Physics – History and Philosophy of Physics
Scientific paper
2011-12-16
Physics
History and Philosophy of Physics
17 pages, no figures
Scientific paper
In 1912, Otto Sackur and Hugo Tetrode independently developed an equation for the absolute entropy of a monoatomic ideal gas. 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. Moreover, Sackur and Tetrode succeeded in corroborating their equation by ingeniously utilizing thermodynamic data on mercury. In essence, they determined $h$ from the equilibrium of liquid and gaseous phases of mercury and compared it with the value previously obtained by Planck from black-body radiation. In this paper we discuss the arguments leading to the derivation of the Sackur-Tetrode equation and describe also the way how they made their equation amenable to an experimental test. Doing a numerical computation similar to that of Sackur and Tetrode, we demonstrate that, with modern mercury data, Planck's constant can be determined with an accuracy of about one percent.
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