Announcements – 9/23/11



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
Pearls
Before
Swine
Problem continued from last time




12 adiabatic
23 isothermal
31 constant volume
Diatomic gas
300 kPa
2
136.87
200 kPa
100 kPa
3
1
V2
1 m3
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
-92185 JJ

Q31= DEint = (5/2)nRDT = (5/2) (P1V1–P3V3) = -250000
Error recognized since I knew |Qh| – |Qc| had to be positive
The issue: I overspecified the parameters. Specifically, P3
cannot be 200 kPa. P2V2 = P3V3  P3 = 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)
heat, Qc
fridge
exhaust, Qh
work

COPrefrigerator: How good is your refrigerator?
Heat Pumps
heat, Qc
heat
pump
“exhaust”, Qh
work

COPheat pump: How good is your heat pump?
“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. Yes
P
state B; TB = 650K
b. No
c. Maybe
state A; T = 300K

A
V
*Other
books’ terminology: reversible vs totally reversible.
Carnot Cycle

All heat added/subtracted
reversibly
a. During constant
temperature processes
b. Drawback: isothermal =
slow, typically
Tc
" eC "  1 
Th
“C” for “Carnot”
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
a. You can’t fully convert heat to work
b. You can’t have an efficiency of 100%
Carnot Theorem:
a. You can’t even have that!
emax
Tc
 eC  1 
Th
Th = max temp of cycle
Tc = 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 coldhot? Then do this:
work
heat
engine
exhaust
What if you could make a perfect engine? Then use it to
power a refrigerator.
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?
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 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:

work
Qc
work
fridge
Qh
engine
exhaust
(at Tc)
Which work is bigger? Can you see the problem?
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
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)