-5) = 3

So 3 down strokes are required.

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