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Entropy and Thermodynamics: A Comprehensive Overview

Explore the concepts of entropy, microstates, and the second law of thermodynamics. Learn about entropy in open and closed systems, engine efficiency, and the evolution of the universe's entropy. Dive into the principles of irreversible processes and the relationship between entropy and information.

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Entropy and Thermodynamics: A Comprehensive Overview

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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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