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Difficulty: EasyPneumatics and Gas Laws

A mechanic pushes down on the handle of a manual air pump, sealing the valve and compressing the trapped air. If the volume of the air chamber is reduced to exactly one-half of its original size while the temperature remains constant, what happens to the air pressure inside the pump?

  1. The pressure doubles.Answer
  2. B
    The pressure is reduced by half.
  3. C
    The pressure remains exactly the same.
  4. D
    The pressure quadruples.

Answer

The pressure doubles.
According to Boyle's Law, the pressure of a given mass of an ideal gas is inversely proportional to its volume when the temperature remains constant. Because the mechanic forces the same amount of air into half the space, the air molecules strike the walls of the pump chamber twice as often, causing the pressure to double.

Step-by-Step Solution

1
Identify the relationship between gas volume and pressure at a constant temperature.
The relationship is inversely proportional, described by Boyle's Law (P1V1=P2V2P_1V_1 = P_2V_2).
Understanding this core gas law is necessary to determine the outcome of volume changes in a sealed pneumatic system.
2
Apply the given volume change to the inverse relationship.
Since the volume is multiplied by 1/21/2, the pressure must be multiplied by the reciprocal, which is 22.
To keep the product of pressure and volume constant, halving one variable strictly requires doubling the other.

Key Concept

Boyle's Law and Gas Compressibility
Estimated Time:45s
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Topics

Pneumatics and Gas Laws

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