Why is k constant in Boyle's law?

Md Ariful Islam

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Md Ariful Islam

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was first formulated as an experimental gas law which described how the pressure of a gas decreased when the volume of said gas increased.

A more formal description of states that the pressure exerted by a mass of ideal gas is inversely proportional to the volume it occupies if temperature and amount of gas remain unchanged.

Mathematically, this can be written as

$P$ $alpha 1/V$, or $PV = "constant"$

This is where a $k$ is usually seen, as it is often used to describe a constant value. So the $k$ you are referring to is

$PV = "constant" = k$

This can be easily derived from the , $PV = nRT$, for the conditions specified by Boyle's law.

We need to keep the amount of gas, which represents the number of , and the temperature constant. Since $R$ is a constant already, the becomes

$PV = nRT = k$

Therefore, $k$ must be constant in order to allow for a relationship to be set between pressure and volume.

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