# Boyle's law

**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) andV(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:

- <math>P \propto \frac{1}{V}</math>

or

- <math> 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 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 (P_{1}) and volume (V_{1}). If you change the pressure to a new value (P_{2}), the volume changes to a new value (V_{2}). We can use Boyle's law to describe both sets of conditions:^{[3]}

- <math>P_1 V_1 = k</math>
- <math>P_2 V_2 = k</math>

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

- <math>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>P_1 V_1 = P_2 V_2</math>
- <math> V_2 = \frac{P_1 V_1}{P_2}</math>
- <math> V_2 = \frac{3*5}{2}</math>
- <math> V_2 = \frac{15}{2}</math>
- <math> 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.^{[2]}^{[4]}^{[5]}

## References

- ↑ Template:Cite book
- ↑
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- ↑ 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