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Entropy and the Increase in Entropy Principle

Entropy and the Increase in Entropy Principle . Overview. The Clausius Theorem Entropy Analogy between the First and Second Laws The T-dS equations. The Clausius Theorem. Clausius’ Theorem. (1). Used in your book to demonstrate the validity of the Clausius inequality.

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Entropy and the Increase in Entropy Principle

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  1. Entropy and the Increase in Entropy Principle

  2. Overview • The Clausius Theorem • Entropy • Analogy between the First and Second Laws • The T-dS equations

  3. The Clausius Theorem...

  4. Clausius’ Theorem (1)

  5. Used in your book to demonstrate the validity of the Clausius inequality

  6. For a irreversible cycle - Clausius’ Theorem (2)

  7. For a reversible cycle - Clausius’ Theorem (3) Have we seen this type of behavior before?

  8. Volume through a cycle:

  9. For a reversible cycle - Clausius’ Theorem This is the behavior of v, P, h, and u also (3) Therefore, δQrev/T must also be a property.

  10. Clausius called this new property he discovered entropy

  11. (4) Entropy - the definition As with u and h, more interested in ΔS than S.

  12. (3) Entropy - the definition

  13. In the special case of an isothermal heat transfer process (which is reversible), it reduces to ΔSsys = Q/T. Therefore ΔSsyscan be negative or positive.

  14. The entropy change between two specified states is the same no matter what path is taken

  15. Increase of entropy principle If a system is isolated, then this principle is: unless the process is reversible.

  16. A system and its surroundings form an isolated system

  17. 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

  18. Increase of entropy principle Some entropy is generated or created during an irreversible process and it is called entropy generation or Sgen. Sgen is always positive or zero.

  19. The entropy change of a system can be negative, but the entropy generation cannot.

  20. So… • 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 generation is a measure of irreversiblilties which degrade an engineering system.

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