Boltzmann and gas constant – ambiguities between energy and force

Version 1

Abstract

Energy and force are distinct fundamental quantities, differing in both their physical meaning and units. In the International System of Units (SI), the Boltzmann constant is one of the seven defining constants. The Bureau International des Poids et Mesures explains the Boltzmann constant k as “a proportionality constant between the quantities temperature (with the unit kelvin) and energy (with the unit joule)” [1]. Consequently, “one kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy kT by 1.380 649 × 10⁻²³ J” [1]. It should be noted that this groundbreaking definition concerns a physical constant, not the concept of energy itself. But a clear distinction is warranted: Energy in any form and expressed in the unit joule (‘thermal energy’, kinetic and potential energy, work and heat, Helmholtz and internal energy, Gibbs energy and enthalpy) is an extensive quantity that scales in direct proportion to the size of a system, whereas intensive quantities such as temperature and force are independent of system size. The concept that a fixed temperature change results in a proportional change of thermal energy kT lacks specification of the entity to which energy is attributed. By relating energy to the individual particle, kT accounts for the quantum structure of nature. The present analysis aims at resolving ambiguities of the term ‘thermal energy kT’ by a focus on SI units and corresponding symbols to describe adequately and clearly the full meaning of any form of energy related to fundamental physical or thermodynamic forces.

Cite:

Gnaiger E (2025) Boltzmann and gas constant – ambiguities between energy and force. BEC preprints 2025.5. https://doi.org/10.26124/becprep.2025-0005