Prayer Wednesday is last lecture on Thermodynamics a. 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: a. Exam review will be Fri 9/30/11, 4 pm, room C460 Announcements – 9/23/11 Pearls Before Swine
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Prayer Wednesday is last lecture on Thermodynamics a. a.Reading assignment for Wed is posted to class website: the “What is entropy” handout in Supplementary.
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Prayer Wednesday is last lecture on Thermodynamics
a. 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:a. Exam review will be Fri 9/30/11, 4 pm, room
C460
Announcements – 9/23/11
PearlsBeforeSwine
Problem continued from last time 12 adiabatic 23 isothermal 31 constant volume Diatomic gas
Error recognized since I knew |Qh| – |Qc| had to be positive
13
2
100 kPa
200 kPa
300 kPa
1 m3V2
The issue: I overspecified the parameters. Specifically, P3 cannot be 200 kPa. P2V2 = P3V3 P3 = 136.87 kPa
-92185 J
136.87 kPa
Demos Stirling engine Thermoelectric engine
Reading Quiz What is the “Clausius statement” of the
Second Law of Thermodynamics?a. Adiabatic processes are reversible.b. Heat energy does not spontaneously flow
from cold to hot.c. It is impossible to convert any heat into
work.d. No real engine can be more efficient than
the equivalent “Carnot engine”.e. There are no truly irreversible processes.
Refrigerators (or air conditioners)
COPrefrigerator: How good is your refrigerator?
fridgeheat, Qc
work
exhaust, Qh
Heat Pumps
COPheat pump: How good is your heat pump?
heatpump
heat, Qc
work
“exhaust”, Qh
“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?
a. Yesb. Noc. Maybe
P
V
state A; TA = 300K
state B; TB = 650K
*Other books’ terminology: reversible vs totally reversible.
Carnot Cycle All heat added/subtracted
reversibly a. During constant
temperature processesb. 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
" " 1 cC
h
Te
T
“C” for “Carnot”
Carnot Theorem
Second Law, Kelvin-Plank statementa. You can’t fully convert heat to workb. You can’t have an efficiency of 100%
Carnot Theorem: a. You can’t even have that!
max 1 cC
h
Te e
T
Th = max temp of cycleTc = min temp of cycle
Carnot Theorem: How to remember
Engine: emax = ?
Refrigerator: COPr,max = ?
Heat pump: COPhp,max = ?
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 coldhot?
What if you could make a perfect engine? Then use it to power a refrigerator.
engineheat
work
exhaust
Then do this:
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?P
V
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
V
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?
fridgeQc
work
Qh engine
work
exhaust(at Tc)
Multi-Stage Carnot Engine? Build a new cycle using only isotherms and
adiabats. Result?
“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: internal heat transfer The Brayton cycle: Used by most non-steam power plants
Image from Wikipedia
Isothermal contour
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)