Question

Using the concepts developed in this chapter, explain the following observations. Automobile tires are flatter on cold days. You are not supposed to dispose of aerosol cans in a fire. The lid of a water bottle pops off when the bottle sits in the sun. d) A balloon pops when you squeeze it.

Short answer

A balloon pops when squeezed due to increased internal pressure exceeding the material's elastic limit.

Step-by-step solution

Understanding the Problem

We need to explain why a balloon pops when squeezed by applying the physical concepts discussed in the chapter. These concepts likely involve pressure, volume, and elasticity.

Identifying Key Concepts

The behavior of a balloon can be explained using the principles of pressure and material elasticity. When you squeeze a balloon, you are changing its volume and therefore its internal pressure. According to the Ideal Gas Law, the pressure of a gas in a closed container is related to its volume and temperature.

Applying the Ideal Gas Law

The Ideal Gas Law is given by \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the gas constant, and \( T \) is the temperature. Squeezing the balloon decreases its volume \( V \), which increases the pressure \( P \) inside the balloon as \( nRT \) remains constant.

Considering Material Limits

A balloon is made of elastic material that has a limit to how much it can stretch (known as tensile strength). As the internal pressure increases due to squeezing, the rubber eventually reaches its elastic limit and cannot stretch any further.

Explaining the Pop

Once the balloon material reaches its elastic limit, it cannot withstand the increased pressure, causing it to rupture suddenly. This is why a balloon pops when it is squeezed beyond its capacity to stretch.

Key concepts

Pressure in the Ideal Gas Law

When discussing pressure in the context of a balloon, it's crucial to understand that it is one of the key variables in the Ideal Gas Law. Pressure (\( P \)) in a gas-filled balloon is caused by the collisions of gas particles with the walls of the balloon. Each collision exerts a force on the walls, collectively contributing to the overall pressure.
This pressure is directly related to the volume (\( V \)) changes in the balloon. As the volume decreases, due to an action like squeezing the balloon, the gas particles have less space to move around. This results in an increase in the frequency of collisions with the balloon's walls, hence increasing the pressure.
According to the Ideal Gas Law, expressed by the formula \( PV = nRT \), where \( n \) is the amount of gas, \( R \) is the gas constant, and \( T \) is the temperature, anything that alters the volume directly impacts the pressure if the temperature and moles of gas remain constant. Therefore, squeezing the balloon elevates \( P \) since \( V \) is reduced.

Volume and Its Impact on Gas Behavior

Volume plays a significant role in the behavior of gases and determines how they exert pressure. In a balloon, the volume is the space the gas particles have to move around in.
A larger volume implies more space for the particles, leading to fewer collisions and hence, lower pressure. Conversely, a smaller volume results in higher pressure due to more frequent particle collisions.
When you apply pressure on a balloon by squeezing it, you're actually reducing its volume. The applied force causes the gas inside to compress, which according to Boyle's Law (a specific case of the Ideal Gas Law when temperature is constant) increases the pressure. Thus, the volume of a gas-filled balloon is inversely proportional to the pressure—meaning as volume decreases, pressure increases, as described in the formula \( P \times V = ext{constant} \).
This relationship demonstrates how any decrease in volume directly leads to an increase in pressure, eventually contributing to why squeezing a balloon too hard can make it pop.

Elasticity and Material Limits of Balloons

Elasticity refers to a material's ability to return to its original shape after being stretched or compressed. For a balloon, elasticity is crucial because it determines how much the balloon can be inflated or squeezed before it bursts.
Balloon rubber is designed to stretch, but has a limit to its elasticity, known as tensile strength. Tensile strength is the maximum amount of tensile stress that a material can withstand while being stretched before failing.

• Elastic limit: The maximum extent to which a balloon can expand before the material begins to deform permanently.
• Tensile strength: Beyond this point, the balloon materials can no longer stretch and may rupture.

As internal pressure builds from the increased force applied by squeezing, the balloon material approaches its elastic limit. If this limit is surpassed, the balloon cannot handle the internal pressure, and it bursts. Thus, the reason a balloon pops when squeezed hard isn't just more pressure—it's also reaching and exceeding its elasticity threshold.