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OUTLINE OF CHAPTER 4

# OUTLINE OF CHAPTER 4 - OUTLINE OF CHAPTER 4 Entropy Recall...

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OUTLINE OF CHAPTER 4 Entropy Recall Observation 5 (Chapter 1): All spontaneous processes in an isolated constant- volume (rigid) system result in the evolution to equilibrium (time invariant and uniform state) Let us try to express this through a balance equation for an isolated and constant-volume or But in a time invariant system 0 d dt θ = Thus, at equilibrium 0 gen = ± Assume we can identify a variable that has a positive generation away from equilibrium and 0 d dt = at equilibrium…

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Since 0 d dt θ > then is increasing and should be MAXIMUM at equilibrium. Thus, we define:
Closed System 0 gen S by definition, which also means 0 gen S = ± at equilibrium. Before using entropy, we need to establish that: a) S is a variable of State. b) 0 gen S ± Equation is a BLACK BOX equation and cannot tell anything about gen S ± , which is coming from internal relaxation processes within the system.

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Special Case in which we can gain insight on gen S ± A and B can interact transferring heat only. A+B is isolated Assumption: Heat transfer takes place, but the systems remain uniform Assume now that the heat transfer takes place very slowly so that no internal generation of entropy takes place (bunch of successive uniform states, or “equilibrium” states. Then But for the combined system (Q=0, S= S A+ S B ), we have Then Here we assumed that the parts are uniform, but we realize the whole system is not!!!
Note: - gen S ± is positive - gen S ± is proportional to the second power of the non-uniformity Integral form of entropy balance

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SECOND LAW (SECOND PRINCIPLE)
Clausius Statement of the Second Law It is not possible to construct a device that operates in a cycle and whose sole effect is to transfer heat from a cold source to a hot sink. Consider one cycle Thus Q 1 =-Q 2 and the entropy balance says or

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BUT S gen >0, which is a contradiction. The machine works well in reverse.
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OUTLINE OF CHAPTER 4 - OUTLINE OF CHAPTER 4 Entropy Recall...

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