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Understanding Entropy and Thermodynamic Relationships

Explore the concept of entropy and the second law of thermodynamics in Lecture 5. Learn about variable dependences of thermodynamic relationships, Carnot cycle, Kelvin-Planck statement, and more. Understand the concept of quasi-static processes in thermodynamics.

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Understanding Entropy and Thermodynamic Relationships

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  1. PHY 341/641 Thermodynamics and Statistical Physics Lecture 5 Entropy Second law of thermodynamics Variable dependences of thermodynamic relationships PHY 341/641 Spring 2012 -- Lecture 5

  2. Entropy for a reversible process (quasi-static via continuous changes in the variables): Note that dS is an “exact differential” dQ is not. Carnot cycle. PHY 341/641 Spring 2012 -- Lecture 5

  3. Square cycle: PHY 341/641 Spring 2012 -- Lecture 5

  4. Second law of thermodynamics • Kelvin-Planck: It is impossible to construct an engine which, operation in a cycle, will produce no other effect than the extraction of energy from a reservoir and the performance of an equivalent amount of work. • Clausius: No process is possible whose sole result is cooling a colder body and heating a hotter body. • Gould-Tobochnik:There exists an additive function of state known as the entropy S that can never decrease in an isolated system. PHY 341/641 Spring 2012 -- Lecture 5

  5. Comment on “quasi-static” restrictions Consider the free expansion of an isolated ideal gas, initially in left chamber at V1 with vacuum in right chamber and finally occupying full volume V2. In order to use the laws of thermodynamics, we must envision a quasi-static process that accomplishes the free expansion PHY 341/641 Spring 2012 -- Lecture 5

  6. Variables and functions: PHY 341/641 Spring 2012 -- Lecture 5

  7. Assume N constant -- PHY 341/641 Spring 2012 -- Lecture 5

  8. Further relations: PHY 341/641 Spring 2012 -- Lecture 5

  9. Mathematical transformations for continuous functions of several variables & Legendre transforms: PHY 341/641 Spring 2012 -- Lecture 5

  10. Mathematical transformations for continuous functions of several variables & Legendre transforms continued: PHY 341/641 Spring 2012 -- Lecture 5

  11. For thermodynamic functions: PHY 341/641 Spring 2012 -- Lecture 5

  12. PHY 341/641 Spring 2012 -- Lecture 5

  13. PHY 341/641 Spring 2012 -- Lecture 5

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