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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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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

Before

Swine


Problem continued from last time

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


Demos

Demos

  • Stirling engine

  • Thermoelectric engine


Reading quiz

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.


Refrigerators or air conditioners

Refrigerators (or air conditioners)

  • COPrefrigerator: How good is your refrigerator?

heat, Qc

fridge

exhaust, Qh

work


Heat pumps

Heat Pumps

  • COPheat pump: How good is your heat pump?

heat

pump

heat, Qc

“exhaust”, Qh

work


Reversible vs irreversible

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.


Carnot cycle

“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


Carnot theorem

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


Carnot theorem how to remember

Carnot Theorem: How to remember

  • Engine: emax = ?

  • Refrigerator: COPr,max = ?

  • Heat pump: COPhp,max = ?


Carnot theorem proof

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:


Carnot theorem proof1

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?


Carnot theorem proof2

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?


Multi stage carnot engine

Multi-Stage Carnot Engine?

  • Build a new cycle using only isotherms and adiabats.

  • Result?


Regeneration

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


Brayton cycle cont

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!


Brayton cycle with regeneration

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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