1. Gestão de Sistemas Energéticos 2015/2016 Exergy Analysis Prof. Tânia Sousa taniasousa@ist.utl.pt

2. Energy Balance in Closed Systems Energy change in the system Flows at the boundaries heat work Moran et al., 2014

3. Energy Balance in Closed Systems Energy Change = Heat - Work Energy change in the system Flows at the boundaries 1 st Law: Energy Conservation Forms of E: U, E c and E p Energy transfer by Q and W Sign of heat and work fluxes Steady state vs. Transient heat work Moran et al., 2014 -

4. Energy What happens to the total energy of the system? Moran et al., 2014

5. Energy vs. Exergy What happens to the total energy of the system? It remains constant (system is isolated)

6. Energy vs. Exergy Can the process occur from the right to the left?

7. Is the first law enough? What happens if you put a dish with ice over a pan with boiling water?

11. Entropy Balance in Adiabatic Systems

12. Entropy change = Entropy production 2 nd Law: In an adiabatic system the entropy must not decrease Steady state vs. Transient

13. Entropy Balance in Closed Systems

14. Entropy change = Entropy transfer in the form of heat + entropy production Entropy flows with heat but not with work

15. 2 nd Law: In an adiabatic system the entropy must not decrease Suppose the combined system (contained in the black boundary) is adiabatic and that T 2 >T 1 What happens to the entropy of the combined system in each case? Entropy Balance in Closed Systems T2T2 T1T1 T2T2 T1T1

16. 2 nd Law: In an adiabatic system the entropy must not decrease 2 nd Law: the arrow of time Entropy production in spontaneous processes Entropy Balance in Closed Systems T2T2 T1T1 T2T2 T1T1

17. The state variable: Entropy Entropy is the state variable that gives unidirectionality to time in physical processes ocurring in isolated & adiabatic systems.

19. Entropy What happens to the total entropy of the system?

20. Energy vs. Exergy Which system has a greater potential for use? Fuel-air combination Warm air mixture

21. Energy vs. Exergy Which system has a greater potential for use? “The fuel might be used to generate electricity, produce steam, or power a car whereas the final warm mixture is clearly unsuited for such applications.” Fuel-air combinationWarm air mixture

22. Energy vs. Exergy Which system has a greater potential for use? “During the process the initial potential for use (and economic value) is predominately destroyed owing to the irreversible nature of that process. ” Fuel-air combinationWarm air mixture

23. Energy vs. Exergy Exergy is the property that quantifies the potential for use and it is exergy that has economic value. Exergy is a property that takes into account the second law of thermodynamics How can we make use of a body at T i >T 0 ?

24. Controlled cooling to produce work Energy vs. Exergy Moran et al., 2014

25. Controlled cooling to produce work The amount of work depends on what? Energy vs. Exergy Moran et al., 2014

26. The Carnot Efficiency – Power Cycle First law: Second law: Ideal (Reversible) Cycle:

27. Controlled cooling to produce work Exergy is the maximum theoretical value for the work W c. What happens to the exergy of the bosy with time? Energy vs. Exergy Moran et al., 2014

28. Controlled cooling to produce work The potential for developing work W c exists because the initial state of the body differs from that of the environment, i.e., T i > T 0. Energy vs. Exergy Moran et al., 2014

29. Could we produce work if T i < T 0 ? Energy vs. Exergy

30. Could we produce work if T i < T 0 ? The potential for developing work W c exists because the initial state of the body differs from that of the environment, i.e., T i < T 0. Energy vs. Exergy Moran et al., 2014 T i < T 0

31. Reference environment: T 0 and P 0 Exergy is the maximum W c obtainable from the system plus the environment as the system comes into equilibrium with the environment (goes to the dead state T 0 & P 0 ). What happened in the case of spontaneous cooling? Defining Exergy

32. Reference environment: T 0 and P 0 Exergy is the maximum W c obtainable from the system plus the environment as the system comes into equilibrium with the environment (goes to the dead state T 0 & P 0 ). W c is null because exergy is destroyed by irreversibilities (spontaneous processes) Defining Exergy

33. Exergy is the maximum W c obtainable from the system plus the environment as the system comes into equilibrium with the environment (goes to the dead state T 0 & P 0 ). Defining Exergy Moran et al., 2014

34. Exergy is the maximum W c obtainable from the system plus the environment as the system comes into equilibrium with the environment (goes to the dead state T 0 & P 0 ). U, V, S, KE, and PE are evaluated at the initial state while U 0, V 0, and S 0 are at the dead state. Does it depend on the process? Expression for specific exergy? Defining Exergy

35. If temperature and/or pressure of a system differ from that of the environment, the system has thermomechanical exergy. Another contribution, called chemical exergy, arises when there is a chemical composition difference between the system and environment. Defining Exergy

36. A balloon filled with oxygen (O 2 ) at 280 K, 1 bar moves with a velocity of 15 m/s at an elevation of 0.5 km, each relative to Earth’s surface where T 0 = 300 K, p 0 = 1 bar. Using the ideal gas model, determine the specific exergy of the oxygen, in kJ/kg. Take g = 9.807 m/s 2. T = 280 K p = 1 bar V = 15 m/s z = 0.5 km T 0 = 300 K p 0 = 1 bar z g Earth Moran et al., 2014 Exercise u(280K)=181.93 kJ.kg -1 u(300K)=195.06 kJ.kg -1 s 0 (280K)=6.35 kJ.kg -1.K -1 s 0 (300K)=6.41 kJ.kg -1.K -1 R=0.26 kJ.kg -1.K -1

