Sackur-Tetrode entropy
The Sackur–Tetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations which give a more detailed description of its regime of validity.
The Sackur–Tetrode equation is named for Hugo Martin Tetrode (1895–1931) and Otto Sackur (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912.
The Sackur–Tetrode equation is written:
where V is the volume of the gas, N is the number of particles in the gas, U is the internal energy of the gas, k is Boltzmann's constant, m is the mass of a gas particle, h is Planck's constant and ln() is the natural logarithm. See Gibbs paradox for a derivation of the Sackur–Tetrode equation. See also the ideal gas article for the constraints placed upon the entropy of an ideal gas by thermodynamics alone.
The Sackur–Tetrode equation can also be conveniently expressed in terms of the thermal wavelength .
Note that the assumption was made that the gas is in the classical regime, and is described by Maxwell–Boltzmann statistics (with "correct Boltzmann counting"). From the definition of the thermal wavelength, this means the Sackur–Tetrode equation is only valid for
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