# Gas laws

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The early gas laws were developed at the end of the eighteenth century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases. Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have molecules which are widely spaced, and nowadays the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.

## Contents

### Boyle's Law

Boyle's Law shows that, at constant temperature, the product of an ideal gas's pressure and volume is always constant. It was published in 1622. It can be determined experimentally using a pressure gauge and a variable volume container. It can also be found through the use of logic; if a container, with a fixed amount of molecules inside, is reduced in volume, more molecules will hit the sides of the container per unit time, causing a greater pressure.

As a mathematical equation, Boyle's law is:

Where P is the pressure (Pa), V the volume (dm3) of a gas, and k1 (measured in joules) is the constant from this equation—it is not the same as the constants from the other equations below.

### Charles's Law

Charles's Law, or the law of volumes, was found in 1787. It says that, for an ideal gas at constant pressure, the volume is proportional to the absolute temperature (in kelvins). This can be found using the kinetic theory of gases or a heated container with a variable volume (such as a conical flask with a balloon).

Where T is the absolute temperature of the gas (in kelvins) and k2 (in m3·K−1) is the constant produced.

### Gay-Lussac's Law

The pressure (or Gay-Lussac's) law was found by Joseph Louis Gay-Lussac in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to the absolute temperature of the gas. This follows from the kinetic theory—by increasing the temperature of the gas, the molecules' speeds increase meaning an increased amount of collisions with the container walls.

As a mathematical formula, this is: