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Review Engines

a. Pictureb. Relationship between Qh, Qc, and |W|

c. Defn of efficiencyd. How to calculate efficiency

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)

COP: How good is your refrigerator?

fridgeheat, Qc

work

exhaust, Qh

Heat Pumps

COP: 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: COPmax = ?

Heat pump: COPmax = ?

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)