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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 1 The T-dS Equations Entropy and the Increase in Entropy Principle

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 2 The T-dS EquationsOverview The Clausius TheoremThe Clausius Theorem EntropyEntropy Analogy between the First and Second LawsAnalogy between the First and Second Laws The T-dS equationsThe T-dS equations

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 3 The T-dS Equations The Clausius Theorem...

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 4 The T-dS Equations Clausius’ Theorem (1)

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 5 The T-dS Equations Used in your book to demonstrate the validity of the Clausius inequality

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 6 The T-dS Equations For a irreversible cycle - Clausius’ Theorem (2)

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 7 The T-dS Equations For a reversible cycle - Clausius’ Theorem (3) Have we seen this type of behavior before?

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 8 The T-dS Equations Volume through a cycle:

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 9 The T-dS Equations For a reversible cycle - Clausius’ Theorem (3) This is the behavior of v, P, h, and u also Therefore, δQ rev /T must also be a property.

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 10 The T-dS Equations Clausius called this new property he discovered entropy

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 11 The T-dS Equations Entropy - the definition (4) As with u and h, more interested in ΔS than S.

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 12 The T-dS Equations Entropy - the definition (3)

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 13 The T-dS Equations In the special case of an isothermal heat transfer process (which is reversible), it reduces to ΔS sys = Q/T. Therefore ΔS sys can be negative or positive.

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 14 The T-dS Equations The entropy change between two specified states is the same no matter what path is taken

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 15 The T-dS Equations Increase of entropy principle If a system is isolated, then this principle is: unless the process is reversible.

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 16 The T-dS Equations

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 17 The T-dS Equations A system and its surroundings form an isolated system

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 18 The T-dS Equations Increase of entropy principle For any process in which an irreversibility exists,the net effect is the increase of the entropy of the universe, or

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 19 The T-dS Equations Increase of entropy principle Some entropy is generated or created during an irreversible process and it is called entropy generation or S gen. S gen is always positive or zero.

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 20 The T-dS Equations The entropy change of a system can be negative, but the entropy generation cannot.

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Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 21 The T-dS EquationsSo… A process must proceed in a direction that complies with the increase in entropy principle.A process must proceed in a direction that complies with the increase in entropy principle. Entropy is a nonconserved property. Entropy is conserved only in a reversible process, otherwise it increases.Entropy is a nonconserved property. Entropy is conserved only in a reversible process, otherwise it increases. Entropy generation is a measure of irreversiblilties which degrade an engineering system.Entropy generation is a measure of irreversiblilties which degrade an engineering system.

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