37. T = 280 K p = 1 bar V = 15 m/s z = 0.5 km T 0 = 300 K p 0 = 1 bar z Moran et al., 2014 e = (–13.13 – 5.20 + 18.96 + 5.02) kJ/kg = 5.65 kJ/kg Exercise

38. Homework https://www.youtube.com/watch?v=EF_xdvn52As

39. Energy vs. Exergy Which system has a greater potential for use? “During the process the initial potential for use (and economic value) is predominately destroyed owing to the irreversible nature of that process. ” Fuel-air combinationWarm air mixture

40. Exergy - the concept

41. Kinetic and potential energies are forms of mechanical energy that can be fully converted into useful work

42. Exergy - the concept The energy transferred in the form of work used to increase the volume to V 0 (push the atmosphere) can’t be used for other purposes; What about V- V 0 >0? P0P0

43. Exergy - the concept S - S 0 > 0 ?????????????

44. Exergy - the concept The energy transferred in the form of heat used to decrease the entropy to S 0 can’t be used for other purposes; What about S - S 0 < 0

45. Change in exergy between two states The change in exergy between two different states

46. Exercise Consider 1 kg of steam initially at 20 bar and 240°C as the system. Determine the change in exergy, in kJ, for each of the following processes: (a)The system is heated at constant pressure until its volume doubles. (b)The system expands isothermally until its volume doubles. Let T 0 = 20°C, p 0 = 1 bar and ignore the effects of motion and gravity. Moran et al. (2014) u 1 =2659.6 kJ.kg -1 v 1 =0.1085 m 3.kg -1 s 1 =6.4952 kJ.kg -1.K -1 u 2 =3410 kJ.kg -1 s 2 =7.867 kJ.kg -1.K -1 u 3 =2690 kJ.kg -1 s 3 =6.88 kJ.kg -1.K -1

47. Exergy Balance in Closed Systems Exergy transfer by heat –What is the maximum amount of work that can be produced with Q?

48. Exergy transfer by heat –What is the maximum amount of work that can be produced with Q? Exergy Balance in Closed Systems Cengel & Boles TbTb

49. Exergy transfer by work –What is the maximum amount of useful work that can be used from W? Exergy Balance in Closed Systems

50. Exergy transfer by work Exergy Balance in Closed Systems Cengel & Boles

51. Exergy Balance in Closed Systems Exergy destruction: irreversibilities destroy exergy 2 nd Law?

52. Exergy Balance in Closed Systems Exergy destruction: irreversibilities destroy exergy 2 nd Law? = 0 (no irreversibilities present within the system) > 0 (irreversibilities present within the system) < 0 (impossible) Ed:Ed:

53. Exergy Balance in Closed Systems Obtain the exergy balance for closed systems from the energy and entropy balances and What happens to the exergy of an isolated system? Exergy Change = exergy transfer by heat - exergy transfer by work - exergy dissipation

54. Exercises Why is the exergy transfer at boundary 1 different from exergy transfer at boundary 2?

55. Exercises u(298K)= 214.07kJ.kg -1 u(450K)= 322.62kJ.kg -1 R=0.287 kJ/kg.K s 0 (298)=1.6952 kJ.kg -1.K -1 s 0 (450)=2.1116 kJ.kg -1.K -1

56. Exergy Rate Balance for Closed Systems The exergy rate balance?

57. Exergy Rate Balance for Closed Systems The exergy rate balance Steady-state?

58. Exergy Rate Balance for Closed Systems The exergy rate balance Steady-state

59. Exergy Rate Balance for Control Volume Systems The exergy rate balance for closed systems The exergy rate balance for open systems

60. Exergy Rate Balance for Control Volume Systems The exergy rate balance for closed systems The exergy rate balance for open systems Steady-state?

61. Exergy Rate Balance for Control Volume Systems The exergy rate balance for closed systems The exergy rate balance for open systems Steady-state?

62. The specific flow exergy What is the specific flow exergy?

63. The specific flow exergy Exergy is the maximum W c obtainable from a mass flow plus the environment as it comes into equilibrium (goes to the dead state T 0 & P 0 ). Obtain an expression for the specific flow exergy

64. The specific flow exergy Exergy is the maximum W c obtainable from a mass flow plus the environment as it comes into equilibrium (goes to the dead state T 0 & P 0 ). The specific flow exergy is:

65. Exercise

66. Figure shows a device to develop power using a heat transfer from a high- temperature industrial process together with a steam input. The figure provides data for steady-state operation. All surfaces are well insulated, except for the one at 500°C, across which heat transfer occurs at a rate of 4.25 kW. The device develops power at a rate of 6.1 kW. Determine, in kW,(a) the rate exergy enters accompanying heat transfer. (b) the net rate exergy is carried in by the steam, (Ef1 - Ef2). (c) the rate of exergy destruction within the device. Ignore the effects of motion and gravity and let T0 = 293 K, p0 = 1 bar. Moran et al., 2014

67. Specific flow exergy vs. specific exergy What is the difference between specific flow exergy and specific exergy?

68. Specific flow exergy vs. specific exergy What is the difference between specific flow exergy and specific exergy? The exergy of flow work