## Clausius Inequality [ENDORSED]

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Payton Kammerer 2B
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Joined: Tue May 01, 2018 3:00 am

### Clausius Inequality

"If qrev in the definition of entropy DS = q(rev)/T is replaced by the smaller quantity q(irrev), then DS = q(irrev)/T. In general, the Clausius inequality is
DS >= q/T
with the equality applicable to a reversible process."

Why is this applicable to a reversible process if we are using the q(irrev) instead of q(rev)????

Chem_Mod
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### Re: Clausius Inequality  [ENDORSED]

Think of the example I did in class with hot system and cold surroundings.

Since T(h) > T(c) then q/T(h) < q/T(c) and the sum of these is positive.

They are only equal to each other at equilibrium, in this case thermal equilibrium, and if both are the same temperature we know there is no heat flow.
Hence the definition of delta S (total) = 0 for systems at equilibrium.

Hope this helps.

Really proud of everyone today. Well done completing your final.

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