Equivalence of Boltzmann and Clausius entropy

Thread starter Bobhawke
Start date Dec 4, 2008
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Boltzmann Clausius Entropy Equivalence

AI Thread Summary

The discussion centers on demonstrating the equivalence of Clausius entropy and Boltzmann entropy at thermal equilibrium. The Clausius entropy formula involves integrating heat transfer over temperature, while Boltzmann entropy relates to the logarithm of the number of microstates. Participants suggest starting with a monoatomic ideal gas to illustrate the concept before seeking a broader generalization. Understanding the connection between these two entropy definitions is crucial for thermodynamics and statistical mechanics. This exploration could enhance comprehension of entropy in various systems.

Dec 4, 2008

Bobhawke

I can't figure out how to show that the Clausius entropy

\Delta S= \int_{T_1}^{T_2} \frac{dQ}{T}

is equivalent to the Boltzmann entropy

S=kln \Omega

at thermal equilibrium.

Does anyone know how to do this?

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Dec 7, 2008

flatmaster

Might want to see how it works for monoatomic ideal gas first, then look for a generalization.

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