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Chapter 11: Problem 4

You are using a bicycle pump to fill a bicycle tire with air. It gets harder and harder to push the plunger on the pump the more air is in the tire. Explain what is going on.

Short Answer

Expert verified
The plunger becomes harder to push due to increased pressure in the tire as more air is added.

Step by step solution

01

Identify the Concept

The scenario involves the principles of gas behavior under pressure. As more air is pumped into the tire, the volume of the tire remains relatively constant while the amount of air increases.
02

Apply the Ideal Gas Law

The ideal gas law is given by the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the universal gas constant, and \( T \) is temperature. As more air (\( n \) increases) gets pumped into the fixed volume \( V \) of the tire, the pressure \( P \) increases if the temperature \( T \) is constant.
03

Analyze the Resistance

With increased pressure inside the tire, more force is required to add additional air. This increased pressure results in greater opposition to the movement of the pump's plunger, making it harder to push.
04

Conclusion on the Difficulty

The resistance to pushing the pump plunger increases because the tire鈥檚 internal pressure rises with more air. This requires greater effort to overcome the external force of the higher pressure to continue inflating the tire.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Ideal Gas Law
The ideal gas law is a foundational concept in understanding how gases behave. It is expressed through the equation \( PV = nRT \). Let's break it down:
  • \( P \) stands for pressure, which measures the force exerted by gas molecules inside a container.
  • \( V \) is volume, indicating the amount of space the gas occupies.
  • \( n \) is the number of moles, representing the amount of gas present.
  • \( R \) is the universal gas constant, a value that ensures the equation is balanced.
  • \( T \) denotes the temperature, given in Kelvin, reflecting the thermal energy available to the gas molecules.
This equation tells us that the pressure, volume, and temperature of a gas are all interrelated. If one variable changes, others adjust accordingly, provided the amount of gas stays constant. In the scenario of a bicycle pump, while the volume of the tire stays almost the same, more air (\( n \)) is being added, which increases the pressure unless there is a change in temperature.
Exploring the Notion of Pressure
Pressure is a measure of how much force is applied to a certain area by gas molecules colliding with the walls of a container. In our everyday life, pressure is what makes a balloon inflate or a tire firm. When you use a bicycle pump, you're pushing more air molecules into the tire. As these molecules pack closer together in the confined space, their collisions with the tire walls increase, resulting in higher pressure. In simple terms:
  • More air molecules equals more collisions inside the tire.
  • This leads to higher pressure, as more force is applied over the same area.
The sensation of the pump getting harder to push is due to this rise in pressure, making it challenging for additional air to easily enter the tire.
The Role of Volume in Gas Behavior
Volume, in the context of gases, refers to the space that the gas occupies. In the case of a bicycle tire, the volume can be considered somewhat fixed because the tire's size doesn't change significantly as it inflates. Here's what happens in a fixed volume scenario:
  • As more air is pumped in, filling the limited space, the pressure rises.
  • The increased air density increases the force exerted by the air molecules against the tire's walls.
This fixed volume therefore leads to an increase in pressure each time more air is added, as per the ideal gas law. Ultimately, the volume that stays constant contributes to why it feels harder to push the pump as you keep inflating the tire.
Function of a Bicycle Pump in Inflating Tires
A bicycle pump is a handy tool that adds air to a tire, understanding why it becomes challenging to push involves several science concepts. When you first start using a pump, the tire has low pressure, and it's relatively easy to push air into it. But here's what makes it get tougher:
  • As you pump air, more is added to the tire, raising the inside pressure.
  • This higher pressure means more force is needed from the pump to overcome the current pressure in the tire.
  • The pump鈥檚 function is to compress air, forcing these molecules into the tire, countering the increasing resistance.
This basic process can be better understood using the ideal gas law, where the increasing number of air molecules in a relatively fixed volume raises tire pressure. In this scenario, the perceived difficulty of pushing the pump's plunger is a practical demonstration of gas laws at work.

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Most popular questions from this chapter

Imagine you fill a balloon with air to a volume of 240 \(\mathrm{mL}\) . Initially, the air temperature is \(25^{\circ} \mathrm{C}\) and the air pressure is 1.0 atm. You carry the balloon with you up a mountain where the air pressure is 0.75 atm and the temperature is \(25^{\circ} \mathrm{C}\) . a. When the balloon is carried up the mountain, what changes? What stays the same? b. The air pressure on the outside of the balloon has decreased. Can the air pressure on the inside decrease so that the pressures are equal? Why or why not? c. What happens to the volume occupied by the air inside the balloon? Explain your thinking. d. Solve for the new volume of the balloon.

A gas collected in a flexible container at a pressure of 0.97 atm has a volume of 0.500 L. The pressure is changed to 1.0 atm. The amount of gas and the temperature of the gas do not change. a. Will the volume of the gas increase or decrease? Explain. b. Which equation should you use to calculate the new volume of the gas? c. Calculate the volume of the gas at a pressure of 1.0 \(\mathrm{atm} .\)

At sea level, the pressure of trapped air inside your body is 1 atm. It is equal to the pressure of air outside your body at sea level. Imagine that you do a deep sea dive. You descend slowly to a depth where the pressure outside your body is 3.5 atm. a. How does the volume of your lungs compare at 3.5 atm with the volume at sea b. Why is it dangerous to hold your breath and ascend quickly?

When water freezes, the water molecules move apart very slightly. What evidence can you provide to support this claim?

Explain what causes air pressure.
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