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What volume (in liters) of air measured at 1.00 atm would have to be put into a bicycle tire with a 1.00-l volume if the pressure in the bike tire is to be 40.0 psi? Assume the temperature of the gas remains constant.
Accepted Answer
To solve this, we'll use Boyle's Law, which states that the product of pressure and volume is constant for a given amount of gas at constant temperature. Here's how we can approach the problem:
1. Convert Units: Make sure all pressure units are the same. Since the tire pressure is in psi (pounds per square inch), we need to convert 1.00 atm to psi:
1.00 atm
14.7 psi/atm = 14.7 psi
2. Apply Boyle's Law: Let V1 be the initial volume of air, P1 be the initial pressure, V2 be the final volume (tire volume), and P2 be the final pressure (tire pressure):
P1
V1 = P2
V2
3. Solve for V1: Plug in the values and solve for the initial volume of air (V1):
14.7 psi
V1 = 40.0 psi
1.00 L
V1 = (40.0 psi
1.00 L) / 14.7 psi
V1 ≈ 2.72 L
Therefore, approximately 2.72 liters of air at 1.00 atm would need to be put into the bicycle tire to reach a pressure of 40.0 psi.
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