Boyle's law

For a fixed amount of gas at constant temperature, Boyle's law states that pressure varies inversely with volume. It can be written PV = k, where P is absolute pressure, V is volume and k is constant for the specified amount of gas and temperature. For two states of the same sample under those conditions, P₁V₁ = P₂V₂. Thus, if the volume is reduced to one-half while temperature and amount remain fixed, the pressure doubles in the idealized model.

The ideal gas equation is PV = nRT, where n is amount of gas, R is the gas constant and T is absolute temperature. When n and T are constant, nRT is constant, so PV is constant; Boyle's law follows directly. In calculations, pressure must be absolute rather than gauge pressure, and temperature is held constant in kelvins.

Compressing a gas in a sealed syringe decreases the space available to its molecules. If the gas does not heat up or leak, collisions with the container walls occur more often per area and pressure rises. This inverse relationship is also relevant to gas volumes changing with ambient pressure, such as air in a diver's buoyancy device during ascent, though practical systems can involve heat transfer and other effects.

Boyle's law is exact for an ideal gas under its stated fixed-temperature, fixed-amount conditions. Real gases approximate it most closely at low density or pressure and can depart from the simple relation, particularly as intermolecular interactions and molecular volume become significant at higher pressures or near condensation. In general, the ideal-gas relation PV = nRT accounts for changes in temperature and amount as well as pressure and volume.

Robert Boyle reported his gas-pressure and volume experiments in the seventeenth century, and the law is named for him. Edme Mariotte independently described the relationship later; Boyle's law is consequently also known as Mariotte's law.