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The Entropy Change: A Single Reason for Everything in Mechanical Engineering

Explore the reversible Carnot gas engine cycle using phase change substances and the performance of reversible cycles. Learn about entropy, molecular complexity, reversible processes, and the nature of reversible machines in this comprehensive guide.

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The Entropy Change: A Single Reason for Everything in Mechanical Engineering

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  1. The Entropy Change P M V Subbarao Professor Mechanical Engineering Department A Single Reason for Every Thing That Happens!!!

  2. Carnot Gas Engine : The Reversible Cycle

  3. Carnot Engine using Phase Change Substance : SSSF CVs HTR Boiler 2 1 Turbine Compressor 4 3 Condenser LTR

  4. Performance of Reversible Cycle Use a generalized indices…

  5. During a time duration  For a reversible cycle with n number heat transfer processes • Where, i shows ith process and n is the number of process in a cycle. • But Qi is a path function and depends on process.

  6. Therefore, k is an initial state and k+1 is a final state. m is the number state Points in a cycle. Therefore for all reversible cycles.

  7. A New cyclic Integral Cyclic integral of this new quantity is zero! Any quantity whose cyclic integral is zero is a property ! For a reversible process an infinitesimal change in this new property is: Boltzman named S as Entropy of a substance. During a reversible process

  8. Entropy, S : A Measure of State of Matter S (gaseous state)> S (liquid state)> S (solid state) So (J/K•mol) H2O(liq) 69.95 H2O(gas) 188.8 For a given substance

  9. Entropy and Order of Molecules of Matter S˚(Br2 liq) < S˚(Br2 gas) S˚(H2O solid) < S˚(H2O liquid)

  10. Entropy, S : Molecular Complexity Increase in molecular complexity generally leads to increase in S.

  11. Standard Molar Entropies

  12. S increases slightly with T S increases a large amount with phase changes Entropy and Temperature

  13. T S Entropy Change during a Reversible Process • From the definition of the entropy, it is known that Q=TdS during a reversible process. • The total heat transfer during this process is given by Qreversible =  TdS • Therefore, it is useful to consider the T-S diagram for a reversible process involving heat transfer • On a T-S diagram, the area under the process curve represents the heat transfer for a reversible process • A reversible adiabatic process

  14. Flow Boiling Process Vapour Vapour T Liquid +Vapour Liquid h

  15. Steam Generation : Expenditure Vs Wastage Vapour Liquid +Vapour h Liquid s

  16. Analysis of Steam Generation at Various Pressures

  17. h Variable Pressure Steam Gneration s

  18. T 1 2 TH TL 3 4 A B S S1=S4 S2=S3 Carnot Cycle • Show the Carnot cycle on a T-S diagram and identify the heat transfer at both the high and low temperatures, and the work output from the cycle. • 1-2, reversible isothermal heat transfer • QH = TdS = TH(S2-S1) area 1-2-B-A • 2-3, reversible, adiabatic expansion • isentropic process, S=constant (S2=S3) • 3-4, reversible isothermal heat transfer • QL = TdS = TL(S4-S3), area 3-4-A-B • 4-1, reversible, adiabatic compression • isentropic process, S1=S4 • Net work Wnet = QH - QL, the area enclosed by 1-2-3-4, the shaded area

  19. Nature of Reversible Machines For all reversible heat engines: For all reversible heat pumps and refrigerators: Therefore all reversible machines in this universe :

  20. h Dh Ds s Process : h-s Diagram : Mollier Diagram • Enthalpy-entropy diagram, h-s diagram: it is valuable in analyzing steady-flow devices such as turbines, compressors, etc. • Dh: change of enthalpy from energy balance (from the first law of thermodynamics) • Ds: change of entropy from the second law. • A measure of the irreversibilities during an adiabatic process.

  21. Enthalpy Vs Entropy Diagram

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