# What is Gay-Lussac’s law? Its Explanation, Applications, and Limitations (with PDF)

Gay-Lussac’s Law is also known as the Law of Pressure or Amonton’s Law. This law correlates with how the pressure of a gas increases with increasing temperature. Gay Lussac’s Law is named after French chemist Joseph Louis Gay-Lussac. He formulated this relationship in 1808. Gay-Lussac’s law is similar to Charles’s law, the only difference being that the term “volume” in Charles’s law is replaced by the term “pressure” in Gay-Lussac’s law.

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## Statement of Gay Lussac Law

For a constant volume of a confined ideal gas, its pressure is directly proportional to absolute temperature at constant volume.

## Explanation of Gay Lussac Law

As the law states, the pressure and temperature of an ideal gas are directly proportional to each other for a given volume and mass of the gas. This statement can be expressed mathematically as follows:

On removing the proportionality, we get,

where,

k is a constant of proportionality.

The above expression can be rearranged as:

Here, the Temperature shall be Kelvin, and Pressure shall be measured in ATM.

The above Gay-Lussac Formula is valid when the volume is constant at a given mass. As the temperature increases, the pressure of the gas increases, and as the temperature decreases, the pressure decreases. The above equation clearly shows that the relationship between pressure and temperature is independent of pressure or temperature at constant volume.

When comparing the same substance under two different conditions, Gay-Lussac’s law can be written as:

P1 T2 = P2 T1

When the pressure of a gas obeying the Gay-Lussac law doubles, the temperature also doubles, as explained below.

The diagram above is a typical experimental set-up required to verify the Gay-Lussac Law. When the air in the chamber is heated with water using a heating source (an electric heater is used in the figure), the temperature of the air increases which tends to increase the kinetic energy associated with air molecules. Air molecules, therefore, exert a more outward force on all walls of the container. Due to the fixed boundaries, the air trapped inside the chamber cannot expand. The number of molecular collisions increases and the air pressure also increases. Using the same analogy, as the air cools, its pressure drops.

## Limitations of Gay Lussac Law

The limitations of Gay Lussac Law are as follows:

• Gay-Lussac Law is only applicable to ideal gases.
• Gay-Lussac’s law applies to real gases at high temperatures and/or low pressure.
• At high pressures, the relationship between pressure and temperature is off. As the pressure increases, the ratio decreases. This decrease is due to the increase in volume at high pressure and is explained by the increase in repulsive forces between molecules at high pressure.

## Applications of Gay Lussac Law in Real Life

Examples of Gay-Lussac’s law include bursting pressure cookers, bursting aerosol cans, and bursting tires. All of these substances explode when exposed to high temperatures. The scientific reason for the explosion is explained by Gay-Lussac’s law.

Gay-Lussac’s law states that the pressure of a gas increases with temperature and vice versa. Gay-Lussac presented experimental results in 1808. He showed a direct relationship between pressure and temperature for a given volume of gas.

There are many examples of the application of Gay-Lussac’s Law that can be observed in everyday life. Below are some of those mentioned.

### Pressure cooker

A pressure cooker is a sealed device for cooking food under the pressure of steam. Usually made of steel or aluminum. When heated, the moisture in the refrigerator evaporates and steam is generated. Steam is released periodically through the valve to maintain operating pressure inside the cooker.

If the valve does not work and the heat flow is not interrupted, the pressure inside the stove will increase. The increase in pressure is based on the Gay-Lussac law. That is the pressure of a constant volume of gas increases with temperature at a constant volume. This high pressure can damage the cooker and lead to an unfortunate accident.

### Aerosol can

An aerosol can or spray is a device that releases an aerosol, a suspension of fine solid particles or liquid droplets, into the air. When the metal can valve is opened, gas is released to form a mist or aerosol. One of the components of an aerosol can is a propellant. Propellants consist of volatile compounds that liquefy under high pressure. Propellant provides thrust to other components when the valve is open. When an aerosol can is exposed to a hot environment, the propellant vaporizes. These vaporized gases exert pressure on the walls of the bottle. According to Gay-Lussac’s law, the pressure on a wall increases with temperature and the can bursts. For this reason, it is recommended to keep aerosol cans away from heat.

### Gun bullet

When a weapon’s projectile is ignited, the chemical energy stored in the projectile’s casing is converted into heat through a chemical reaction. This heat causes the temperature to rise, which in turn causes the pressure to rise according to the Gay-Lussac law. Bullets are fired from guns because of the high pressure.

### Automobile tires

Inflated car tires can burst on hot summer days. Tire bursts are caused by the Gay-Lussac law. Inflated tires are under high pressure. As the temperature of the air increases, the pressure of the gas inside the tube increases. Tires break after excruciating spots.

### Water Heater

An electric kettle is similar to a pressure cooker. Cold water is heated by a heating wire inside the heater. The hot water produced is discharged through the outlet nozzle. Modern electric heaters automatically adjust the water temperature. In the event of system or relief valve failure, continuous power is supplied to generate steam which can damage the heater. If the steam pressure exceeds the permissible limits, the heater may explode.

## Summary

Gay-Lussac Law is one of the Gas Laws in which Pressure will vary and volume will remain constant.. Charles’ Law states that at least one of the container’s boundaries is movable. As the temperature rises, the air inside the container expands. This expansion keeps the pressure constant according to Charles’ law. Gay-Lussac’s law states that the volume remains constant and the pressure changes.

Atul Singla

Hi ! I 'm Atul. I am PMP certified Mechanical (Piping) Engineer with more than 17 Years of experience. Worked in the field of Plant design for various industries such as refinery, petrochemical & chemical, Fertilizer, gas Processing industries. Developed passion about Piping while working with national & international engineering consultants on diverse projects involving international clients. Developed courses on Piping Engineering to share the knowledge gained after working with many industry experts, through out these years.