1 / 29

Chapter 2: Sections 6 and 7

Chapter 2: Sections 6 and 7. Lecture 04: Energy Analysis of Cycles. Quiz Today?. Today’s Objectives:. Be able to explain what a Power Cycle is Be able to explain what a Refrigeration Cycle is Be able to explain what a Heat Pump Cycle is

kyra-chavez
Download Presentation

Chapter 2: Sections 6 and 7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2: Sections 6 and 7 Lecture 04: Energy Analysis of Cycles Quiz Today?

  2. Today’s Objectives: • Be able to explain what a Power Cycle is • Be able to explain what a Refrigeration Cycle is • Be able to explain what a Heat Pump Cycle is • Be able to calculate thermal efficiencies for Power and Heat Pumps Be able to calculate COP for Refrigeration Cycles. • Be able to intelligently discuss method of energy storage. Reading Assignment: • No Reading Assignment Homework Assignment: From Chap 2: Problems 73, 75, 84, 90

  3. Sec 2.4: Energy Transfer by Heat Recall past concepts: Work, W: W > 0 : Work done BY the system W < 0 : Work done ON the system Q > 0 : Heat transferred TO the system Q < 0 : Heat transferred FROM the system Heat, Q: 1st Law of Thermodynamics: system Qin Wout ΔE

  4. Sec 2.2.1: Sign Convention Work done by Gas System W > 0 : Expansion of Gas W < 0 : Compression of Gas Run Animation

  5. Sec 2.6: Energy Analysis of Cycles Energy Analysis of Cycles A cycle is any process that returns to its original state. • Ecycle= Qcycle - Wcycle • therefore: Ecycle= 0 • and Qcycle = Wcycle

  6. Sec 2.6: Energy Analysis of Cycles Schematic models of Cycles: Refrigeration (Heat pump) Cycle Power cycle

  7. Sec 2.6.2: Power Cycles Power Cycle • Wcycle= Qcycle = Qin - Qout • Qin : Heat in from hot body • (chemical reaction, geothermal) • Qout : Heat out to cold body • (surroundings) • Qin > Qout  W > 0 • Thermal efficiency • when η = 1, efficiency = 100% so want to minimize Qout

  8. Sec 2.6.3: Refrigeration and Heat Pump Cycles Refrigeration Cycle • Wcycle= Qcycle = Qout - Qin • Qout : Heat out to warm body • Qin : Heat in from cold body • W > 0  Qout> Qin • Refrigeration Coefficient of Performance

  9. Sec 2.6.3: Refrigeration and Heat Pump Cycles Heat Pump Cycle • Wcycle= Qcycle = Qout - Qin • Qout : Heat out to warm body • Qin : Heat in from cold body • W > 0  > Qout> Qin • Heat Pump Coefficient of Performance

  10. A quick comparison Refrigeration Cycle Heat Pump Cycle Objective is to do Work to Add heat to a system. Objective is to do Work to Remove heat from system.

  11. Example 1 (Problem 2.76): A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with PV = constant, U3 = U2 Process 3-1: Constant pressure, P = 1.4 bar, W31 = -10.5 kJ There are no significant changes in kinetic or potential energy. • Sketch to cycle on a PV diagram • Calculate the net work for the cycle, in kJ • Calculate the heat transfer for process 2-3, in kJ • Calculate the heat transfer for process 3-1, in kJ Is this a power cycle or a refrigeration cycle?

  12. Example 2 (Problem2.83): A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kWh. Based on the cost of fuel, the cost to supply Qin is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ • the value of electricity generated per year and • the annual fuel cost • Is operation profitable?

  13. Example 3 (Problem2.91): A heat pump maintains a dwelling at 68oF. When operating steadily, the power input to the heat pump is 5 hp, and the heat pump receives energy by heat transfer from 55oF well water at a rate of 500 BTU/min. a) Determine the COP. b) Evaluating electricity at $0.10 per kW-hr, determine the cost of electricity in a month when the heat pump operate for 300 hr.

