Sackur–Tetrode equation

The Sackur–Tetrode equation provides the entropy ($S$) of an ideal gas (classical). It is given by

$S=Nk_{B}\ln \left[\left({\frac {2\pi mk_{B}T}{h^{2}}}\right)^{3/2}{\frac {k_{B}T}{p}}\exp(5/2)\right]$

where $k_{B}$ is the Boltzmann constant, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the temperature, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} is the pressure, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} is the mass of the gas particle, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is the numer of particles and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h} is the Planck constant.

References

1. O. Sackur "Die universelle Bedeutung des sog. elementaren Wirkungsquantums", Annalen der Physik 40 pp. 67-86 (1913)
2. H. Tetrode "Die chemische Konstante der Gase und das elementare Wirkungsquantum", Annalen der Physik 38 pp. 434-442 (1912)
3. H. Tetrode "Berichtigung zu meiner Arbeit: 'Die chemische Konstante der Gase und das elementare Wirkungsquantum'", Annalen der Physik 39 pp. 255-256 (1913)