Boyle's law

File:Boyle.jpg

Diagram of Boyle's mercurial gauge, "to discover the degrees both of rarified and condensed air." Boyle's diagram from a later experiment used a Torricellian barometer in which the mercury reservoir was contained within a glass vessel which was evacuated by an air pump.

Boyle's law (sometimes called the Boyle Mariotte law) is one of the gas laws. Boyle's Law is named after the Irish natural philosopher Robert Boyle (1627-1691) who discovered it in 1662. Edme Mariotte (1620-1684) was a French physicist who discovered the same law independently of Boyle in 1676, so this law is often known as Mariotte's or Mariotte Boyle law.

Boyle's Law states that the product of the volume and pressure of a fixed quantity of an ideal gas is constant, given constant temperature. Expressed mathematically, the formula for Boyle's law is:

$\qquad \qquad PV=k$

where:

• V is volume of the gas.
• P is the pressure of the gas.
• k is a constant.

(Actually, k is a function of temperature, a fact that may be ignored provided the constant temperature constraint explicitly included in the statement of Boyle's law is not ignored.)

The value of k is computed from measurements of volume and pressure for a fixed quantity of gas. After making a change to the system, typically by forcing a change in the volume of the vessel containing the fixed quantity of gas, the new volume and new pressure are measured. The result of computing the product of the measured new volume and the new pressure should be the original value of the constant k. Without being too rigorous at this point, the equation says that, after 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" (subscript 1) and "after" (subscript 2) 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:

$\qquad P_{1}V_{1}=P_{2}V_{2}$

In practice, this equation is solved for one of the two "after" quantities to determine the effect that a change in the other "after" quantity will have. For example:

$\qquad P_{2}=P_{1}V_{1}/V_{2}$

Boyle's law, Charles's 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.

See also

• Scientific laws named after people

External links

• Boyle's Law at the Scuba Guide. Understanding Boyle's law is an important part of scuba certification; see Boyle's law explained in a scuba context.