Boyle's law
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Boyle's law (sometimes referred to as the Boyle Mariotte law) is one of the gas laws. It states that:
- For a fixed mass of ideal gas at fixed temperature, the product of pressure and volume is a constant.
[edit] 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 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 Mariotte Boyle law.
[edit] Equation
The mathematical expression for Boyle's law is:
where:
- P is the pressure of the gas
- V is the volume of the gas
- k is a constant, and has units of force times distance.
As long as the fixed temperature constraint, and the fixed mass of gas constraint, both explicitly included in the statement of Boyle's law, are not violated, the computed value of k will not change as the pressure and volume are changed.
The value of k is computed from measurements of volume and pressure for a fixed mass 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" 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:
- Pafter Vafter = Pbefore Vbefore
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:
- Pafter = Pbefore Vbefore / Vafter
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.
