# Charles's law

Charles's law states that, at constant presuure, the volume, V, of a given mass of gas is directly proportional to the absolute temperature.

This directly proportional relationship can be written as:
$V\propto T\mathrm{or}\frac{V}{T}=k$

where:

V is the volume of the gas.

T is the temperature of the gas (measured in Kelvin).

k is a constant.

Because the formula is equal to a constant, Charles's law can be rewritten as: $\frac{{V}_{1}}{{T}_{1}}=\frac{{V}_{2}}{{T}_{2}}$

The law was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s.

Example:

A gas with a volume of 2 liters at 100 K is heated to 200 K. What is the new volume with no change in pressure?

$\frac{{V}_{1}}{{T}_{1}}=\frac{{V}_{2}}{{T}_{2}}$

${V}_{2}={V}_{1}x\frac{{T}_{2}}{{T}_{1}}=3\mathrm{liters}x\frac{200K}{100K}=6\mathrm{liters}$

Charles's law is based upon absolute temperature. The absolute temperature is calculated by adding 273 to the temperature in Celsius scale. 10°C is equiavalent to 283 K.

${T}_{}=10\mathrm{\xb0C}+273=283K$