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CHAPTER

Learn about entropy, a measure of disorder in a system, and its importance in thermodynamics. Understand the entropy change of specific states, pure substances, and isolated systems. Explore entropy in heat transfer processes and its application in various diagrams.

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  1. 6 CHAPTER Entropy:A Measureof Disorder

  2. 6-1 System Considered in the Development of Claussius inequity

  3. (Fig. 6-3) 6-2 The Entropy Change Between Two Specific States The entropy change between two specific states is the same whether the process is reversible or irreversible

  4. 6-3 The Entropy Change of an Isolated System The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero

  5. The entropy of a pure substance is determined from the tables, just as for any other property (Fig. 6-10) 6-4 The Entropy Change of a Pure Substance

  6. (Fig. 6-11) 6-5 Schematic of the T-s Diagram for Water

  7. (Fig.6-14) 6-6 System Entropy Constant During Reversible, adiabatic (isentropic) Process

  8. (Fig. 6-16) 6-7 Level of Molecular Disorder (Entropy) The level of molecular disorder (entropy) of a substance increases as it melts and evaporates

  9. 6-8 Net Disorder (Entropy) Increases During Heat Transfer During a heat transfer process, the net disorder (entropy) increases (the increase in the disorder of the cold body more than offsets the decrease in the disorder in the hot body)

  10. On a T-S diagram, the area under the process curve represents the heat transfer for internally reversible processes (Fig. 6-23) d 6-9 Heat Transfer for Internally Reversible Processes

  11. 6-11 h-s Diagram for Adiabatic Steady-Flow Devices For adiabatic steady-flow devices, the vertical distance ²h on an h-s diagram is a measure of work, and the horizontal distance ²s is a measure of irreversibilities

  12. (Fig. 6-27) 6-10 Schematic of an h-s Diagram for Water

  13. (Fig. 6-33) 6-12 Entropy of an Ideal Gas The entropy of an ideal gas depends on both T and P. The function s° represents only the temperature-dependent part of entropy

  14. (Fig. 6-36) 6-13 The Isentropic Relations of Ideal Gases The isentropic relations of ideal gases are valid for the isentropic processes of ideal gases only

  15. (Fig. 6-37) 6-14 Using Pr data to Calculate Final Temperature During Isentropic Processes The T-ebow of an ordinary shower serves as the mixing chamber for hot- and cold-water streams.

  16. (Fig. 6-41) 6-15 Reversible Work Relations for Steady-Flow and Closed Systems

  17. (Fig. 6-45) 6-16 P-v Diagrams of Isentropic, Polytropic, and Isothermal Compression Processes P-v Diagrams of isentropic, polytropic, and isothermal compression processes between the same pressure limits

  18. (Fig. 6-46) 6-17 P-v andT-s Diagrams for a Two-Stage Steady-Flow Compression Process

  19. (Fig. 6-59) 6-18 The h-s Diagram for the Actual and Isentropic Processes of an Adiabatic Turbine

  20. (Fig. 6-61) 6-19 The h-s Diagram of the Actual and Isentropic Processes of an Adiabatic Compressor

  21. (Fig. 6-64) 6-20 The h-s Diagram of the Actual and Isentropic Processes of an Adiabatic Nozzle

  22. 6-21 Mechanisms of Entropy Transfer for a General System

  23. (Fig. 6-73) 6-22 A Control Volume’s Entropy Changes with MassFlow as well as Heat Flow

  24. 6-23 Entropy Generation During Heat Transfer Graphical representation of entropy generation during a heat transfer process through a finite temperature difference

  25. The second law of thermodynamics leads to the definition of a new property called entropy, which is a quantitative measure of microscopic disorder for a system. 6-24 Chapter Summary

  26. The definition of entropy is based on the Clausius inequality, given bywhere the equality holds for internally or totally reversible processes and the inequality for irreversible processes. 6-25 Chapter Summary

  27. Any quantity whose cyclic integral is zero is a property, and entropy is defined as 6-26 Chapter Summary

  28. For the special case of an internally reversible, isothermal process, it gives 6-27 Chapter Summary

  29. The inequality part of the Clausius inequality combined with the definition of entropy yields an inequality known as the increase of entropy principle, expressed aswhere Sgen is the entropy generated during the process. 6-28 Chapter Summary

  30. Entropy change is caused by heat transfer, mass flow, and irreversibilities. Heat transfer to a system increases the entropy, and heat transfer from a system decreases it. The effect of irreversibilities is always to increase the entropy. 6-29 Chapter Summary

