Boyle's law

Boyle's law, also called the Boyle–Mariotte law, is an important rule in physics that explains how the pressure and volume of a gas are related. It says that if the temperature and amount of gas stay the same, the pressure of the gas goes up when the volume goes down, and the pressure goes down when the volume goes up. This is called an inverse relationship. The rule only works if the temperature does not change.^[1][2][3]

This relationship can be written as a formula:

${\displaystyle P\propto {\frac {1}{V}}\quad {\text{or}}\quad PV=k}$

In this formula, P means pressure, V means volume, and k is a constant number that stays the same if the gas does not change in amount or temperature. This means that if you squeeze a gas into a smaller space, its pressure will increase. If you give it more space, its pressure will decrease.^[1]

Robert Boyle, a scientist from Ireland, published this law in 1662. He worked with another scientist named Robert Hooke. Together, they did experiments using a J-shaped glass tube filled with mercury. They trapped a fixed amount of air in the tube and changed the volume by adding or removing mercury. Then they measured how the pressure changed. These experiments were very important in the early history of science.^[2] Later, in 1676, a French scientist named Edme Mariotte discovered the same rule on his own. He published his work a few years after Boyle. Because both scientists found the same result, the law is sometimes called the Boyle–Mariotte law, especially in Europe.^[3]

Boyle’s law works best for ideal gases. These are gases where the gas particles do not stick together or take up much space. Real gases do not always follow this law exactly, especially when they are at high pressure or low temperature. But in many situations, Boyle’s law still gives a good idea of how gases behave. This law is very important in science. It is used in chemistry, physics, engineering, and weather science. Boyle’s law helps explain how syringes work, how animals breathe, and what happens to gases in closed containers.^[4]

The law can be stated as follows:^[5]

For a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional.

In other words, the volume of a constant mass of ideal gas at a constant temperature is inversely proportional to the pressure applied on it.^[6]

In symbols, the law is:

${\displaystyle P\propto {\frac {1}{V}}}$

or

${\displaystyle PV=k}$

where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

For a given mass of gas at a constant temperature, the product of the pressure and the volume is constant. As the volume decreases, the pressure increases in proportion, and vice versa. For example, when the pressure halves, the volume doubles.

Suppose you have a tank that contains a certain volume of gas at a certain pressure. When you decrease the volume of the tank, the same number of gas particles is now contained in a smaller space. Therefore, the number of collisions increases. Therefore, the pressure is greater.^[7]

Imagine you have a gas at a certain pressure (P₁) and volume (V₁). If you change the pressure to a new value (P₂), the volume changes to a new value (V₂). We can use Boyle's law to describe both sets of conditions:^[7]

${\displaystyle P_{1}V_{1}=k}$

${\displaystyle P_{2}V_{2}=k}$

The constant, k, is the same in both cases, so we can say the following:^[7]

${\displaystyle P_{1}V_{1}=P_{2}V_{2}}$

Example: The pressure of a gas is 3 atm and the volume is 5 litres. If the pressure is reduced to 2 atm, what is the volume?

${\displaystyle P_{1}V_{1}=P_{2}V_{2}}$

${\displaystyle V_{2}={\frac {P_{1}V_{1}}{P_{2}}}}$

${\displaystyle V_{2}={\frac {3*5}{2}}}$

${\displaystyle V_{2}={\frac {15}{2}}}$

${\displaystyle V_{2}=7.5}$

∴ The volume will be 7.5 litres.

The law was found by Robert Boyle in 1662, and afterwards independently by Edme Mariotte in 1679.^[6][8][9]