Short Answer

Gay-Lussac’s law states that the pressure of a gas increases when its temperature increases, and the pressure decreases when the temperature decreases, provided the volume of the gas remains constant. This means gas pressure is directly proportional to temperature.

This law explains why heated gases create higher pressure, such as in pressure cookers, gas cylinders, and car tyres. When temperature rises, gas particles move faster and collide more strongly with the container walls, causing pressure to increase.

Detailed Explanation

Gay-Lussac’s Law

Gay-Lussac’s law is an important gas law that explains how the pressure of a gas changes with temperature when its volume remains constant. This law is named after the French scientist Joseph Louis Gay-Lussac, who studied the behaviour of gases under controlled conditions. According to Gay-Lussac’s law, the pressure of a gas is directly proportional to its temperature when the volume does not change. In simple words, if the temperature increases, pressure increases; if temperature decreases, pressure decreases.

This law helps us understand why gases become more active when heated and why pressure-related changes occur in many everyday situations. It is especially important in closed containers, where gas cannot expand freely and must respond to temperature changes through changes in pressure.

Direct Relationship Between Pressure and Temperature

The key idea of Gay-Lussac’s law is the direct relationship between pressure and temperature. This means that both quantities increase or decrease together. If the temperature of a gas is raised, its particles gain kinetic energy and begin to move faster. Faster movement leads to more frequent and stronger collisions with the walls of the container. These stronger collisions produce higher pressure.

When the temperature decreases, gas particles move slowly. Their collisions with the container walls become weaker and less frequent, which lowers the pressure. Because the volume remains constant, gas particles cannot spread out or compress further, so the only way to adjust to temperature change is through pressure.

Explanation Using Kinetic Theory

The kinetic theory of gases helps explain Gay-Lussac’s law. According to this theory, gas particles are always moving. Their movement depends on their kinetic energy, which is directly linked to temperature. Higher temperature means higher kinetic energy.

When kinetic energy increases:

Particles move faster.
More collisions occur with container walls.
Collisions occur with greater force.
Pressure increases.

When kinetic energy decreases:

Particles move slowly.
Collisions become weaker and less frequent.
Pressure decreases.

This clear connection between motion and pressure shows why Gay-Lussac’s law works.

Mathematical Expression of the Law

Gay-Lussac’s law is expressed as:
P ∝ T (Pressure is directly proportional to temperature)
Temperature must be measured in Kelvin for correct results.

The law can also be written as:
P₁ / T₁ = P₂ / T₂

Where:

P₁ = initial pressure
T₁ = initial temperature
P₂ = final pressure
T₂ = final temperature

This equation means the ratio of pressure to temperature remains constant if volume stays the same.

Everyday Examples of Gay-Lussac’s Law

Gay-Lussac’s law can be seen in many real-life situations:

Pressure Cookers:
When heated, the gas inside the cooker increases in temperature. As a result, pressure rises and cooks food faster.
Car Tyres:
Tyre pressure increases in summer or when driving long distances because the air inside heats up.
Aerosol Cans:
Cans contain gas under pressure. When kept in sunlight or near heat, the temperature rises, increasing pressure, which can make the can burst.
Gas Cylinders:
If exposed to heat, the gas molecules inside a cylinder move faster, increasing pressure. This is why cylinders must be kept away from high temperatures.
Balloons:
A balloon kept near a flame expands because the gas inside becomes hot and pressure increases.

These examples show how temperature influences gas pressure when the volume does not change.

Scientific and Practical Importance

Gay-Lussac’s law is essential in many fields, including chemistry, engineering, aviation, and meteorology. It helps scientists understand how gases behave in closed systems and helps engineers design safe pressure equipment. It also explains atmospheric pressure changes and plays a role in weather forecasting.

The law is also part of the combined gas law and contributes to understanding the ideal gas equation, making it an important part of gas studies.

Conclusion

Gay-Lussac’s law states that the pressure of a gas is directly proportional to its temperature when the volume remains constant. Higher temperature increases pressure, and lower temperature reduces pressure. This law explains many everyday phenomena and is vital for understanding gas behaviour in closed containers. It is widely used in science, industry, and daily life.