# Boyle's law

Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

## Overview

Boyle's law (sometimes referred to as the Boyle-Mariotte law) is one of the gas laws and basis of derivation for the ideal gas law, which describes the relationship between the product pressure and volume within a closed system as constant when temperature and moles remain at a fixed measure; both entities remain inversely proportional.[1][2] The law was named after chemist and physicist, Robert Boyle who published the original law in 1662. The law itself can be defined succinctly as follows:

 “ For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional (while one increases, the other decreases).[2] ”

## History

Boyle's Law is named after the Irish natural philosopher Robert Boyle (Lismore, County Waterford, 1627-1691) who was the first to publish it in 1662. The relationship between pressure and volume was brought to the attention of Boyle by two friends and amateur scientists, Richard Towneley and Henry Power, who discovered it. Boyle confirmed their discovery through experiments and published the results. According to Robert Gunther and other authorities, Boyle's assistant Robert Hooke, who built the experimental apparatus, may well PITO have helped to quantify the law; Hooke was accounted a more able mathematician than Boyle. Hooke also developed the improved vacuum pumps necessary for the experiments. The French physicist Edme Mariotte (1620-1684) discovered the same law independently of Boyle in 1676, so this law may be referred to as Mariotte's or the Boyle-Mariotte law.

## Definition

### Relation to kinetic theory and ideal gases

Boyle's law states that the volume of a gas increases when the pressure decreases at a constant temperature. Also it is the most fundamental of the 23 gas laws. The law was not likely to have deviations at the time of publication due to limits upon technology, but as further technological advances occurred limitations of the approach would have become known, as Boyle's law relates more effectively to real gases[3] due to its description of such gases consisting of large numbers of particles moving independently of each other.[3]

In 1738, Daniel Bernoulli derived Boyle's law using Newton's laws of motion with application on a molecular level, but remained ignored until c. 1845, when John Waterston published a paper building the main precepts of kinetic theory, but was rejected by the Royal Society of England until the later works of James Prescott Joule, Rudolf Clausius and Ludwig Boltzmann firmly established the kinetic theory of gases and brought attention to both the theories of Bernoulli and Waterston.[4]

The ongoing debate between proponents of Energetics and Atomism led Boltzmann to write a book in 1898, which endured criticism up to his suicide in 1901.[4] Albert Einstein in 1905 showed how kinetic theory applied to the Brownian motion of a fluid-suspended particle, which was confirmed in 1908 by Jean Perrin.[4] From these perspectives upon kinetic theory, the derivation of Boyle's Law can be achieved through its assumptions.

### Equation

The mathematical equation for Boyle's law is:

${\displaystyle \qquad \qquad PV=k}$

where:

P denotes the pressure of the system.
V is the volume of the gas.
k is a constant value representative of the pressure and volume of the system.

So long as temperature remains constant at the same value the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant. However, due to the derivation of pressure as perpendicular applied force and the probabilistic likelihood of collisions with other particles through collision theory, the application of force to a surface may not be infinitely constant for such values of k, but will have a limit when differentiating such values over a given time.

Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure p must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure.

Boyle's law is commonly used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The "before" and "after" volumes and pressures of the fixed amount of gas, where the "before" and "after" temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation:

${\displaystyle p_{1}V_{1}=p_{2}V_{2}.\,}$

Boyle's law, Charles' law, and Gay-Lussac's Law form the combined gas law. The three gas laws in combination with Avogadro's law can be generalized by the ideal gas law.