The Entropy Change

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