Boyle's law

File:Boyles Law animated.gif

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 its pressure.

In symbols, the law is:

[math]\displaystyle{ P \propto \frac{1}{V} }[/math]

or

[math]\displaystyle{ PV = k }[/math]

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 proprotion, 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:

[math]\displaystyle{ P_1 V_1 = k }[/math]

[math]\displaystyle{ P_2 V_2 = k }[/math]

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

[math]\displaystyle{ P_1 V_1 = P_2 V_2 }[/math]

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?

[math]\displaystyle{ P_1 V_1 = P_2 V_2 }[/math]

[math]\displaystyle{ V_2 = \frac{P_1 V_1}{P_2} }[/math]

[math]\displaystyle{ V_2 = \frac{3*5}{2} }[/math]

[math]\displaystyle{ V_2 = \frac{15}{2} }[/math]

[math]\displaystyle{ V_2 = 7.5 }[/math]

∴ The volume will be 7.5 litres.

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