2. Entropy & Real Processes P M V Subbarao Professor Mechanical Engineering Department Entropy View of Real Engineering Process …..

3. Practical Processes are influenced by Irreversibilities Fluid friction Solid friction Electrical resistance Thermo-chemical Reactions (Combustion) Unrestrained motion Heat Transfer with a finite temperature difference

4. Solid Friction is an Irreversibility PEKE Q

5. Solid Friction is an Irreversibility PEKE Q

6. Solid Friction is an Irreversibility PEKE Q

7. Solid Friction is an Irreversibility Q Q Reverse THIS IS NOT POSSIBLE. Q ?

8. Solid Friction is an Irreversibility Q 1 2 4 3

9. Irreversible Machines The efficiency of an irreversible heat engine will always less than the efficiency of a reversible engine working between the same reservoirs. The COP of an irreversible heat pump will always less than the COP of a reversible heat pump working between the same reservoirs.

10. Increase of Entropy Principle Entropy change Entropy Generation The principle states that for an isolated Or a closed adiabatic Or System + Surroundings; A process can only take place such that S gen  0 where S gen = 0 for a reversible process only and S gen can never be less than zero. Entropy Transfer (due to heat transfer) Increase of Entropy Principle Define entropy generation S gen as, For a general Process

11. Implications of Increase of Entropy Principle Entropy, unlike energy, is non-conservative since it is always increasing. The entropy of the universe is continuously increasing, in other words, it is becoming disorganized and is approaching chaotic. The entropy generation is due to the presence of irreversibilities. Therefore, the higher irreversibilities lead to the higher the entropy generation and the lower the efficiency of a device. The above is Engineering statement of the second law

12. Second Law & Entropy Balance Increase of Entropy Principle is another way of stating the Second Law of Thermodynamics: Second Law : Entropy can be created but NOT destroyed In contrast, the first law states: Energy is always conserved. Note that this does not mean that the entropy of a system cannot be reduced, it can. However, total entropy of a system + surroundings cannot be reduced.

13. Entropy of Universe A quantity of heat  Q is spontaneously transferred from the surroundings at temperature T 0 to the control mass at temperature T. Let the work done during this process be  W. For this process by control mass and write For the surroundings at T 0,  Q is negative, and we assume a reversible heat extraction so

14. The total net change of entropy is therefore Since T 0 > T, the quantity [(1/T) - (1/T 0 )] is positive, and we conclude that Net Change in Entropy of Universe

15. If T > T 0, the heat transfer is from the control mass to the surroundings It should be noted that the right-hand side of above equation represents an external entropy generation due to heat transfer through a finite temperature difference.

16. The Third Law of Thermodynamics The entropy change of a system during a reversible isothermal process tends towards zero when the thermodynamic temperature of the system tends towards zero. In the neighbourhood of absolute zero, all reactions in a liquid or solid in internal equilibrium take place with no change in entropy. [Nernst 'principle'].

17. Planck’s statement of the 3rd law In 1911, Planck one step further and made the hypothesis that not only does the entropy difference vanish as T → 0, but that: Planck’s statement of the Third Law: The entropy of every solid or liquid substance in internal equilibrium at absolute zero is itself zero. Planck is just saying:

18. The flow of energy from a source to a sink through an intermediate system orders that system. Morowitz [1992] The Earth : A System to Create Usable Forms of Energy Sources

19. Characteristics of Biosphere Slowly driven systems naturally self-organize into a critical state. {Per Bak,1994} Biospheres and the universe create novelty and diversity as fast as….. without destroying the accumulated propagating organization …… {Kauffman, 2000} Matter cycles in regions of energy flow; such cycles, visible in natural complex structures, including those of life, occur as limited material resources scramble to provide a vehicle for entropy export. {Schneider & Sagan, 2005}

20. Engineering Relations from Second Law

21. Entropy as A Rate Equation The second law of thermodynamics was used to write the balance of entropy for a infinitesimal variation for a finite change. Here the equation is needed in a rate form so that a given process can be tracked in time. Take the incremental change and divide by  t. We get

22. For a given control mass we may have more than one source of heat transfer, each at a certain surface temperature (semi- distributed situation). The rate of entropy change is due to the flux of entropy into the control mass from heat transfer and an increase due to irreversible processes inside the control mass.

23. Entropy Rate Equation for CV Rate of change in entropy of a CV = Entropy in flow rate –Entropy out flow rate + the flux of entropy into the control mass from heat transfer + Rate of Entropy generation

24. Analysis of SSSF Adiabatic Work Transfer CVs SSSF: Conservation of mass First Law :