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# Charles's Law

### Gas volume varies with temperature

Charles's law (also known as the law of volumes) is an experimental gas law which describes how gases tend to expand when heated.

An animation demonstrating the relationship between volume and temperature.- From Wikipedia

Charles's law (also known as the law of volumes) is an experimental gas law which describes how gases tend to expand when heated. It was first published by French natural philosopher Joseph Louis Gay-Lussac in 1802,[1] although he credits the discovery to unpublished work from the 1780s by Jacques Charles. The law was independently discovered by British natural philosopher John Dalton by 1801, although Dalton's description was less thorough than Gay-Lussac's.[2] The basic principles had already been described a century earlier by Guillaume Amontons.

Whatever the priority of the discovery, Gay-Lussac was the first to demonstrate that the law applied generally to all gases, and also to the vapours of volatile liquids if the temperature was more than a few degrees above the boiling point. His statement of the law can be expressed mathematically as:

$V_{100} - V_0 = kV_0\,$

where V100 is the volume occupied by a given sample of gas at 100 °C; V0 is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant pressure. Gay-Lussac's value for k was 1⁄2.6666, remarkably close to the present-day value of 1⁄2.7315.

A modern statement of Charles's law is:

At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature on the absolute temperature scale (i.e. the gas expands as the temperature increases).

which can be written as:

$V \propto T\,$

where V is the volume of the gas; and T is the absolute temperature. The law can also be usefully expressed as follows:

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.

$\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \mathrm{or} \qquad \frac {V_2}{V_1} = \frac{T_2}{T_1} \qquad \mathrm{or} \qquad V_1 T_2 = V_2 T_1.$

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