# Charles's law

An animation demonstrating the relationship between volume and temperature
Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant kB = R/NA = n R/N  (in each law, properties circled are variable and properties not circled are held constant)

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

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.[1]

This relationship of direct proportion can be written as:

${\displaystyle V\propto T}$

So this means:

${\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}$
where:

V is the volume of the gas,

T is the temperature of the gas (measured in kelvins),

and k is a non-zero constant.

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:

${\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}\qquad {\text{or}}\qquad {\frac {V_{2}}{V_{1}}}={\frac {T_{2}}{T_{1}}}\qquad {\text{or}}\qquad V_{1}T_{2}=V_{2}T_{1}.}$

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

1. ^ Fullick, P. (1994), Physics, Heinemann, pp. 141–42, ISBN 978-0-435-57078-1.