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Philip Koeck

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In summary, the conversation discusses the possibility of finding an expression similar to the Sackur-Tetrode equation for the statistical entropy of fermions or bosons, particularly in the context of electron or photon gases. The speakers mention sources such as a PDF from ETH Zürich and lecture notes from David L. Feder on statistical mechanics. They also mention a potential mistake in Feder's notes and reference a book by J. E. Mayer and M. G. Mayer for comparison.

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Philip Koeck

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Lord Jestocost

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Philip Koeck

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I was thinking more along these lines: For the BoItzmann distribution I would write:

n_{i} = g_{i} e^{-α} e^{-β ui}

ln W ≈ ∑n_{i} (1 - ln (n_{i} / g_{i})) = N + αN + βU

α = - μ / kT ; β = 1 / kT

S = k ln W = k N - μ N / T + U / T

Inserting expressions for μ and U for an ideal gas gives the Sackur-Tetrode equation.

Is something similar possible for FD or BE?

n

ln W ≈ ∑n

α = - μ / kT ; β = 1 / kT

S = k ln W = k N - μ N / T + U / T

Inserting expressions for μ and U for an ideal gas gives the Sackur-Tetrode equation.

Is something similar possible for FD or BE?

Last edited:

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Lord Jestocost

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Philip Koeck

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Thanks for your help. I'll look at both texts during summer.

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Philip Koeck

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Anyway: I'd like to know if it's possible to simplify this expression as sketched in the text. My problem is that I'm left with 1 term I can't simplify at the end of section 3. Do you know if this is done anywhere?

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Lord Jestocost

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The expression for entropy of fermions or bosons is given by **S = k _{B}lnΩ**, where

The entropy of fermions or bosons is different from classical particles because they obey different statistical distributions. Fermions follow the Fermi-Dirac distribution, which results in a maximum entropy at zero temperature. Bosons, on the other hand, follow the Bose-Einstein distribution, which results in a non-zero entropy at zero temperature.

No, the expression for entropy of fermions or bosons only applies to systems in thermal equilibrium, where the particles are indistinguishable and obey either the Fermi-Dirac or Bose-Einstein distribution.

Yes, the expression for entropy of fermions or bosons can be derived from statistical mechanics and quantum mechanics principles, such as the Pauli exclusion principle and the indistinguishability of particles.

The second law of thermodynamics states that the total entropy of a closed system always increases or remains constant. In the case of fermions and bosons, the entropy is related to the number of available microstates, which increases with increasing temperature. Therefore, as the temperature increases, the entropy of fermions and bosons also increases, in accordance with the second law of thermodynamics.

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