6Stang7
Oct1-06, 03:16 PM
This question for my physics book seems fairly straight forward, but my answer doesn't agree with the book (which is notorious for having the wrong answers). The question is:
"The cylinder of a manual bicycle tire pump is 35cm long; its inside diameter is 2.5cm. When the piston is pulled up, the valve to the tire is closed and air at atmospheric pressure enters the cylinder through the gap between the piston and the wall of the cylinder, which acts like another valve. When the piston is pushed down, the air in the cylinder is compressed. The valve to the tire opens when the pressure in the tire is reached, and air is transferred to the tire during the rest of the stroke. The last 5% of the volume of air remains in the cylinder and the hose. Suppose that you are pumping up a tire that already has 2.5 atm gauge pressure. How much air is transferred to the tire at this pressure? What is the volume of this air at atmospheric pressure? Assume that the temperature is constant."
Since the temp is constant I figured this boiled down to P1V1=P2V2. The tire is at 2.5 atm gauge, so it has 3.5 atm of pressure. The total volume of the cylinder is ((1.25)^2)PI(35)), which is V1. P1 is 1 atm and P2 is 3.5 atm. When I solve for V2 I get 49.087. I then do V2-(V2(5%)) to get about 46cm^3 of air transferred into the tire. my book says it's 40.5cm^3 of air.
Where am I going wrong here, or is it the book again?
"The cylinder of a manual bicycle tire pump is 35cm long; its inside diameter is 2.5cm. When the piston is pulled up, the valve to the tire is closed and air at atmospheric pressure enters the cylinder through the gap between the piston and the wall of the cylinder, which acts like another valve. When the piston is pushed down, the air in the cylinder is compressed. The valve to the tire opens when the pressure in the tire is reached, and air is transferred to the tire during the rest of the stroke. The last 5% of the volume of air remains in the cylinder and the hose. Suppose that you are pumping up a tire that already has 2.5 atm gauge pressure. How much air is transferred to the tire at this pressure? What is the volume of this air at atmospheric pressure? Assume that the temperature is constant."
Since the temp is constant I figured this boiled down to P1V1=P2V2. The tire is at 2.5 atm gauge, so it has 3.5 atm of pressure. The total volume of the cylinder is ((1.25)^2)PI(35)), which is V1. P1 is 1 atm and P2 is 3.5 atm. When I solve for V2 I get 49.087. I then do V2-(V2(5%)) to get about 46cm^3 of air transferred into the tire. my book says it's 40.5cm^3 of air.
Where am I going wrong here, or is it the book again?