Energy. on this world and elsewhere. Instructor: Gordon D. Cates Office: Physics 106a, Phone: (434)

Transcription

1 Energy on this world and elsewhere Instructor: Gordon D. Cates Office: Physics 106a, Phone: (434) Course web site available at click on classes and find Physics or at Lecture #7 September 12, 2017

2 Announcements Please purchase Beyond Smoke and Mirrors by Burt Richter, 2 nd addition. Date for quiz: Thursday September 14. Review sheet (version 1.0) is available on the course web site. Version 1.1 will be up shortly. Review sessions tonight (Tuesday) and tomorrow (Wednesday), the 12th and the 13th. Material for quiz: - Lectures 1-7 (through today). - Chapters 1-3 of the class notes. - Chapters 1, 3 and 5 of Feynman s book. - Isaac Asimov s short story, The Last Question.

3 The First Law of Thermodynamics The first law of thermodynamics is essentially an expression of the conservation of energy

4 The conservation of energy applied to the heat engine Looking at the flow of energy as illustrated in the diagram at right, we can write down: Hot reservoir, T H Q H Q H = W + Q C This is essentially the statement that the ENERGY IN must equal the ENERGY OUT. Rearranging: Q C work W = Q H - Q C Cold reservoir, T C

5 Re-expressing the efficiency of a heat engine Using the following equation from the previous slide W = Q H - Q C We divide through by Q H : Hot reservoir, T H Q H W Q H W Q H = = Q H Q C Q - H QH Q C 1 - QH Q C Cold reservoir, T C work efficiency = Q C 1 - QH

6 Next we will look at how the 2 nd law of thermodynamics can help us understand the efficiency of heat engines. But first, we want to discuss the 2nd law of thermodynamics itself...

7 The second law of thermodynamics The second law is basically what Feynman calls the principle of irreversibility

8 The distinction of past and future If we take a (high speed) movie of the solar system and watch the planet going around the sun, we might not quickly realize it if we ran the movie backwards. Things governed by gravity look the same whether time is running forwards or is reversed.

9 The distinction of past and future But a tank with two separated sections of water, one dyed, and one not, will mix spontaneously, but will not un-mix spontaneously. We might explain this by saying that probability dictates that things must become more random.

10 demo

11 The distinction of past and future For a simple process, like two pucks colliding, the basic laws of physics don t recognize the difference between time running forwards or backwards. For processes in which large numbers of things are involved, however, it is easy to recognize a transition from being more ordered to less ordered.

12 The principle of irreversibility is central to the functioning of a heat engine Heat engines take advantage of the fact that heat flows from hot objects to cold objects, and not the reverse. If we have NO temperature differential, we cannot do work! More on this soon...

13 The concept of entropy an important and useful idea when discussing reversible and irreversible processes. Entropy provides a measure of the degree to which a system is disordered or chaotic. A system has more entropy when it is more chaotic. A system has less entropy when it is less chaotic.

14 Change in entropy during transfer of thermal energy m T C T H The change of entropy for a gas is DEFINED as: Q ΔS = Q/T Where Q is the heat ADDED to the gas. Here we assume that during this addition of heat, the temperature doesn t change much.

15 The second law tells us that the NET change in entropy for any collection of processes must always be positive m T C T H Q ΔS NET = Q 1 /T 1 + Q 2 /T 2 + > 0

16 What does the second law say about heat engine? We know that: ΔS Net 0 Hot reservoir, T H Using the definition of entropy, we can calculate the net change in entropy of the heat engine during one full cycle: Q H ΔS Net = Q Q - H + C 0 TC T H work With some algebra, the equation above tells us: Q C 1 - QH T C 1 - TH Q C Cold reservoir, T C

17 What does the second law say about heat engine? But since, for a heat engine: Hot reservoir, T H Q H Efficiency = Q C 1 - QH work Q C Cold reservoir, T C So we find the incredibly important result. Efficiency = Q C 1 - QH T C 1 - TH

18 The Carnot Efficiency for a heat engine: Hot reservoir, T H Q H work Q C Cold reservoir, T C This is the absolute maximum that is possible

19 The second law of thermodynamics Again, second law embodies the idea that Feynman calls the principle of irreversibility

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21 In what way does the 2nd law of thermodynamics figure into Asimov s story.

22 What are the implications of the second law for the universe?

23 What does the Carnot efficiency tell us about the universe? How is this related to what we were just discussing?

24 What do you think Asimov is saying with the ending?

25 Isaac Asimov s The Last Question First posed by Alexander Adell and Bertram Lupov on the occasion during which - The energy of the Sun was stored, converted, and utilized directly on a planet-wide scale. All Earth turned off its burning of coal its fissioning uranium, and flipped the switch that connected all of it to a small station, one mile in diameter, circling the Earth at half the distance of the Moon. All Earth ran by invisible beams of sunpower. The question was posed to Mulitvac, the most advanced computer. They asked the question, by the way, by typing into a teletype machine. The question was: - - Will mankind one day without the net expenditure of energy be able to restore the Sun to its full youthfulness even after it had died of old age? Alternatively, How can the net amount of entropy of the universe be massively decreased?

26 Isaac Asimov s The Last Question Question is repeated by Jerrodd, who with his family, is emigrating to the star X-23. Question is repeated again by VJ-23 who doesn t want to submit a pessimistic report to the Galactic Council, once his friend points out that the galaxy will be filled up within five years. Again, the question is asked by Zee Prime, some type of ethereal being who s exact nature is not exactly clarified. In each case, the answer is roughly: insufficient data for a meaningful answer

27 Isaac Asimov s The Last Question In the final few lines of the story, the Cosmic AC, which exists solely in hyperspace, finally says: Let there be light, and there was light. Is this a religious statement? Is it an actual speculation about our future? Is it just a cheap trick on the part of the author? Whether or not it is a cheap trick, I would suggest that Asimov is admitting to two facts: There are things about the physical universe that we do not understand, such as the Big Bang and many things about black holes. It is a fact that we exist, and in a certain sense, we do not know why.

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29 Back to Heat Engines

30 There are many types of heat engines External Combustion Engines. - Cannonball Engine. - Steam-driven turbines in power plants, where the heat can come from: - Coal Nuclear Solar thermal Sterling Engines Internal Combustion Engines - Otto Cycle engines in our cars and trucks. - Diesel cycle engines in our cars and trucks. - Turbines in jet aircraft, helicopters, tanks, etc. - Turbines in natural-gas turbine-based power plants.

31 4-stroke internal combustion engine 1. Intake stroke 3. Power or work 2. Compression stroke 4. Exhaust stroke

32 Stirling Engine Note that this is CLOSE CYCLE. That is, while heat is absorbed and expelled, the medium (a gas) that expands and contracts stays within the engine.

33 Stirling Engine

34 Solar-thermal technology: one example

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