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Understanding the Second Law of Thermodynamics: Entropy & Processes

Explore the principles of the second law of thermodynamics, focusing on entropy, processes, and changes in systems. Learn about heat engines, pumps, refrigerators, and the Third Law of Thermodynamics.

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Understanding the Second Law of Thermodynamics: Entropy & Processes

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  1. SECOND LAW OF THERMODYNAMICS

  2. Heat engine

  3. HEAT ENGINE, HEAT PUMP, REFRIGERATOR

  4. Source & sink

  5. Entropy increase principle

  6. Clausius Inequality: • For internally reversible cycles:

  7. Entropy • Sgen > 0 irreversible processes = 0 reversible processes < 0 impossible processes

  8. Isentropic Processes • Isentropic process; internally reversible, adiabatic, entropy remains constant Δs = 0 or s2 = s1

  9. Entropy • Essentially Isentropic Processes • Pumps • Turbines • Nozzles • Diffusers

  10. Property Diagrams • Temperature-entropy (T-s) diagrams • Area under process curve on a T-s diagram equals heat transfer during an internally reversible process

  11. Property Diagrams • Isentropic processes are a vertical line on T-s diagrams

  12. Entropy • Entropy is: measure of molecular disorder, molecular randomness

  13. Entropy • Boltzmann equation: S = k ln(p) where k =1.3806*10-23 J/K p = thermodynamic probability, number of possible microscopic states of system

  14. Third Law of Thermodynamics • The entropy of a pure crystalline substance at absolute zero temperature is zero, since there is no uncertainty about the state of the molecules at that instant • Provides an absolute reference point for determining entropy

  15. Entropy • Work changed to heat increases entropy

  16. Entropy • During heat transfer net entropy increases

  17. Entropy • To find the change in entropy, need to do the cycle integral of δQ/T. • If isothermal, only need the function for Q • If not isothermal, need functions for Q and T

  18. Entropy

  19. Entropy

  20. Entropy • Can find entropy by integration of either equation • Need to know the relationship between du or dh and temperature • For ideal gases • du = cv dT • Or dh = cp dT • And Pv=RT

  21. Entropy Changes of Liquids and Solids • Liquids and solids are incompressible • dv = 0 • Also cv= cp=c and du= c dT

  22. Entropy Change of Ideal Gases • In the basic equation, substituting du = cv dT and P = RT/v • Substituting dh = c dT and v = RT/P

  23. Entropy Change of Ideal Gases • Need the relationship between the specific heats and temperature • Assume constant specific heats, simpler integration, approximate analysis • Work with variable specific heats, use tables, exact analysis

  24. Constant Specific Heats (Approximate Analysis)

  25. Variable Specific Heats (Exact Analysis) • If temperature change is large • Specific heats are non-linear with temperature • Need accurate relationships • Calculate integrals with respect to reference entropy (at absolute zero)

  26. Variable Specific Heats (Exact Analysis) • So we can find • And substituting into • Get

  27. Variable Specific Heats (Exact Analysis)

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