On the 100th anniversary of the Sackur-Tetrode equation

TL;DR

This paper reviews the historical development and significance of the Sackur-Tetrode equation, emphasizing its derivation, the role of phase space discretization, and its experimental validation using thermodynamic data from mercury vapor.

Contribution

It provides a comprehensive historical overview and analysis of the Sackur-Tetrode equation's derivation, testing, and its importance in quantum and thermodynamic theory.

Findings

The Sackur-Tetrode equation accurately predicts the entropy of monoatomic gases.

Discretization of phase space was crucial for deriving quantum statistical mechanics.

Experimental data from mercury vapor supported the theoretical predictions.

Abstract

In 1912, Otto Sackur and Hugo Tetrode independently put forward an equation for the absolute entropy of a monoatomic ideal gas and published it in "Annalen der Physik." The grand achievement in the derivation of this equation was the discretization of phase space for massive particles, expressed as \delta q \delta p = h, where q and p are conjugate variables and h is Planck's constant. Due to the dependence of the absolute entropy on Planck's constant, Sackur and Tetrode were able to devise a test of their equation by applying it to the monoatomic vapor of mercury; from the satisfactory numerical comparison of h obtained from thermodynamic data on mercury with Planck's value from black-body radiation, they inferred the correctness of their equation. In this review we highlight this almost forgotten episode of physics, discuss the arguments leading to the derivation of the Sackur--Tetrode equation and outline the method how this equation was tested with thermodynamic data.