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Entropy Lecturer: Professor Stephen T. Thornton

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Reading Quiz: Entropy is A) another form of energy. B) the name of a famous heat engine. C) related to the 4th Law of Thermodynamics. D) the primary reason your bedroom is (or may be) so messy.

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Answer: D Entropy is related to disorder and the probability of events in the universe. There is not much you can do about the fact that your bedroom naturally becomes messy, unless you expend a good deal of work. Unfortunately that leads to a heat death of the universe.

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Last Lecture Second Law of Thermodynamics Carnot cycle and Carnot engine Heat engines Refrigerators Air conditioners Heat pumps

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Today Entropy Statistical interpretation - entropy 3 rd Law of Thermodynamics

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Entropy There are several ways to look at entropy, but eventually they are all equal. Entropy is related to disorder in a system. A messy bedroom has more entropy than a clean one. The natural order of the universe is to increase entropy. Your bedroom never naturally becomes clean; it always naturally becomes messy.

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Entropy is also related to probability. There is a higher probability that a block of ice will melt at room temperature than it will get colder. Thermodynamics does not prevent either action. The probability of the latter is incredibly small.

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Conceptual Quiz: Humpty Dumpty falls off and breaks. Can he get back together again? A) Yes, very easily. B) Yes, but with extremely low probability. C) No, there is no possibility. D) Are you kidding us? Humpty Dumpty sat on a wall, Humpty Dumpty had a great fall; All the King's horses and all the King's men, Couldn't put Humpty together again.

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Answer: B From what we just learned, this is only a question of probabilities. And no, I am not kidding!

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Entropy is a very fundamental property and is a state variable. It is determined by the heat flow Q divided by the temperature T.

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When the temperature changes, things are a little more complicated. Consider the change of entropy from state a to state b. This is for a reversible process. ΔS depends only on states a and b, because entropy is a state variable (like P, V, T, but not like Q which is not a state variable).

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For a reversible heat engine, the total entropy of the engine cycle is

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Copyright © 2009 Pearson Education, Inc. Any reversible cycle can be written as a succession of Carnot cycles; therefore, what is true for a Carnot cycle is true of all reversible cycles.

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Copyright © 2009 Pearson Education, Inc. Entropy and the Second Law of Thermodynamics The total entropy always increases when heat flows from a warmer object to a colder one in an isolated two-body system. The heat transferred is the same, and the cooler object is at a lower average temperature than the warmer one, so the entropy gained by the cooler one is always more than the entropy lost by the warmer one.

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Copyright © 2009 Pearson Education, Inc. The fact that after every interaction the entropy of the system plus the environment increases is another way of putting the second law of thermodynamics: The entropy of an isolated system never decreases. It either stays constant (reversible processes) or increases (irreversible processes).

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The total entropy of the universe increases whenever an irreversible process occurs. The total entropy of the universe is unchanged whenever a reversible process occurs. This is another way to state the 2 nd Law of Thermodynamics.

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There is some really bad news here. Because the universe actually works through irreversible processes, the entropy is gradually increasing. There will eventually be a gradual “heat death” of the universe. The universe will be full of energy which cannot be used to perform work! We are doomed!

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Order, Disorder, and Entropy As we have stated, entropy is related to disorder. As the entropy of a system increases, its disorder increases as well. GOOD NEWS: When you go home, and your mother fusses about how messy your bedroom is, tell her it is because entropy is increasing, and it is the natural order of the universe. There is little you or your mother can do about it (without doing a lot of work!). She will be impressed by how much physics you have learned!

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Expanding Ideal Gas. An ideal gas expands isothermally (T = 410 K) from a volume of 2.50 L and a pressure of 7.5 atm to a pressure of 1.0 atm. What is the entropy change for this process?

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Copyright © 2009 Pearson Education, Inc. Entropy is a measure of the disorder of a system. This gives us yet another statement of the second law: Natural processes tend to move toward a state of greater disorder. Example: If you put milk and sugar in your coffee and stir it, you wind up with coffee that is uniformly milky and sweet. No amount of stirring will get the milk and sugar to come back out of solution.

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Copyright © 2009 Pearson Education, Inc. Another example: When a tornado hits a building, there is major damage. You never see a tornado approach a pile of rubble and leave a building behind when it passes.

