The full volume of a bicycle pump is 437 mL. If the pressure inside the pump starts at 1.00 atm, what is the final pressure inside the pump if the volume is decreased to 125 mL while the valve is closed?
We can solve this problem using Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Mathematically, this can be expressed as:
P1V1 = P2V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
P1 = 1.00 atm
V1 = 437 mL
V2 = 125 mL
Using the formula, we can solve for P2:
P2 = (P1 * V1) / V2
P2 = (1.00 atm * 437 mL) / 125 mL
P2 = 437 / 125 atm
P2 = 3.496 atm
Therefore, the final pressure inside the pump is approximately 3.496 atm when the volume is decreased to 125 mL while the valve is closed.
To find the final pressure inside the pump, we can use the combined gas law, which states that the initial pressure multiplied by the initial volume is equal to the final pressure multiplied by the final volume.
Given:
Initial volume (Vi) = 437 mL
Initial pressure (Pi) = 1.00 atm
Final volume (Vf) = 125 mL
Pi * Vi = Pf * Vf
Substituting the given values:
1.00 atm * 437 mL = Pf * 125 mL
Now we can solve for Pf, the final pressure:
Pf = (1.00 atm * 437 mL) / 125 mL
Pf = 4.37 atm
Therefore, the final pressure inside the pump, when the volume is decreased to 125 mL while the valve is closed, is 4.37 atm.
To answer this question, we need to apply Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation representing Boyle's Law is:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given that the initial volume (V1) is 437 mL and the initial pressure (P1) is 1.00 atm, and the final volume (V2) is 125 mL, we can rearrange the equation to solve for P2:
P2 = (P1 * V1) / V2
Substituting the values we have:
P2 = (1.00 atm * 437 mL) / 125 mL
P2 = 4.37 atm
Therefore, the final pressure inside the pump, when the volume is decreased to 125 mL while the valve is closed, is 4.37 atm.