# Boyle's law

experimental gas law

Boyle's law (also called Mariotte's law and the Boyle-Mariotte law) is a law about ideal gases. An animation showing the relationship between pressure and volume.The amount and temperature of the gas are constant.

The law can be stated as follows:

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.

In symbols, the law is:

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

$PV=k$ 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.

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:

$P_{1}V_{1}=k$ $P_{2}V_{2}=k$ The constant, k, is the same in both cases, so we can say the following:

$P_{1}V_{1}=P_{2}V_{2}$ 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?

$P_{1}V_{1}=P_{2}V_{2}$ $V_{2}={\frac {P_{1}V_{1}}{P_{2}}}$ $V_{2}={\frac {3*5}{2}}$ $V_{2}={\frac {15}{2}}$ $V_{2}=7.5$ ∴ The volume will be 7.5 litres.

The law was found by Robert Boyle in 1662, and afterwards independently by Edme Mariotte in 1679.