  31. Entropy is a property, and it can be expressed in terms of more familiar properties through the Tds relations, expressed asand 6-30 Chapter Summary Tds = du +Pdv Tds = dh - vdP

  32. These two relations have many uses in thermodynamics and serve as the starting point in developing entropy-change relations for processes. The successful use of Tds relations depends on the availability of property relations. Such relations do not exist for a general pure substance but are available for incompressible substances (solids, liquids) and ideal gases. 6-31 Chapter Summary

  33. The entropy-change and isentropic relations for a process can be summarized as follows: 6-32 Chapter Summary 1. Pure substances: Any process:s = s2 - s1 [kJ/(kg-K)] Isentropic process: s2 = s1

  34. The entropy-change and isentropic relations for a process can be summarized as follows: T2 T1 6-33 Chapter Summary 2. Incompressible substances: Any process:s2 - s1 = Cav1n[kJ/(kg-K)] Isentropic process: T2 = T1

  35. The entropy-change and isentropic relations for a process can be summarized as follows: T2 v2 T1 v1 T2 P2 T1 P1 6-34 Chapter Summary 3. Ideal gases: a. Constant specific heats (approximate treatment): Any process: s2 - s1 = Cv,av 1n + R1n [kJ/(kg-K)] s2 - s1 = Cp,av 1n + R1n [kJ/(kg-K)] and

  36. T2 v2 T1 v1 T2 P2 T1 P1 6-35 Chapter Summary • The entropy-change and isentropic relations for a process can be summarized as follows: 3. Ideal gases: a. Constant specific heats (approximate treatment): On a unit-mole basis, s2 - s1 = Cv,av 1n + Ru1n [kJ/(kmol-K)] s2 - s1 = Cp,av 1n + Ru1n [kJ/(kmol-K)] and

  37. 6-36 Chapter Summary 3. Ideal gases: a. Constant specific heats (approximate treatment): Isentropic process:

  38. P2 P1 P2 P1 6-37 Chapter Summary • The entropy-change and isentropic relations for a process can be summarized as follows: 3. Ideal gases: b. Variable specific heats (exact treatment): Any process, o o s2 - s1 = s2 - s1 - R1n [kJ/(kg-K)] s2 - s1 = s2 - s1 - Ru1n [kJ/(kmol-K)] or o o

  39. P2 o o s2 = s1 - R1n [kJ/(kg-K)] P1 6-38 Chapter Summary 3. Ideal gases: b. Variable specific heats (exact treatment): Isentropic process, where Pr is the relative pressure and vr is the relative specific volume. The function so depends on temperature only.

  40. The steady-flow work for a reversible process can be expressed in terms of the fluid properties as 6-39 Chapter Summary

  41. For incompressible substances (v = constant) steady-flow work for a reversible process simplifies to 6-40 Chapter Summary

  42. The work done during a steady-flow process is proportional to the specific volume. Therefore, v should be kept as small as possible during a compression process to minimize the work input and as large as possible during an expansion process to maximize the work output. 6-41 Chapter Summary

  43. The reversible work inputs to a compressor compressing an ideal gas from T1, P1, to P2 in an isentropic (Pvk = constant), polytropic (Pvn = con-stant), or isothermal (Pv = constant) manner, are determined by integration for each case with the following results: 6-42 Chapter Summary

  44. Isentropic:(kJ/kg) 6-43 Chapter Summary

  45. Polytropic:(kJ/kg) 6-44 Chapter Summary

  46. Isothermal:(kJ/kg) 6-45 Chapter Summary

  47. The work input to a compressor can be reduced by using multistage compression with intercooling. For maximum savings from the work input, the pressure ratio across each stage of the compressor must be the same. 6-46 Chapter Summary

  48. Most steady-flow devices operate under adiabatic conditions, and the ideal process for these devices is the isentropic process. 6-47 Chapter Summary

  49. The parameter that describes how efficiently a device approximates a corresponding isentropic device is called isentropic or adiabatic efficiency. It is expressed for turbines, compressors, and nozzles as follows: In the relations above, h2a and h2s are the enthalpy values at the exit state for actual and isentropic processes, respectively. Isentropic compressor work wsh2s - h1Actual compressor work wah2a - h1 ~ = = = Actual KE at nozzle exit V2ah1 - h2aIsentropic KE at nozzle exit h1 - h2s 2 ~ = = = V2s 2 6-48 Chapter Summary Actual turbine work wah1 - h2aIsentropic turbine work wsh1 - h2s ~ = = =

  50. The entropy balance for any system undergoing any process can be expressed in the general form as 6-49 Chapter Summary

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