What Is Boyle's Law?
Boyle's Law: The Inverse Relationship Between Gas Pressure and Volume
Boyle's law states that the pressure of a fixed amount of gas varies inversely with its volume when temperature is held constant. For two equilibrium states, it can be written P1V1 = P2V2.
Robert Boyle and Robert Hooke investigated compressed and rarefied air using an improved vacuum pump and a sealed column of mercury. Boyle reported the pressure-volume relation in the 1662 edition of New Experiments Physico-Mechanicall, Touching the Spring of the Air. Edme Mariotte later described the relation independently.
If the absolute pressure doubles under isothermal conditions, the ideal-gas volume halves. A graph of P against V forms a hyperbola, while P plotted against 1/V is linear over the range in which the law is a good approximation.
The kinetic explanation is that reducing the volume shortens the average distance molecules travel before reaching a wall. At unchanged temperature, their speed distribution is unchanged, but collisions with the container occur more frequently, increasing the rate of momentum transfer and therefore the pressure.
The requirement of constant temperature is essential. Compression can heat a gas and expansion can cool it, so a rapid process may not obey the isothermal relation. The system must exchange sufficient heat with its surroundings, or otherwise be controlled, for temperature to remain fixed.
Boyle's law is contained in the ideal-gas equation PV = nRT. Real gases approach the law at low density but deviate when molecular volume and intermolecular forces become significant, particularly near condensation or at high pressure.
The relation is used in syringes, pumps, breathing, pneumatic systems, diving calculations, and laboratory gas handling. Care is needed to use absolute rather than gauge pressure and consistent units when comparing states.
Historically, Boyle's law was important because a repeatable macroscopic relation later received a corpuscular explanation. The law can be established experimentally without seeing molecules, while kinetic theory explains why the relation emerges from their collective motion.
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