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The question says it all.

How can I best convince a non-physicist that the Boltzmann constant describes the world around us?

Are there any striking effects around us that are due directly to the Boltzmann constant?

failedtitration
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KlausK
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1 Answers1

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The short answer to

Are there any striking effects around us that are due directly to the Boltzmann constant?

is that energy and temperature are measured in different units.

If $k_B$ were smaller by a factor 2, then our absolute temperature values (using the kelvin unit) would be larger by a factor of 2 (so that $k_BT$ is unchanged). The change is not in the physics, but in the scale values we use.

As I suggested in the comment, the Boltzmann constant $k_B$ is essentially an conversion factor between energy and temperature for accounting purposes because of the way energy and temperature were historically defined.

I would argue that $k_BT$ (the energy-equivalent of temperature) is more physical than either $k_B$ or $T$. In other words, we might have defined a quantity $\tau=k_BT$ and write all of our equations with $\tau$ (like $PV=N\tau$) and never have to see $k_B$. In fact, using the notion of "thermodynamic-beta" ($\beta=\frac{1}{k_BT}$) we can already write the ideal gas law as $PV=N/\beta$ or maybe $PV\beta=N$.

Furthermore, from the definition of entropy $S=k_B \ln \Omega$, the $k_B$ is just there to give units to the entropy [because of the way energy and temperature have been historically defined]. The physics is in the multiplicity $\Omega$, not in the Boltzmann constant $k_B$.

In natural units (as in https://en.wikipedia.org/wiki/Boltzmann_constant#Value_in_different_units ), $k_B$ is set to unity, which effectively swaps out temperature $T$ (in kelvin) for $\tau=k_BT$ (in units of energy).

robphy
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