  14. End of Lecture 04 • Slides which follow show solutions to example problems

  15. Example (2.76): A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with PV = constant, U3 = U2 Process 3-1: Constant pressure, P = 1.4 bar, W31 = -10.5 kJ There are no significant changes in kinetic or potential energy. • Sketch to cycle on a PV diagram • Calculate the net work for the cycle, in kJ • Calculate the heat transfer for process 2-3, in kJ • Calculate the heat transfer for process 3-1, in kJ Is this a power cycle or a refrigeration cycle? p 3 3 V

  16. Example (2.76): Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with PV = constant, U3 = U2 Process 3-1: Constant pressure, P = 1.4 bar, W31 = -10.5 kJ • Sketch to cycle on a PV diagram 2 1.4 P(bar) 1 3 0.0028 V(m3)

  17. Example (2.76): Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with pV= constant, U3 = U2 Process 3-1: Constant pressure, p= 1.4 bar, W31 = -10.5 kJ • Calculate the net work for the cycle, in kJ for Process 1-2: for Process 3-1: for Process 2-3:

  18. Example (2.76): Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with pV= constant, U3 = U2 Process 3-1: Constant pressure, p= 1.4 bar, W31 = -10.5 kJ • Calculate the net work for the cycle, in kJ • We now have, • Then, • Since Wcycle >0, the cycle is a power cycle

  19. Example (2.76): A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with pV= constant, U3 = U2 Process 3-1: Constant pressure, p= 1.4 bar, W31 = -10.5 kJ There are no significant changes in kinetic or potential energy. • Calculate the heat transfer for process 2-3, in kJ • Find Q23, using an energy balance for Process 2-3. • 0 0 0

  20. Example (2.76): A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with pV = constant, U3 = U2 Process 3-1: Constant pressure, p = 1.4 bar, W31 = -10.5 kJ There are no significant changes in kinetic or potential energy. • Calculate the heat transfer for process 3-1, in kJ • 0 0 • so • o • to find U31: • then:

  21. Example (2.76): A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2 : Constant volume, V = 0.028 m3, U2-U1=26.4 kJ Process 2-3: Expansion with pV = constant, U3 = U2 Process 3-1: Constant pressure, p = 1.4 bar, W31 = -10.5 kJ There are no significant changes in kinetic or potential energy. • Double check math on heat calculations • We can also calculate the efficiency of this cycle

  22. Example (2.83): A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kWh. Based on the cost of fuel, the cost to supply Qin is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ • the value of electricity generated per year • the waste heat returned to the environment • the annual fuel cost • Is operation profitable? Qin • Fuel • Wout=100 MW • Air Qout

  23. Example (2.83): A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kWh. Based on the cost of fuel, the cost to supply Qin is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ • the value of electricity generated per year and • next find the heat generated and the heat returned to the environment

  24. Example (2.83): A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kWh. Based on the cost of fuel, the cost to supply Qin is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ • Cost of fuel? • Is operation profitable? • Profit = Revenue – Costs • So, this could be profitable, but the calculation ignore other costs such as capital and labor.

  25. Example 3 (Problem2.91): A heat pump maintains a dwelling at 68oF. When operating steadily, the power input to the heat pump is 5 hp, and the heat pump receives energy by heat transfer from 55oF well water at a rate of 500 BTU/min. a) Determine the COP. b) Evaluating electricity at $0.10 per kW-hr, determine the cost of electricity in a month when the heat pump operates for 300 hr. Principle: COP for heat pump (written in terms of power) where: and therefore:

  26. Example 3 (Problem2.91): A heat pump maintains a dwelling at 68oF. When operating steadily, the power input to the heat pump is 5 hp, and the heat pump receives energy by heat transfer from 55oF well water at a rate of 500 BTU/min. a) Determine the COP. b) Evaluating electricity at $0.10 per kW-hr, determine the cost of electricity in a month when the heat pump operate for 300 hr. Principle: Cost = Cost of energy * Power * time where: therefore:

More Related