# Boyle's law

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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:[1]

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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.[2]

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.[3]

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:[3]

$P_1 V_1 = k$
$P_2 V_2 = k$

The constant, k, is the same in both cases, so we can say the following:[3]

$P_1 V_1 = P_2 V_2$

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.[2][4][5]

## References

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5. West, John B. (2005-01-01), "Robert Boyle's landmark book of 1660 with the first experiments on rarified air", Journal of Applied Physiology, 98 (1), pp. 31–39, doi:10.1152/japplphysiol.00759.2004