Boyle's law

An animation showing the relationship between pressure and volume.The amount and temperature of the gas are constant.

Boyle's law (also called Mariotte's law and the Boyle-Mariotte law) is a law about ideal gases.

The law can be stated as follows: Template:Quote

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 a 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.