## How to use our Gay-Lussac’s law calculator?

Our Gay-Lussac’s law calculator helps to calculate the values of the Gay-Lussac’s law. This law has 4 different values:

- P1 is the initial pressure of the gas
- T1 is the initial temperature of the gas
- P2 is the final pressure of the gas
- T2 is the final temperature of the gas

When 3 of these values are given in the calculator, it will automatically calculate and display the empty value.

The pressure is by default expressed in Pa and the temperature in °K. These units can be changed by clicking on it and selecting another unit.

**Table of contents:**

- Gay-Lussac’s law
- Definition
- Explanation
- Gay-Lussac’s law formula
- Limitation of the Gay-Lussac’s law
- Real life application of the Gay-Lussac’s law

## Gay-Lussac’s law

The Gay-Lussac’s law is one of the laws of the thermodynamics constituting the law of ideal gases. The Gay-Lussac’s law links the pressure and the temperature of an ideal gas at a constant volume.

The law was named after the French physicist and chemist Louis Joseph Gay-Lussac (1778 – 1850).

The Gay-Lussac’s law is also sometimes given to the Charles’s law that link the volume and the temperature at a constant pressure. Indeed, the Charles’s law was enunciated for the first time by Louis Joseph Gay-Lussac in 1802, but it was discovered by Jacques Charles in 1787. So, the good practice is to reserve the name Charles’s law for the relation between volume and temperature with constant pressure and the name of the Gay-Lussac’s law for the relation between pressure and temperature at a constant volume.

## Definition

The Gay-Lussac’s law describes the relation between the pressure and the temperature of a gas. This law specifies that at constant volume, the pressure of a certain quantity of an ideal gas is proportional to its temperature.

## Explanation

This definition means that when the volume is kept constant, an increase in the temperature of a gas leads to an increase of its pressure. On the other hands, when the temperature of the gas decreases, the pressure of the gas decreases.

The graphic of the pressure in function of the temperature (at constant volume) is typical of a directly proportional relation. The mathematical expression of this type of curve is:

P ∝ T or P/T = constant or P = kT

There is no need to know the exact value of the constant to apply the law between two same volumes of a gas under different temperature and pressure. Indeed, the Gay-Lussac’s law formula allows to compare two situations of the same gas when the quantity of gas and the volume are constant.

## Gay-Lussac’s law formula

The definition of the Gay-Lussac’s law gives the following formula:

P1 / T1 = P2 / T2

Where:

- P1 is the initial pressure of the gas in Pa
- T1 is the initial temperature of the gas in °K
- P2 is the final pressure of the gas in Pa
- T2 is the final temperature of the gas in °K

## Limitation of the Gay-Lussac’s law

The law is not available at high pressure and low temperature.

## Real life application of the Gay-Lussac’s law

The law has daily life applications. The first one is the pressure cooker. As the temperature of the water inside the cooker increases, water vapour is produced (gas state). This water vapour cannot escape the pressure cooker. By consequence, the volume can’t change. So the volume is constant and the pressure increases, but also the temperature of the liquid water and the water vapour which exceed the normal boiling point of water (100°C).

Another example is the car’s tires. After driving, the friction between the tires and the road cause heats. The air inside the tires heats up. But because the volume of the tires is constant, the air cannot expand. By consequence, the pressure increases.