Derivation of sackur-tetrode equation

[ralden]

how sackur-tetrode equation derive?, can it derive without the use of macrocanonical ensemble? only by classical thermodynamics? thank you.

 

[vanhees71]

The Sackur-Tetrode formula can only be derived properly as the classical limit of quantum statistics, which is Boltzmann statistics for both fermions and bosons, taking into account the indistinguishability of particles, which is a specific quantum-mechanical phenomenon. Classical statistics leads to the Gibbs paradoxon and a wrong (non-extensive) expression for the entropy which is solved by the Sackur-Tetrode formula.

 

[wbandersonjr]

You can derive the Sackur-Tetrode equation by solving for the entropy of an ideal gas using Stirling's approximation applied to the multiplicity formula. My thermodynamics text does not go through the whole derivation, but that is how it says to derive it.

 

[vanhees71]

Yes, that you can do, but you have to assume the indistinguishability of particles, which leads to an additional factor $1/N!$ compared to classical mechanics. This factor cannot justified without the indistinguishability argument that is generically quantum theoretical.