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# Lecture14A - Spontaneity(20.4-5 Remember the Zeroth Law...

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Lecture 14 1 Spontaneity!(20.4-5) Remember the Zero th Law: heat flows from a warm to a cold body (spontaneously!). Consider two isolated systems A and B at different temperatures. isolated Remember what isolated means? (no heat, no matter flow) isolating barrier V A , T A V B , T B Now remove the isolating barrier between systems A and B so they are in thermal contact. V A , T A V B , T B isolated U A +U B =constant V A ,V B = constant (no work!) say T B >T A S=S A +S B

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Lecture 14 2 ( 29 ( 29 no work system is isolated A rev A A B rev B B A dU q T dS dU q T dS dU δ δ = = = = = - 1 1 A B B B A B A B A B B B A dU dU dU dU dS dS dS T T T T dS dU T T = + = + = - + = - th is negative by the Zero law (heat flows out of B) 1 1 is negative since B B A B A dU T T T T - So, dS >0 for spontaneous process in an isolated system When T B =T A , dS=0 (and the system is in equilibrium). So for isolated systems in equilibrium dS=0.
Lecture 14 3 (trickier, but makes sense when you think about it) dS=0 for any reversible process in an isolated system, since reversible implies (by definition) that the system is in equilibrium.

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