Question

Discuss the following phenomena in terms of the gas laws: (a) the pressure increase in an automobile tire on a hot day, (b) the "popping" of a paper bag, (c) the expansion of a weather balloon as it rises in the air, (d) the loud noise heard when a lightbulb shatters.

Short answer

(a) Due to increased temperature, pressure inside the tire rises. (b) Rapid compression increases internal pressure, causing it to pop. (c) Rising causes lower external pressure, leading to balloon expansion. (d) Sudden pressure equalization causes a loud noise.

Step-by-step solution

Understanding Pressure Increase in a Tire

As the temperature increases on a hot day, the air molecules inside the tire gain kinetic energy. According to Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature if volume is constant, the pressure inside the tire increases. Therefore, as the tire temperature rises, the pressure in the tire also rises.

Explaining the Popping of a Paper Bag

Popping a paper bag can be understood through Boyle's Law, which states that pressure is inversely proportional to volume when temperature is constant. When you rapidly compress the bag by slapping it, the volume inside decreases quickly, increasing the pressure, causing it to pop.

Expansion of a Weather Balloon

A weather balloon expands as it rises due to the decreasing atmospheric pressure. According to Boyle's Law, as the external pressure decreases at higher altitudes, the gas inside the balloon expands to fill a larger volume, therefore causing the balloon to expand.

Loud Noise from a Shattering Lightbulb

When a lightbulb shatters, the sudden release of internal vacuum or pressure causes air to rush inside. This rapid change in pressure can be associated with Boyle's Law, explaining the loud noise due to the abrupt increase in pressure as the vacuum is broken and the volume changes rapidly.

Key concepts

Gay-Lussac's Law

Gay-Lussac's Law is a fundamental concept in thermodynamics that relates the pressure and temperature of a gas. It states that the pressure of a given mass of gas is directly proportional to its absolute temperature, provided that the volume remains constant. This can be expressed mathematically as \( P \propto T \). Thus, any increase in temperature will lead to an increase in pressure if the gas is contained within a fixed volume.

This law explains why an automobile tire's pressure increases on a hot day. As the temperature outside rises, the air molecules inside the tire gain kinetic energy. This greater energy results in more forceful and frequent collisions against the tire's walls, increasing the pressure within the tire. It’s crucial for drivers to monitor tire pressure, especially during warm weather, to avoid blowouts caused by excessively high internal pressures.

Boyle's Law

Boyle's Law is another key principle when discussing the behavior of gases. It describes the inverse relationship between the pressure and volume of a gas at constant temperature. Mathematically, it is expressed as \( PV = k \), where \( k \) is a constant. If you decrease the volume that a gas occupies, the pressure increases, provided the temperature remains unchanged.

This principle explains the 'popping' of a paper bag. When you compress the bag quickly, the internal volume decreases sharply, boosting the pressure inside. This rapid rise in pressure can exceed the material's strength, causing the bag to burst noisily.

Boyle's Law also applies to the shattering of a lightbulb. The vacuum inside the bulb ensures minimal pressure when intact. Once shattered, air rushes in to fill the space, causing significant pressure changes and the loud noise we hear.

Pressure and Temperature Relationship

The relationship between pressure and temperature in gases is a critical aspect of gas behavior, often examined under Gay-Lussac's Law. As mentioned, when the temperature of a gas increases, so does its pressure, assuming volume doesn't change. This relationship is crucial in various real-world scenarios involving gases.

• Automobile tires: Rising temperatures can increase tire pressure, potentially leading to damage if not monitored.
• Weather phenomena: Changes in atmospheric temperatures can significantly influence air pressure and weather patterns, impacting activities like flying and driving.

Understanding this relationship allows for better management and prevention of potential hazards related to changing temperatures and pressures in various settings.

Volume and Pressure Relationship

The volume and pressure relationship in gases is notably described by Boyle’s Law, highlighting how they are inversely related when temperature is constant. This means that if you reduce the volume of a gas, the pressure increases, and vice versa.

• Weather balloons: As they ascend, external pressure decreases. According to Boyle’s Law, the balloon’s volume must increase, ensuring it expands and can be used to gather atmospheric data efficiently.
• Everyday scenarios: Compressing air using a bicycle pump reduces its volume and increases its pressure, effectively inflating the tire.

Comprehending this relationship is essential for applications involving the compression or expansion of gases, ensuring their efficient and safe use.