0

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
  • 63
KlausK
  • 727
  • 3
    What do you mean "due to the Boltzmann constant"? Do you mean if it were a different size? Its presence is not negotiable. – ProfRob Aug 04 '22 at 20:11
  • In some sense, the Boltzmann constant $k_B$ arises from the historical choices of units for energy and for [absolute] temperature. – robphy Aug 04 '22 at 20:28
  • $k_B$ is the order of magnitude of the average kinetic energy of a particle $\langle \mathcal E_1 \rangle$ per unit temperature $T$ in equilibrium: $k_B \approx \langle \mathcal E_1 \rangle/T$ – hyportnex Aug 04 '22 at 20:39
  • duplicate? https://physics.stackexchange.com/questions/231017/is-the-boltzmann-constant-really-that-important?rq=1 – hft Aug 04 '22 at 22:51
  • If you want an everyday way to measure $k$, this is equivalent to measuring the ideal gas constant, $R=kN_A$ (k × avagadro's number). Steve Mould did a video on one way to do this https://youtu.be/wR2tOLShFmY. You can also take two data points of $P,V,T$ for a volume of gas, and extrapolate, backing out $k$ – RC_23 Aug 05 '22 at 00:30

1 Answers1

4

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
  • 11,748