Sackur–Tetrode equation

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

S=N k_B \ln \left[ \left( \frac{2 \pi m  k_B T}{h^2} \right)^{3/2} \frac{k_BT}{p}  \exp(5/2)\right]

where k_B is the Boltzmann constant, T is the temperature, p is the pressure, m is the mass of the gas particle, N is the numer of particles and h is the Planck constant.


  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)