# Boltzmann constant

In thermodynamics, the Boltzmann constant kB is the ratio of the gas constant R to Avogadro’s number NA: [1]

$k_{B} = \frac{R}{N_{\rm A}}\,$

which numerically equates to 1.38E-23 J/K = (8.314  J /K*mol)/(6.022E23 particles/mol). The constant is named after Austrian physicist Ludwig Boltzmann.

History
In 1901, German physicist Max Planck calculated value for what he called “universal constants”, one being Planck constant h, the other being: [2]

k = 1.346 * 10E-16 erg / deg

which he said he first made in his 1900 paper “Entropy and Temperature of Radiant Heat.” [3] In 1920, Planck commented on his calculation that: [4]

“This constant is often referred to as Boltzmann's constant, although, to my knowledge, Boltzmann himself never introduced it, a peculiar state of affairs, which can be explained by the fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant.”

It may be, however, that similar variations or formulations of this constant may have been used by Walther Nernst (1893) and Willard Gibbs (1901).

References
1. Perrot, Pierre. (1998). A to Z of Thermodynamics (pg. 22). Oxford: Oxford University Press.
2. Planck, Max. (1901). "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff.
3. Planck, Max. (1900). “Entropy and Temperature of Radiant Heat.” (Entropie und Temperatur strahlender Wärme) Annalen der Physik, vol. 1. no 4. April, pg. 719-37.
4. Planck, Max. (1920). “The Genesis and Present State of Development of the Quantum Theory.” Nobel Lecture, Jun 02.