Problem 95 - Chemistry

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.

Step-by-Step Solution

Answer

Situation A uses Gay-Lussac's Law to explain how temperature affects pressure in an automobile tire. Situation B uses Boyle's Law to explain how volume and pressure relate in the 'popping' of a paper bag. Situation C also uses Boyle's Law, demonstrating how a decrease in pressure can increase volume in a weather balloon. Situation D, like B, applies Boyle's law, showing how a sudden change in pressure, when a lightbulb shatters, causes a loud noise.

Step 1: Situation A: Automobile tire on a hot day

The pressure inside a tire increases on a hot day due to Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when volume is held constant. In this case, as the temperature increases (from the day becoming hot), so does the pressure inside the tire.

Step 2: Situation B: Popping of a paper bag

The 'popping' of a paper bag is a result of a rapid change in volume and therefore pressure - related to Boyle's Law which states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. The rapid increase in volume when the bag pops causes a decrease in pressure, producing the 'pop' sound.

Step 3: Situation C: Expansion of a weather balloon

The expansion of a weather balloon as it rises in the air can be explained by Boyle's Law - as the balloon rises, the outside air pressure decreases, causing the volume of the gas inside the balloon to expand. Because the law says that pressure and volume are inversely proportional (assuming a constant temperature), a decrease in one will cause an increase in the other.

Step 4: Situation D: Noise when a lightbulb shatters

The loud noise heard when a lightbulb shatters is due to a sudden change in pressure. When the lightbulb shatters, the gas inside the bulb escapes rapidly, creating a change in pressure - this can be again related to Boyle's law.

Key Concepts

Gay-Lussac's Law

Gay-Lussac's Law helps us understand the relationship between the pressure and temperature of a gas. According to this law, for a given amount of gas at a constant volume, the pressure is directly proportional to its absolute temperature. This means if the temperature of a gas increases, its pressure increases too, provided that the volume does not change.

When you find yourself on a hot day, the air inside your car tire expands.

• This expansion is due to the increase in temperature, which leads to an increase in pressure inside the tire.
• Gay-Lussac's Law explains this phenomenon: as the temperature outside rises, so does the pressure inside the tire.
• The tires could become over-inflated, which is something to watch out for!

This law is a crucial part of understanding how gases behave when subjected to temperature changes.

Boyle's Law

Boyle’s Law shines in scenarios where gas volume and pressure are considered, keeping temperature constant. It tells us that the pressure of a gas is inversely proportional to its volume. If the volume of a gas increases, the pressure decreases and vice versa.

Consider a paper bag that bursts.

• When you blow air into a paper bag and it pops, that's a clear illustration of Boyle's Law.
• Initially, the bag is stable with a balance of pressure and volume.
• Suddenly, the volume inside the bag increases rapidly, causing the pressure to drop, which results in the 'pop' sound.

This law is a great tool to predict how a gas will react under different volume conditions.

Pressure and Temperature

Pressure and temperature have a fascinating relationship that forms the basis of Gay-Lussac's Law. When a gas is heated, its particles move faster, which increases force and pressure against container walls, assuming volume stays constant.

In real-world applications:

• If you heat a sealed container, gas particles inside will exert more pressure.
• This principle explains why tires can burst on exceedingly hot days!

Simply understanding this relationship helps us grasp the bigger picture of how gases behave in varying thermal environments.

Volume and Pressure

Volume and Pressure play a critical role in understanding gas behavior through Boyle's Law. Naturally, if you squeeze a gas into a smaller space (decreasing volume), the pressure it exerts will increase.

Imagine a weather balloon:

• As it rises, the external air pressure decreases.
• According to Boyle's Law, the gas inside the balloon expands, increasing its volume, which balances out the reduced pressure.

This concept helps in understanding how expansion and compression of gases happen in different environments.

Gas Expansion

Gas Expansion is a key concept when discussing gas behavior. Gases naturally expand when pressure decreases or temperature increases.

Think about a weather balloon again.

• When it climbs through the atmosphere, it reaches areas of lower external pressure.
• This encourages the gas inside to expand, causing the balloon to grow larger.
• Understanding gas expansion is crucial for applications like forecasting weather patterns using balloons and understanding why balloons can burst if they rise too high.

This concept showcases the adaptable and dynamic nature of gases in various atmospheric conditions.