Question

Why is k constant in Boyle's law?

Answer 1

Boyle's law 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 Boyle's law 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 ideal gas law, `PV = nRT`, for the conditions specified by Boyle's law.

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

`PV = nRT = k`

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