The energy meaning of Boltzmann's constant

TL;DR

This paper explores the fundamental link between Boltzmann's constant and atomic-scale vibrational energies, proposing a classical model to derive its value from quantum energy considerations.

Contribution

It introduces a classical atomic model to derive Boltzmann's constant from vibrational energy, connecting quantum and thermodynamic scales.

Findings

Vibrational frequency of a classical hydrogen atom is in the far-infrared range.

Quantum of energy of this vibration yields Boltzmann's constant.

The approach links atomic vibrations to temperature measurement.

Abstract

The atomic scale is the only relevant thermodynamic scale in our universe, since quantum properties restrict classical considerations of subatomic physics and disappear for larger scales. Then the characteristic energy that dictates the value of the unit of temperature can be the classical thermal energy defined for simplest atoms. It is shown that vibrational frequency of a classical model hydrogen atom, of the radius of its Rydberg wavelength, is in far-infrared range and from its quantum of energy one can obtain the value of Boltzmann's constant that serves as the measure of the absolute temperature in kelvins.