# Boyle’s law calculator

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## How to use our Boyle’s law calculator?

The Boyle’s law calculator helps to calculate the values of the Boyle’s law, which is composed of 4 different values:

P1 is the initial pressure of the gas
V1 is the initial volume of the gas
P2 is the final pressure of the gas
V2 is the final volume 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 volume in m³. These units can be changed by clicking on it and selecting another one.

## Boyle’s law

The Boyle’s law (also known as the Boyle-Mariotte law or Mariotte’s law) is one of the laws of the thermodynamics constituting the law of ideal gases. The Boyle’s law links the pressure and the volume of an ideal gas at a constant temperature.

The law was named after the Irish physicist and chemist Robert Boyle (1627- 1691) and the French physicist Edme Mariotte (1620 – 1684). The law was first discovered by Robert Boyle in 1662 and then by Edme Mariotte in 1676. The French physicist and engineer Guillaume Amontons clarified the law by adding that the law is only available at constant pressure and that the law was more precise at low pressure.

## Definition

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

## Explanation

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

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

P ∝ 1/V or PV = constant

There is no need to know the exact value of the constant to apply the law between two volumes of gas under different pressures at the same temperature. Indeed, the Boyle’s law formula allows to compare two situations of the same gas when the quantity of gas and the temperature are constant.

## Boyle’s law formula

The definition of the Boyle’s law gives the following formula:

P1V1 = P2V2

Where:

• P1 is the initial pressure of the gas in Pa
• V1 is the initial volume of the gas in m3
• P2 is the final pressure of the gas in Pa
• V2 is the final volume of the gas in m³

## Limitations of the Boyle’s law

The Boyle’s law is only applicable at low pressure, generally less than 10 bar (100 kPa).

## The Boyle’s law used in the everyday life

Probably the most important everyday life use of the Boyle’s law is to explain the human breathing system.

But the Boyle’s law is also used for other applications, like for example the autonomy of a gas bottle.