Final Lecture on Thermodynamics and Key Concepts Review

1. Announcements - 1 Feb 2011 • Prayer • Friday is last lecture on Thermodynamics • Reading assignment “handout” will be posted on website • Exam 1 starts Tuesday of next week • Exam review session: Friday, Saturday, or Monday?  I will send out survey today

2. Review • Engines • Picture • Relationship between Qh, Qc, and |W| • Defn of efficiency • How to calculate efficiency • Class-designed engine continued from last time

3. 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.

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

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

6. 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.

7. “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

8. 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

9. Carnot Theorem: How to remember • Engine: emax = ? • Refrigerator: COPmax = ? • Heat pump: COPmax = ?

10. 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:

11. 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?

12. 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?

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

14. 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

15. 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!

16. 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)