Sackur–Tetrode equation

The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas.

[1] It is named for Hugo Martin Tetrode[2] (1895–1931) and Otto Sackur[3] (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912.

of a monatomic ideal gas in terms of its thermodynamic state—specifically, its volume

The above expressions assume that the gas is in the classical regime and is described by Maxwell–Boltzmann statistics (with "correct Boltzmann counting").

The Sackur–Tetrode constant, written S0/R, is equal to S/kBN evaluated at a temperature of T = 1 kelvin, at standard pressure (100 kPa or 101.325 kPa, to be specified), for one mole of an ideal gas composed of particles of mass equal to the atomic mass constant (mu = 1.66053906892(52)×10−27 kg‍[5]).

Its 2018 CODATA recommended value is: In addition to the thermodynamic perspective of entropy, the tools of information theory can be used to provide an information perspective of entropy.

[8] Summing the four pieces, the Sackur–Tetrode equation is then given as The derivation uses Stirling's approximation,

Strictly speaking, the use of dimensioned arguments to the logarithms is incorrect, however their use is a "shortcut" made for simplicity.

Entropy vs temperature curves of classical and quantum ideal gases ( Fermi gas , Bose gas ) in three dimensions. Though all are in close agreement at high temperature, they disagree at low temperatures where the classical entropy (Sackur–Tetrode equation) starts to approach negative values.