Announcements – 9/21/12
Prayer
 Remote Desktop check
 Exam starts a week from tomorrow
a. Avoid Oct 1 and Oct 3 if possible
 Results of doodle.com voting:
a. Exam review will be Wed 5-6:30, room to be
announced

Pearls
Before
Swine
From warmup

Extra time on?
a. Example of a near-perfect Carnot engine; especially
if a video of one exists (sped up, of course), or if
we could see a demo of a Carnot engine in class.

Other comments?
a. I really don't get irreversibility. Can't you
adiabatically compress and then immediately
decompress a gas? If it's insulated well enough,
don't you get nearly all the energy back?
Worked Problem from last time
P
303000 Pa
202000 Pa
3, 320 K
Qh
Qh
2
Qc
1, 320K
V
V2=?
T2=?

0.001 m3
Game plan:
a.Find unknown state variables
b.Find Q for each leg
c.Find |Wnet|
d.Then e = |Wnet|/Qh
Demos


Stirling engine
Thermoelectric engine
Review:

Second Law
a. Kelvin-Plank
b. new: “Clausius statement”
Refrigerators (or air conditioners)
heat, Qc
fridge
exhaust, Qh
work

COPrefrigerator: How good is your refrigerator?
From warmup

Why would you want to use a heat pump
(instead of an electric heater) to heat your
house when 100% of the energy in an electric
heater can be converted directly to heat? Isn't
that more efficient? Explain.
a. No, because a heat pump is usually around
400% effective. That is, you get 4 times
more energy (in the form of heat) out than
you put in (in the form of work). Because it
pulls energy from the air surrounding it,
instead of just relying on the work that you
put into it.
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.”
Warmup: Give an example of a process that would be
considered reversible if not for that qualifier
a. Yesterday at the physics social we froze things in
liquid nitrogen. When a balloon went in, it
compressed greatly. Then, when it was taken out,
its volume expanded back to its original state.
*Other
terminology: internally reversible vs totally reversible.
“Reversible” vs. “Irreversible”

Warmup: Give an example of a process that would be
considered reversible if not for that qualifier
a.
(My answer) Pretty much any
line that you can draw on a PV
diagram would be reversible if
not for that condition. Consider
a constant volume change, a
vertical line on a PV diagram. If
the surroundings are hot, the
gas will move up the line
towards higher temperature.
By making the surroundings
cold, the gas will move down
the exact same line, reversing
its path.
P
state B; TB = 650K
state A; TA = 300K
V
From warmup

The Carnot engine is completely impractical… Why
then do we bother? What is important about this
engine?
a. It is important as a standard to measure the
efficiency of other, more practical engines, and
also as a measure of what is possible for
humankind to achieve.

Why doesn't the Carnot engine have perfect
efficiency?
a. Because no engine can have 100% efficiency
b. Because that would require a cold reservoir at 0K,
which is impossible.
Carnot Cycle

All heat added/subtracted
reversibly
a. During constant
temperature processes
b. Drawback: isothermal =
slow, typically
" eC "  emax
Tc
 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”



Any engineers in the crowd?
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)