Source: /cirosantilli/boltzmann-constant

= Boltzmann constant
{c}
{title2=$k_B$, $1.38×10^{-23}$}
{wiki}

This is not a truly "fundamental" constant of nature like say the <speed of light> or the <Planck constant>.

Rather, it is just a definition of our <Kelvin> temperature scale, linking average microscopic energy to our macroscopic temperature scale.

The way to think about that link is, at 1 <Kelvin>, each particle has average energy:
$$
1/2 kT
$$
per degree of freedom.

This is why the units of the Boltzmann constant are <Joules> per <Kelvin>.

For an ideal <monatomic gas>, say <helium>, there are 3 degrees of freedom. so each helium atom has average energy:
$$
3/2 k_B T
$$

If we have 2 atoms at 1 K, they will have average energy $6/2 k_B J$, and so on.

Another conclusion is that this defines <temperature> as being proportional to the total energy. E.g. if we had 1 helium atom at 2 K then we would have about $6/2 k_B J$ energy, 3 K $9/2 k_B J$ and so on.

This energy is of course just an average: some particles have more, and others less, following the <Maxwell-Boltzmann distribution>.