Why is k constant in Boyle's law?

1 Answer
Stefan V.
Jan 9, 2015

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.

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