What is the relationship between Charles law and the kinetic theory of gases?

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Answer 1 · 2017-06-06T07:01:04

From the kinetic theory, one derives the pressure equation,

$p = (mnv^2)/2$ where $m$ is mass of a molecule, $n$ is no. of molecules in unit volume, and $v$ is rms speed.

Thus, $n = N/V$ where, $N$ is total number of gas molecules.

Therefore, one may write,

$pV = (mNv^2)/3$

Now, $(mv^2)/2 = E$ where $E$ is the kinetic energy of a molecule.

Thus, $pV = (2NE)/3$

Now from the kinetic interpretation of temperature,

$E = (3kT)/2$ where $k$ is the Boltzmann constant.

Thus, $pV = NkT$

Now since, $N$ and $k$ are constants, then for a fixed $p$ ,

$V/T =$ constant

This is Charles' law from kinetic theory.