1. 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

2. 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

3. 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...

4. 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)

5. 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

6. 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)

7. 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?

8. 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:

9. 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.

10. 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

11. 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.

12. 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)

13. 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.

14. 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

15. 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.

16. 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

17. 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

18. 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

19. 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.

20. 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.

21. 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.