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Copyright © 2009 Pearson Education, Inc. Another consequence of the second law: In any natural process, some energy becomes unavailable to do useful work. If we look at the universe as a whole, it seems inevitable that, as more and more energy is converted to unavailable forms, the ability to do work anywhere will gradually vanish. This is called the heat death of the universe. Unavailability of Energy; Heat Death

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Copyright © 2009 Pearson Education, Inc. Statistical Interpretation of Entropy and the Second Law Microstate: a particular configuration of atoms Macrostate: a particular set of macroscopic variables (in thermodynamics P, V, T, S) This example uses coin tosses:

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Copyright © 2009 Pearson Education, Inc. Statistical Interpretation of Entropy and the Second Law The most probable distribution of speeds in a gas is Maxwellian: The most probable state is the one with the greatest disorder, or the greatest entropy. With k being Boltzmann’s constant and W the number of microstates, Boltzmann showed Highly unlikely

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Copyright © 2009 Pearson Education, Inc. Statistical Interpretation of Entropy and the Second Law In this form, the second law of thermodynamics does not forbid processes in which the total entropy decreases; it just makes them exceedingly unlikely.

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Conceptual Quiz: According to the second law of thermodynamics, for any process that may occur within an isolated system, which one of the following choices applies? A) Entropy increases. B) Entropy remains constant. C) Entropy decreases. D) Both A and B are possible. E) Both A and C are likely.

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Answer: D) Both A and B are possible. Entropy can increase for an irreversible process or remain constant for a reversible process, but that is all that is likely.

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Copyright © 2009 Pearson Education, Inc. Thermodynamic Temperature Since the ratio of heats exchanged between the hot and cold reservoirs in a Carnot engine is equal to the ratio of temperatures (Q L /Q H = T L /T H ), we can define a temperature scale using the triple point of water: T = (273.16K)(Q/Q tp ). Here, Q and Q tp are the heats exchanged by a Carnot engine with reservoirs at temperatures T and T tp.

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Copyright © 2009 Pearson Education, Inc. there is no way to achieve a temperature of absolute zero. This is the third law of thermodynamics: It is not possible to reach absolute zero in any finite number of processes. Also, since the maximum efficiency of a heat engine is Third Law of Thermodynamics

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Copyright © 2009 Pearson Education, Inc. Thermal Pollution, Global Warming, and Energy Resources Over 90% of the energy used in the U.S. is generated using heat engines to drive turbines and generators—even nuclear power plants use the energy generated from fission to heat water for a steam engine. The thermal output Q L of all these heat engines contributes to warming of the atmosphere and water. This is an inevitable consequence of the second law of thermodynamics.

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Dice Probabilities. Calculate the relative probabilities, when you throw two dice, of obtaining (a) a 7, (b) an 11, (c) a 4.

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Coin Probabilities & Entropy. (a) Suppose you have four coins, all with tails up. You now rearrange them so two heads and two tails are up. What was the change in entropy of the coins? (b) Suppose your system is the 100 coins in a given table; what is the change in entropy of the coins if they are mixed randomly initially, 50 heads and 50 tails, and you arrange them so all 100 are heads? (c) Compare these entropy changes to ordinary thermodynamic entropy changes, such as given in textbook examples.

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Refrigeration Units. Refrigeration units can be rated in “tons.” A 1-ton air conditioning system can remove sufficient energy to freeze 1 British ton (2000 pounds = 909 kg) of 0°C water into 0°C ice in one 24-h day. If, on a 35°C day, the interior of a house is maintained at 22°C by the continuous operation of a 5-ton air conditioning system, how much does this cooling cost the homeowner per hour? Assume the work done by the refrigeration unit is powered by electricity that costs $0.10 per kWh and that the unit’s coefficient of performance is 15% that of an ideal refrigerator. 1 kWh = 3.60 x 10 6 J.

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Conceptual Quiz In the closed thermodynamic cycle shown in the P-V diagram, the work done by the gas is: A) positive B) zero C) negative V P

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Conceptual Quiz In the closed thermodynamic cycle shown in the P-V diagram, the work done by the gas is: A) positive B) zero C) negative The gas expands at a higher pressure and compresses at a lower pressure. In general, clockwise = positive work; counterclockwise = negative work. V P

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Conceptual Quiz: Which of the following is a statement of the third law of thermodynamics? A) If two objects are in equilibrium with a third, then they are in thermal equilibrium with one another. B) All reversible engines operating between the same two temperatures have the same efficiency. C) The entropy of the universe cannot decrease. D) The entropy of the universe cannot increase. E) It is impossible to lower the temperature of an object to absolute zero in a finite number of steps.

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Answer: E) The other answers do not refer to the third law of thermodynamics.

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Conceptual Quiz Which of the following statements is not true? A)Entropy of an isolated system tends to increase. B)Natural systems move to a state of greater order. C)In any natural process, some energy becomes unavailable to do useful work. D)It is not possible to reach absolute zero in any number of finite number of processes.

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Conceptual Quiz B) Natural systems move to a state of greater disorder, not order. Remember that your bedroom always become messy, not clean.

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Copyright © 2009 Pearson Education, Inc.

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