Equivalence of Boltzmann and Clausius entropy

Bobhawke

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

[tex] \Delta S= \int_{T_1}^{T_2} \frac{dQ}{T}[/tex]

is equivalent to the Boltzmann entropy

[tex] S=kln \Omega [/tex]

at thermal equilibrium.

Does anyone know how to do this?

Bobhawke

bump

flatmaster

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

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Bobhawke	Equivalence of Boltzmann and Clausius entropy Tweet I can't figure out how to show that the Clausius entropy [tex] \Delta S= \int_{T_1}^{T_2} \frac{dQ}{T}[/tex] is equivalent to the Boltzmann entropy [tex] S=kln \Omega [/tex] at thermal equilibrium. Does anyone know how to do this?

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