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Announcements – 9/23/11

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- 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

- 12 adiabatic
- 23 isothermal
- 31 constant volume
- Diatomic gas
Done last time:

- P1V1g = P2V2g
V2 = V1 (P1/P2)1/g = 0.4562 m3

- Q12=0
- Q23= -Won = nRTln(V3/V2) = P2V2ln(V3/V2) = 107408 J
- Q31= 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

- Stirling engine
- Thermoelectric engine

- 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.

- COPrefrigerator: How good is your refrigerator?

heat, Qc

fridge

exhaust, Qh

work

- COPheat pump: How good is your heat pump?

heat

pump

heat, Qc

“exhaust”, Qh

work

P

state B; TB = 650K

state A; TA = 300K

V

- “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.

“C” for “Carnot”

- 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

- 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

- Engine: emax = ?
- Refrigerator: COPr,max = ?
- Heat pump: COPhp,max = ?

work

heat

engine

exhaust

- 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 coldhot?

What if you could make a perfect engine? Then use it to power a refrigerator.

Then do this:

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

- 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?

work

engine

Qc

fridge

exhaust

(at Tc)

Qh

work

- 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?

- Build a new cycle using only isotherms and adiabats.
- Result?

Isothermal contour

- …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

- 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!

- 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)