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Lec 16: Refrigerators, heat pumps, and the Carnot cycle

Lec 16: Refrigerators, heat pumps, and the Carnot cycle. For next time: Read: § 6-5 to 6-6 and 6-8 to 6-9 Outline: Refrigerators Heat pumps Carnot cycle Important points: Understand the different performance measures for cyclic devices. Realize that COPHP and COPR are different

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Lec 16: Refrigerators, heat pumps, and the Carnot cycle

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  1. Lec 16: Refrigerators, heat pumps, and the Carnot cycle

  2. For next time: • Read: § 6-5 to 6-6 and 6-8 to 6-9 • Outline: • Refrigerators • Heat pumps • Carnot cycle • Important points: • Understand the different performance measures for cyclic devices. • Realize that COPHP and COPR are different • Start learning to recognize systems that violate the 2nd Law of Thermodynamics

  3. Second Law of Thermodynamics

  4. Review--Heat Engine or Cycle Efficiency

  5. Refrigerators, air conditioners and heat pumps Hot reservoir at TH System Cold reservoir at TL

  6. Refrigerators/‘air conditioners’ Remember: the purpose of a refrigerator or ‘air conditioner’ is to remove heat QL from a cold region at TL.

  7. Refrigerator Basic components and typical operating conditions

  8. Heat Pump Remember: the purpose of a heat pump is to add heat QH to a warm region at TH.

  9. Coefficient of Performance Refrigerators/Air conditioners

  10. Coefficient of Performance Refrigerators/Air conditioners

  11. Coefficient of Performance for Heat Pumps

  12. Coefficient of Performance for Heat Pumps

  13. TEAMPLAY Problem 6-52

  14. Perpetual Motion Machines (PMM) • PMM1--A perpetual motion machine of the first kind violates the first law or the law of conservation of energy. An example would be an adiabatic system that supplies work with no change in internal energy, kinetic energy or potential energy.

  15. Perpetual Motion Machines (PMM)--Teamplay • PMM2--A perpetual motion machine of the second kind violates the second law of thermodynamics. • Your book has Figure 6-34 and goes into a correct explanation of why it violates the first law. • The contraption in Figure 6-34 also violates the second law, as does the machine in Figure 6-35. Why?

  16. Carnot Cycle • Composed of four internally reversible processes. • Two isothermal processes • Two adiabatic processes

  17. Carnot cycle for a gas. TL=const

  18. The Carnot cycle for a gas might occur as visualized below. QL TL

  19. This is a Carnot cycle involving two phases--it is still two adiabatic processes and two isothermal processes. • It is always reversible--a Carnot cycle is reversible by definition. TL TL TL

  20. Carnot refrigeration cycle for a gas.

  21. Analytical form of KP Statement: • Conservation of Energy for a cycle says • E = 0 = Qcycle - Wcycle, or Qcycle = Wcycle • We have not limited the number of heat reservoirs (or work interactions, for that matter). Qcycle could be QH - QC, for example.

  22. Analytical form of KP statement. • Let us limit ourselves to the special case of one TER (thermal energy reservoir): TER Q HE W

  23. TEAMPLAY • Can the system on the previous slide do work while operating in a cycle? If not, what does it violate?

  24. Analytical form of the KP statement. • However, it would not violate the KP statement if work were done on the system during the cycle, or if work were zero. These are analytical forms of the KP statement.

  25. Analytical forms of the KP statement. • Both the equations may be regarded as analytical forms of the KP statement. • It can be shown that the equality applies to reversible processes and that the inequality applies to irreversible processes. • Consider a cycle for which the equality applies, that is Qcycle = Wcycle.

  26. Carnot’s first corollary • The thermal efficiency of an irreversible power cycle is always less than the thermal efficiency of a reversible power cycle when each operates between the same two reservoirs.

  27. Hot reservoir QH QH WR R I WI QC=QH-WR Cold reservoir

  28. Carnot’s first corollary • Each engine receives identical amounts of heat QH and produces WR or WI. • Each discharges an amount of heat Q to the cold reservoir equal to the difference between the heat it receives and the work it produces.

  29. Hot reservoir QH QH QH WR R I WI WR QC=QH-WR QC Cold reservoir

  30. Carnot’s first corollary. • Taken together, • Now reverse the reversible engine.

  31. QH QH QH R I WI WR QC=QH-WR QC Cold reservoir

  32. Carnot’s first corollary • If WI  WR, the system puts out net work and exchanges heat with one reservoir. This violates KP. So, WI cannot be  WR.

  33. Carnot’s first corollary • If WI = WR, QC = Q′C And the irreversible engine is identical to the reversible engine, i.e., it is just the reversible engine.

  34. Carnot’s first corollary • So, WI  WR, and • So th,I  th,R

  35. Carnot’s second corollary • All reversible power cycles operating between the same two thermal reservoirs have the same thermal efficiencies.

  36. Hot reservoir QH QH QH WR,1 R1 R2 WR,2 WR,1 QC QC QC Cold reservoir

  37. Carnot’s second corollary • Both engines receive QH, and Qcycle = 0 and Wcycle= 0 for both engines with one reversed because they are both reversible. • Now, with engine 1 reversed. Wcycle = 0 = WR,1-WR,2 and WR,1 = WR,2

  38. Carnot’s second corollary • And • so

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