Chapter U3.58, Problem 4E

Interpretation Introduction

Interpretation: Comprehend the reason for getting harder and harder to push the plunger on the pump to fill more air in the tire.

Concept Introduction:

Due to random movement of gas particles, they colloid with other gas particles and also colloid with wall of container. The collision between gas particles of air and wall of container exert pressure on the wall of container.

Answer to Problem 4E

It becomes harder and harder to push more air in the tire because of increase in the collision of more gas particles which requires more energy to push the air in the tire.

Explanation of Solution

The gas pressure is inversely proportional to the volume of gas. This is because as the gas pressure increases, the gas particles come close to each other. It decreases the intermolecular distance between particles and volume decreases.Similarly, as the pressure decreases, the intermolecular distance between particles increases that increase the volume of gas.

  $\text{Pressure α }\frac{\text{1}}{\text{volume }}$

This is called as Boyle’s law. It states that at constant temperature and amount of gas molecules, the volume is inversely proportional to the pressure of gas.

When air is filled in the tire, initially tire is empty and there is more space (volume) therefore air (gas) particles occupy the empty space. It becomes harder and harder to push more air in the tire because of increase in the collision of more gas particles which requires more energy to push the air in the tire.