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Today. Efficiency How efficient is the heat engine that converts heat energy into useful mechanical or electrical energy? What is the best possible efficiency? Turn it all around, and use a ‘heat pump’.

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Today

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  1. Today Efficiency How efficient is the heat engine that converts heat energy into useful mechanical or electrical energy? What is the best possible efficiency? Turn it all around, and use a ‘heat pump’. All power point images are only for the exclusive use of Phys3070/Envs3070 Spring term 2014

  2. Let water fall through some machine to do work.

  3. Let temperature = hot stuff fall from hot (Thot) to cold (Tcold) places (reservoirs) through a heat engine, which does work.

  4. A Law and a Definition • Energy is conserved Heat in = heat out + work done Qin = Qout + W Or---QHot = QCold + W • Efficiency = e = Work done/Heat energy in = W / Qin = (Qin-Qout)/ Qin (careful! Heat in calories or Btu, work in Joules or kW-hr)

  5. There is a limit to the efficiency of any heat engine. • Since we cannot extract all the heat energy, since to do so would have to exhaust at absolute zero, equal to -273 deg C. • Called the Carnot or ideal efficiency eCarnot = 1 – Tcold/Thot

  6. Best example Integral Gas-turbine Combined Cycle = IGCC • Turn coal into burnable gas • Burn that gas in a jet turbine engine electricity • Use the very hot exhaust of that turbine to make steam electricity

  7. syngas

  8. syngas Q in W Q out e=W / Q in = 47.8%

  9. Another kind of ‘efficiency’ ----CO2

  10. Turn the problem aroundThe Heat Pump • Use some energy to move heat energy from a cool spot to a hot spot. • Why can this be useful?

  11. A Heat Pump Qcold + W = Qhot

  12. A law and a definition • Conservation of energy Work + Qcold = Qhot • Coefficient of Performance (sorta like efficiency) COP = Qhot / W together: COP = Qhot / (Qhot – Qcold) = 1 / (1-Qcold/Qhot)

  13. Best, ideal, Carnot COP COP = 1 / (1- Qcold/Qhot) definition = 1 / (1-Tcold/Thot) best T’s in degrees KELVIN !!!!!! Example: an air conditioner Tcold(inside) = 20 deg C (68 deg F)= 293 deg K Thot(outside) = 40 deg C (104 deg F !) = 313 deg K Best COP = 1 / (1-293/313) = 1 / 0.0639 =15.65 YES- this can be greater than one! You are moving heat, not just creating it.

  14. WINTER Heat pump = Air conditioner Q hot W Q cold

  15. example Tcold (outside) = 0 deg C = 273 deg K Thot (inside) = 20 deg C = 293 deg K COPCarnot = = 1 / (1-Tcold/Thot) =1 / (1 – 273/293) = 1 / (1-0.9317) =14.65 COP = Qhot / W Qhot = 14.65 * W You pay for one unit of energy (work) and get 14.65 units, one from the W and 13.65 from the environment.

  16. Two ways to heat your home with gas Q1 in COP=Q2hot/W2=1./0.3 = 3.3 Gas! W1 = W2 Q2hot Q2cold Q1 out e1= W1 / Q1in=0.3 / 0.9 = 33% e=1.0 / 1.4 = 71%

  17. Next week Monday: Exam 1 HW #3 due Wednesday: Electricity– making it, moving it. Friday: Transportation and energy: Chapter 8 !

  18. Beyond the text!!!! DQ=M*DT*specific heat ‘Energy intensity’ and ‘emergy ratios’ Hubbert curves Balancing atoms and masses in simple chemical reactions Especially the amount of CO2 from combustion

  19. How to prepare for the exam • Be familiar with where to find data or information to carry out numerical problems. • Be familiar with where to find data/graphs/numbers to back up your written or numerical arguments. • Understand the basic principles, including the posted ‘not in the text’ ideas and skills • Study smart—not the tiny details

  20. How to take the exam Scan/triage—start with the easiest, and be sure of every point. Defer hardest to last. 2. Put down your pencil to start each question. Sketch? 3.Is an equation useful? Write in it standard form, list the known/unknown ingredients and their UNITS. Do they match? Will the units work out? 4. Convert units to the same language in your table of ingredients. 5. Build your ‘equation’ with the help of the units. Check cancellation. 6. Put in the numbers, step-by-step, with the thinking clear to the grader in case partial credit is due. Naked answers will not get full credit! 7.Look at your answer. Did you answer the question? Does it make sense? Are the units OK? Is it worthy of some relevant comment? 8.For an essay answer, make a mental or written outline of your argument. Give evidence to back your words. 9. In general—slow down! 9. Hardest last

  21. The Fischer-Tropsch process turns coal (carbon=C) into gasoline=octane (=C8H18) by a series of chemical reactions. The first reaction combines carbon with water (steam) and heat to make water gas or coal gas, a mixture of hydrogen and carbon monoxide. C+H2OH2 + CO. More hydrogen is added to run the F-T reaction. The final reaction is 17 H2 + 8 CO C8H18 + 8 H2O. A)(5) How many molecules of carbon do you need to react to make enough CO to make one molecule of octane? B) (5) How many tons of carbon do you need to react to make one ton of CO?C)(10) How many tons of octane can you make from that one ton of CO (and the other ingredients)?

  22. 2. (10) There is a temperature difference between very deep ocean water (4 deg C) and surface waters (25 deg C). This difference allows you to construct a heat engine. What is the best possible (Carnot) efficiency for such a hypothetical engine? Why don’t remote tropical islands use this for power? 3. (5) Instead, image a heat engine that burns waste on that island and exhausts its waste heat into that 25 deg C water. How hot must the fire be (in deg C) to attain 30% Carnot efficiency?

  23. 4.(10) A power plant converts the heat energy in coal to electricity with 35% efficiency. Transmission losses are 10%. A factory then uses that electricity to make a new exotic and special rocket fuel, with 60% efficiency. What is the total efficiency of converting coal energy into the final energy product?

  24. 5.a) (5) If Congress taxes CO2 at $40 per ton (ofCO2), what is the tax on one ton (2000 pounds) of burned coal which is 60% carbon? b)(5) How much heat energy can you get from burning that coal? Take the book value per ton of coal to represent this 60% variety. c)(5) What is the tax on one ton of burned methane (CH4)? First, write the reaction for complete combustion in air. d) (5) Methane gas has a density of 0.0443 pounds per cubic foot. How many cubic feet are in that ton? e) (5) How much heat energy can be gained from that ton of methane? Use the book number for natural gas. f)(10) Make a brief summary of what you would write Rep. Polis (D-2d District of CO) about these four energy and tax numbers.

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