Review Engines a. a.Picture b. b.Relationship between Q h, Q c, and |W| c. c.Defn of efficiency d. d.How to calculate efficiency Class-designed engine continued from last time

Reading Quiz What is the “Clausius statement” of the Second Law of Thermodynamics? a. a.Adiabatic processes are reversible. b. b.Heat energy does not spontaneously flow from cold to hot. c. c.It is impossible to convert any heat into work. d. d.No real engine can be more efficient than the equivalent “Carnot engine”. e. e.There are no truly “irreversible” processes.

Refrigerators (or air conditioners) COP: How good is your refrigerator? fridge heat, Q c work exhaust, Q h

Heat Pumps COP: How good is your heat pump? heat pump heat, Q c work “exhaust”, Q h

“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. a.Yes b. b.No c. c.Maybe P V state A; T A = 300K state B; T B = 650K * Other books’ terminology: reversible vs totally reversible.

Carnot Cycle All heat added/subtracted reversibly a. a.During constant temperature processes b. b.Drawback: isothermal = slow, typically HW 11-5 – 11-7: find efficiency for a specific Carnot cycle Optional HW: e C derived for a general Carnot cycle “C” for “Carnot”

Carnot Theorem Second Law, Kelvin-Plank statement a. a.You can’t fully convert heat to work b. b.You can’t have an efficiency of 100% Carnot Theorem: a. a.You can’t even have that! T h = max temp of cycle T c = min temp of cycle

Carnot Theorem: How to remember Engine: e max = ? Refrigerator: COP max = ? Heat pump: COP 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? What if you could make a perfect engine? Then use it to power a refrigerator. engine heat 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 > e max. 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? fridge QcQc work QhQh engine work exhaust (at T c )

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 (who apparently got it from a textbook)