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Announcements – 9/23/11

Announcements – 9/23/11. Prayer Wednesday is last lecture on Thermodynamics Reading assignment for Wed is posted to class website: the “What is entropy” handout in Supplementary Material section at bottom Results of doodle.com voting: Exam review will be Fri 9/30/11, 4 pm, room C460. Pearls

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Announcements – 9/23/11

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  1. Announcements – 9/23/11 • Prayer • Wednesday is last lecture on Thermodynamics • Reading assignment for Wed is posted to class website: the “What is entropy” handout in Supplementary Material section at bottom • Results of doodle.com voting: • Exam review will be Fri 9/30/11, 4 pm, room C460 Pearls Before Swine

  2. Problem continued from last time 2 • 12 adiabatic • 23 isothermal • 31 constant volume • Diatomic gas Done last time: • P1V1g = P2V2g  V2 = V1 (P1/P2)1/g = 0.4562 m3 • Q12=0 • Q23= -Won = nRTln(V3/V2) = P2V2ln(V3/V2) = 107408 J • Q31= DEint = (5/2)nRDT = (5/2) (P1V1–P3V3) = -250000 J Error recognized since I knew |Qh| – |Qc| had to be positive 300 kPa 136.87 kPa 200 kPa 3 1 100 kPa V2 1 m3 -92185 J The issue: I overspecified the parameters. Specifically, P3 cannot be 200 kPa. P2V2 = P3V3 P3 = 136.87 kPa

  3. Demos • Stirling engine • Thermoelectric engine

  4. Reading Quiz • What is the “Clausius statement” of the Second Law of Thermodynamics? • Adiabatic processes are reversible. • Heat energy does not spontaneously flow from cold to hot. • It is impossible to convert any heat into work. • No real engine can be more efficient than the equivalent “Carnot engine”. • There are no truly irreversible processes.

  5. Refrigerators (or air conditioners) • COPrefrigerator: How good is your refrigerator? heat, Qc fridge exhaust, Qh work

  6. Heat Pumps • COPheat pump: How good is your heat pump? heat pump heat, Qc “exhaust”, Qh work

  7. P state B; TB = 650K state A; TA = 300K V “Reversible” vs. “Irreversible” • “In order for a process to be [totally*] reversible, we must return the gas to its original state without changing the surroundings.” • Thought question: Is this [totally] reversible? • Yes • No • Maybe *Other books’ terminology: reversible vs totally reversible.

  8. “C” for “Carnot” Carnot Cycle • All heat added/subtracted reversibly • During constant temperature processes • Drawback: isothermal = slow, typically HW 11-5 – 11-7: find efficiency for a specific Carnot cycle Optional HW: eC derived for a general Carnot cycle

  9. Carnot Theorem • Second Law, Kelvin-Plank statement • You can’t fully convert heat to work • You can’t have an efficiency of 100% • Carnot Theorem: • You can’t even have that! Th = max temp of cycle Tc = min temp of cycle

  10. Carnot Theorem: How to remember • Engine: emax = ? • Refrigerator: COPr,max = ? • Heat pump: COPhp,max = ?

  11. work heat engine exhaust Carnot Theorem: Proof • Part 1 of proof: The Kelvin-Plank statement of the Second Law is equivalent to the Clausius statement. Clausius: Heat energy does not spontaneously flow from cold to hot. Kelvin-Plank: You can’t fully convert all heat to work. What if you could make heat go from coldhot? What if you could make a perfect engine? Then use it to power a refrigerator. Then do this:

  12. Bottom line: you could build a system to do that, but it couldn’t be built from an engine/heat reservoirs that look like this: P P V V Carnot Theorem: Proof • Part 2 of proof: A totally reversible engine can be run backwards as a refrigerator. (Obvious? It’s really: “Only a totally reversible…”) Why not this?

  13. work engine Qc fridge exhaust (at Tc) Qh work Carnot Theorem: Proof • Part 3 of proof: Suppose you had an engine with e > emax. Then build a Carnot engine using the same reservoirs, running in reverse (as a fridge). Use the fridge’s heat output to power the engine: Which work is bigger? Can you see the problem?

  14. Multi-Stage Carnot Engine? • Build a new cycle using only isotherms and adiabats. • Result?

  15. Isothermal contour “Regeneration” • …so you know something Dr. Durfee doesn’t  • …and so you engineers know a little about what’s coming • The other way that you can transfer heat without changing entropy: internalheat transfer • The Brayton cycle: Used by most non-steam power plants Image from Wikipedia

  16. Brayton cycle, cont. • What does temperature look like at each point? • Use “T-S” diagram. “S” = entropy, we’ll talk much more about on Monday • For now, just know that adiabatic = constant S. • Focus on y-axis Look here!

  17. Brayton cycle with regeneration • Add another compressor & another turbine to increase the range over which regeneration can be done • With an infinite number of compressors/turbines, you get the Carnot efficiency! (even with const. pressure sections) Image from http://web.me.unr.edu/me372/Spring2001/The%20Brayton%20Cycle%20with%20Regeneration.pdf (who apparently got it from a textbook, but I’m not sure which one)

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