# Charles's Law (Law of Volumes)

Charles' Law

For a fixed mass of gas at constant pressure, the volume is directly proportional to temperature (in Kelvin). This is mathematically

$V = constant x T$

That means, for example, that if you double the temperature from, say to 300 K to 600 K, at constant pressure, the volume of a fixed mass of the gas will double as well. You can express this mathematically as

Is this consistent with pV = nRT ?

• You have a fixed mass of gas, so n (the number of moles) is constant.
• R is the gas constant.
• Charles' Law demands that pressure is constant as well.

If you rearrange the pV = nRT equation by dividing both sides by p, you will get

V = nR/p x T

But everything in the nR/p part of this is constant. That means that V = constant x T, which is Charles' Law.