Lei de Boyle (P1V1=P2V2)

Boyle's law: P₁·V₁ = P₂·V₂

Hold the temperature steady and the pressure of a fixed amount of ideal gas runs inversely with its volume: P·V = constant. Robert Boyle worked this out in 1662, and it covers isothermal compression. Push a piston in and the pressure climbs by the same factor that the volume drops. Take 10 L at 1 atm, squeeze it to 2 atm, and you get V₂ = (1·10)/2 = 5 L. The same thing happens to divers. Ambient pressure doubles roughly every 10 m down, so 6 L of air in the lungs at the surface becomes 3 L at 10 m. That is exactly why you never hold your breath on the way up: the air expands again and the lungs can rupture.

Applications

It shows up in scuba safety math, in engine piston design where the compression ratio matters, in high-altitude balloons, in syringes and aerosol sprays, across the compressed-gas cylinder industry, and in the breathing simulators used for lung-function testing.

FAQ

Which units must I use? Whatever you like, as long as both sides match. Atm and litres, Pa and m³, mmHg and mL all work. The only rule is that P₁ and P₂ share a unit, and V₁ and V₂ share one too.

Does it work for real gases? For an ideal gas it is exact. Real gases start to drift off at high pressures or close to condensation, and at that point you reach for van der Waals or the compressibility factor Z.

What if temperature changes? Switch to the combined gas law, P₁V₁/T₁ = P₂V₂/T₂. Boyle's law is what you get from it when temperature stays put (T₁ = T₂).