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Entropy

Physics 102 Professor Lee Carkner Lecture 8. “Entropy isn’t what it used to be.” --Anonymous physicist. Entropy. Auto Engine. If an automobile engine outputs 149200 joules per second to the drive train and has an input heat of 746000 joules per second, what is the efficiency?

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Entropy

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  1. Physics 102 Professor Lee Carkner Lecture 8 “Entropy isn’t what it used to be.” --Anonymous physicist Entropy

  2. Auto Engine • If an automobile engine outputs 149200 joules per second to the drive train and has an input heat of 746000 joules per second, what is the efficiency? • Note: can write as 20% • If gas is $1.50 per gallon, how much money per gallon are you wasting? • (1.50) X (0.8) = 1.2

  3. PAL # 8 Refrigerators • How does temperature of house change if you add a refrigerator with the door open? • More heat added than removed, room heats up • Because of work needed to run compressor

  4. Reversibility • Carnot engines are maximally efficient because they are reversible • No real engine is reversible • e.g. When you add heat to a gas to raise a piston and produce work, can you put the work back in and compress the gas to get your heat back out? • Can get close to reversible by reducing friction, doing process slowly, etc.

  5. The Second Law -- A Look Back • How can you express the second law? • Can’t move heat from cold to hot without doing work • These formulations suggest there is a preferred direction processes want to move in

  6. Heat, Temperature and Entropy • The efficiency of an engine is • For a Carnot engine: QC/QH = TC/TH QC/TC = QH/TH • Q/T is known as the change in entropy (DS) • Entropy is a state variable (property of the system)

  7. Determining Entropy • For any process: DS = Q/T • Losing heat decreases entropy (-Q means -DS), gaining heat increases it (+Q means +DS) • How does the entropy change? • For a reversible (Carnot) system • +DSC = -DSH • DSnet = 0

  8. Second Law of Thermodynamics • If a process is irreversible: • Since QC is larger for a non-Carnot engine • +DSC > -DSH • Irreversible processes have DS>0, reversible processes have DS=0 DS>0 • This is the second law of thermodynamics: Entropy always increases

  9. Today’s PAL • Demonstrate that the second law of thermodynamics holds when a 1 kg block of ice (at 0 C) melts in a 20 C room

  10. Randomness • What is entropy? • A universe with objects sorted by temperature is ordered • A universe at a uniform temperature is disordered • As heat flows from hot to cold, the disorder increases • Note that the overall entropy of the universe always increases, even if in some small area it decreases

  11. Entropy and Reversibility • The second law explains why some processes are not reversible • Examples: • These processes only happen in one direction because: • Work into heat creates more disorder • Heat is a less ordered form of energy

  12. Statistical Mechanics • Statistical mechanics uses microscopic properties to explain macroscopic properties • The box contains 4 indistinguishable molecules

  13. Molecules in a Box • There are 16 ways that the molecules can be distributed in the box • Since the molecules are indistinguishable there are only 5 configurations • If all microstates are equally probable, the configuration with equal distribution is the most probable

  14. Distributions Configuration I Probability = (1/16) Configuration II Probability = (4/16)

  15. Probability • There are more microstates for the configurations with roughly equal distributions • There are a lot of ways to fill up the room, only one way to get bunched in a corner

  16. Entropy and Probability • The equal distribution is just the most probable • The universe is governed by probability, it only seems deterministic because the number of events is so large

  17. Today’s PAL • If you put a drop of ink in a bowl of water, does the entropy increase, decrease or stay the same? Explain. • If the ink in the tinted water comes together in a dot, does the entropy increase, decrease or stay the same? Explain. Why do we never see this happen?

  18. Skepticism • Many people claim to have invented engines that violate first or second law • Laws have been verified over and over again • Don’t rely just on credentials: • Carkner’s Law:

  19. Arrows of Time • Three arrows of time: • Thermodynamic • Psychological • Cosmological

  20. Entropy and Memory • When we remember things, order is increased • A brain or a computer cannot store information without the output of heat

  21. Synchronized Arrows • Why do all the arrows go in the same direction? • Can life exist with a backwards arrow of time? • Does life only exist with a forwards arrow of time? (anthropic principle)

  22. Fate of the Universe • If the universe has enough mass, its expansion will reverse • Cosmological arrow will go backwards • Universe seems to be open

  23. Heat Death • Entropy keeps increasing • Stars burn out • Universe becomes completely random radiation field

  24. Department of Entropy

  25. Next Time • Exam #1 Friday • Covers all of Ch 16-18 • Lectures 1-8 • About 10 multiple choice (~25%) • 3-4 problems (~75%) • Equation and constant sheet given • Review questions posted on WebAssign • Won’t be graded

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