Table of Contents
What is Boyle's Law?
Boyle's Law, discovered by Robert Boyle in 1662, states that for a fixed amount of ideal gas at constant temperature, the pressure and volume are inversely proportional. When you compress a gas to half its volume, its pressure doubles. When you allow it to expand to twice its volume, the pressure is halved. This fundamental gas law is a cornerstone of thermodynamics and chemistry.
The law is an excellent approximation for real gases at moderate pressures and temperatures, where intermolecular forces are negligible. At very high pressures or very low temperatures, real gas behavior deviates from Boyle's Law because molecules interact more strongly and have finite volume. The van der Waals equation provides corrections for these non-ideal effects.
The Formula
Where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is absolute temperature. The product PV remains constant when temperature and amount of gas are fixed.
Examples
| Scenario | P1 | V1 | P2 | V2 |
|---|---|---|---|---|
| Scuba diving (10m depth) | 1 atm | 6 L | 2 atm | 3 L |
| Syringe compression | 1 atm | 50 mL | 5 atm | 10 mL |
| Weather balloon at altitude | 1 atm | 1 m³ | 0.25 atm | 4 m³ |
| Bicycle tire pump | 1 atm | 200 mL | 6.9 atm | 29 mL |
Frequently Asked Questions
Why must temperature be constant?
Boyle's Law isolates the pressure-volume relationship by holding temperature constant (isothermal process). If temperature changes, both pressure and volume are affected by the temperature change as well, and you would need to use the combined gas law or ideal gas law instead. In practice, slow compression or expansion processes approximate isothermal conditions if the gas can exchange heat with its surroundings.
How does Boyle's Law apply to diving?
As a diver descends, water pressure increases by approximately 1 atmosphere per 10 meters of depth. According to Boyle's Law, air spaces in the body (lungs, sinuses, ears) compress proportionally. At 10m depth (2 atm), lung volume is halved. This is why divers must equalize pressure in air spaces and why breathing compressed air at depth causes nitrogen narcosis and decompression sickness upon ascent.
Does Boyle's Law apply to liquids?
No, Boyle's Law specifically applies to gases. Liquids are nearly incompressible, meaning their volume changes very little even under enormous pressure changes. The bulk modulus of water is about 2.2 GPa, meaning you need to apply 220 atmospheres of pressure to reduce water's volume by just 1%. This is why hydraulic systems use liquids to transmit force efficiently.