Derivation of sackur-tetrode equation

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SUMMARY

The Sackur-Tetrode equation is derived as the classical limit of quantum statistics, specifically Boltzmann statistics, which applies to both fermions and bosons. This derivation requires the consideration of particle indistinguishability, a quantum-mechanical phenomenon that resolves the Gibbs paradox and provides a correct expression for entropy. The derivation involves applying Stirling's approximation to the multiplicity formula for an ideal gas. Classical thermodynamics alone cannot justify the necessary factor of 1/N! without invoking quantum theory.

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  • Understanding of Boltzmann statistics
  • Familiarity with Stirling's approximation
  • Knowledge of classical thermodynamics principles
  • Concept of particle indistinguishability in quantum mechanics
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Students and researchers in physics, particularly those focusing on statistical mechanics, thermodynamics, and quantum theory. This discussion is beneficial for anyone looking to understand the derivation and implications of the Sackur-Tetrode equation.

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

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