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Announcements – 9/23/11 PowerPoint PPT Presentation

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

Announcements – 9/23/11

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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

Before

Swine

Problem continued from last time

2

• 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

• Stirling engine

• Thermoelectric engine

• What is the “Clausius statement” of the Second Law of Thermodynamics?

• 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)

• COPrefrigerator: How good is your refrigerator?

heat, Qc

fridge

exhaust, Qh

work

Heat Pumps

• 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

“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.

“C” for “Carnot”

Carnot Cycle

• 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

• 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

• Engine: emax = ?

• Refrigerator: COPr,max = ?

• Heat pump: COPhp,max = ?

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:

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?

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?

• Build a new cycle using only isotherms and adiabats.

• Result?

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.

• 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

• 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)