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Boyle's law

At a fixed temperature, squeeze a gas into half the space and its pressure doubles; release the pressure and it expands.

Boyle's law says that for a fixed amount of gas at a steady temperature, pressure and volume are inversely proportional: multiply them together and you always get the same number. Halve the volume and the pressure doubles; double the volume and the pressure halves.

Robert Boyle published the law in 1662, using apparatus built by his assistant Robert Hooke. The French physicist Edme Mariotte found it independently in 1679, so in parts of Europe it is called Mariotte's law.

The law helps explain breathing. When your diaphragm and chest muscles enlarge your lungs, the air inside spreads into more space, its pressure falls below that of the air outside, and air flows in. An iron lung did this from the outside, by lowering the pressure around a patient's chest; a modern ventilator does the opposite, pushing air in at higher pressure.

It matters underwater too. Water pressure rises by about one atmosphere for every 10 metres of depth, so air trapped in an upturned bucket or a diving bell is squeezed to half its surface volume at 10 metres, a third at 20 metres and a quarter at 30 metres, unless more air is pumped in. A diver rising with a lungful of air faces the reverse: the air expands, which is why divers are taught never to hold their breath while ascending.

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