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Chapter 22 Entropy and the Second Law of Thermodynamics

Chapter 22 Entropy and the Second Law of Thermodynamics. Configuration Configuration – certain arrangement of objects in a system Configuration for N spheres in the box, with n spheres in the left half. Microstates Microstate – one of the ways to prepare a configuration

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Chapter 22 Entropy and the Second Law of Thermodynamics

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  1. Chapter 22 Entropy and the Second Law of Thermodynamics

  2. Configuration • Configuration – certain arrangement of objects in a system • Configuration for N spheres in the box, with n spheres in the left half

  3. Microstates • Microstate – one of the ways to prepare a configuration • An example of 4 different microstates for 4 spheres in the box, with 3 spheres in the left half

  4. Multiplicity • Multiplicity ( W ) – a number of microstates available for a given configuration • From statistical mechanics:

  5. Multiplicity

  6. Multiplicity

  7. Multiplicity

  8. Multiplicity

  9. Entropy • For identical spheres all microstates are equally probable • Entropy ( S ):

  10. Entropy • For identical spheres all microstates are equally probable • Entropy ( S ): • For a free expansion of • 100 molecules • Entropy is growing for • irreversible processes in • isolatedsystems

  11. Entropy • Entropy, loosely defined, is a measure of disorder in the system • Entropy is related to another fundamental concept – information. Alternative definition of irreversible processes – processes involving erasure of information • Entropy cannot noticeably decrease in isolated systems • Entropy has a tendencyto increase in open systems

  12. Entropy in cosmology • In modern cosmology, our universe is an isolated system, freely (irreversibly) expanding: total entropy of the universe increases and gives time its direction • The evolution equation of the universe (the Friedman equation) has two solutions (positive t and negative t) – entropy is increasing in two time directions from a minimum point

  13. Entropy in open systems • In open systems entropy can decrease: • Chemical reactions

  14. Entropy in open systems • In open systems entropy can decrease: • Chemical reactions • Molecular self-assembly

  15. Entropy in open systems • In open systems entropy can decrease: • Chemical reactions • Molecular self-assembly • Creation of information

  16. Entropy in thermodynamics • In thermodynamics, entropy for open systems is • The change in entropy is • For isothermal process, the change in entropy: • For adiabatic process, the change in entropy:

  17. Entropy as a state function • First law of thermodynamics for an ideal gas: • For irreversible processes, to calculate the change in entropy, the process has to be replaced with a reversible process with the same initial and final states or use a statistical approach

  18. The second law of thermodynamics • In closed systems, the entropy increases for irreversible processes and remains constant for reversible processes • In real (not idealized) closed systems the process are always irreversible to some extent because of friction, turbulence, etc. • Most real systems are open since it is difficult to create a perfect insulation

  19. Nicolas Léonard Sadi Carnot (1796–1832) • Engines • In an ideal engine, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc. • Carnot engine:

  20. Carnot engine (continued) • Carnot engine on the p-V diagram: • Carnot engine on the T-S diagram:

  21. Engine efficiency • Efficiency of an engine (ε): • For Carnot engine:

  22. Perfect engine • Perfect engine: • For a perfect Carnot engine: • No perfect engine is possible in which a heat from a thermal reservoir will be completely converted to work

  23. Gasoline engine • Another example of an efficient engine is a gasoline engine:

  24. Heat pumps (refrigerators) • In an ideal refrigerator, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc. • Performance of a refrigerator (K): • For Carnot refrigerator :

  25. Perfect refrigerator • Perfect refrigerator: • For a perfect Carnot refrigerator: • No perfect refrigerator is possible in which a heat from a thermal reservoir with a lower temperature will be completely transferred to a thermal reservoir with a higher temperature

  26. Questions?

  27. Answers to the even-numbered problems Chapter 22 Problem 6 24.0 J

  28. Answers to the even-numbered problems • Chapter 22 • Problem 10 • 870 MJ • 330 MJ

  29. Answers to the even-numbered problems Chapter 22 Problem 30 − 610 J/K

  30. Answers to the even-numbered problems Chapter 22 Problem 40 0.507 J/K

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