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"Chaos rules the universe. Scientists call it 'ENTROPY'" | "Everything is breaking down tending towards GREATER AND GREATER DISORDER." | "It's great to be on the winning side." |
1.4.1. Are chaos and disorder the same thing?
1.4.2. Is there such as thing as structured disorder?
1.4.3. Can a system be in a constrained yet unpredictable state?
1.4.4. These questions and others follow from a flaw in the law of conservation of energy. We will examine that flaw in some detail in section 2 below. Meanwhile let's define "thermodynamics."
1.5.1. Thermo: Heat
1.5.2. Dynamics: Motion & Forces
1.5.3. Why Thermodynamics?1.5.3.1. Conservation of Energy is Incomplete
1.5.3.2. Cannot explain irreversibility of some energy transformations
1.5.3.3. Leads to other things
2.1.1. Work is converted to energy
2.1.1.1. Work is done to climb to the platform
2.1.1.2. Diver has potential energy while on the platform
2.1.1.3. Potential energy is converted to kinetic energy during the dive
2.1.1.4. Diver does work on water as she loses energy upon impact
2.1.1.5. Energy is conserved when the diver hits the water
2.1.1.6. Kinetic energy of diver is converted to motion of the water
2.1.1.7. energy of water increases, energy of diver decreases
2.1.1.8. no violation of conservation principle is noted2.1.2. Reverse video Clip of Diver
2.1.3. What prevents the reverse from happening?
2.1.3.1. wave energy is used to raise diver's potential energy
2.1.3.2. energy of water decreases
2.1.3.3. diver is hurled out of water to land back on platform
2.1.3.4. no violation of conservation of energy is noted
2.2.1. certain processes do not occur although they are permitted by conservation of energy
2.2.2. any process which "looks funny" when played in reverse
2.3.1. a jar of beans spills onto the floor
2.3.2. gas diffuses to fill available volume
2.3.3. heat flows from hot to cold
3.3.1. heat flows from warm to cold
3.3.2. specific heats, latent heats
3.3.3. gas laws
3.6.1. thought to be a form of matter (Caloric)
3.6.2. mechanical equivalent was a significant step
3.6.3. formulated by Joule and Mayer in early 1800s
3.7.1. Published by Joule and Mayer in 1843
3.7.2. Energy can be transformed or used to do work
3.7.3. Amount of energy does not change
3.8.1. physicists use Q for heat, chemists use H.
ModelAll heat flows from hot to cold, no work is done. Heat out of TH -QH) equals heat into TC (QC) |
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6.4.1. Heat Transfer
6.4.2. entropy does not decrease during spontaneous heat flow (it increases in this case. The amount of change is 1 J/K)
6.4.3. heat lost by hot object equals heat gained by cold object
6.4.4. heat is transferred from hot to cold
6.4.5. these are laws 2, 1, 0
7.6.1. beyond casual observer
7.6.2. has power to describe and explain many situations
7.6.3. led to design and construction of energy transformation machines
7.7.1. required statistical mechanics, atomic theory and kinetic theory to be understood first
7.7.2. concepts are simple and understandable without sophisticated mathematics
7.8.1. Heat flows spontaneously only from hot to cold
7.8.2. Added as an afterthought to other laws
7.9.1. The Work Energy Theorem
7.9.2. energy in many forms can be transformed or transferred between objects7.9.2.1. work is a mechanical process by which energy is transformed or transferred
7.9.2.2. note how we define work in terms of energy whereas before we defined energy in terms of work
7.10.1. many different ways to say it
7.10.2. imposes maximum efficiency on heat transformations
7.10.3. some energy becomes unavailable during transformations
7.10.4. no transformation is completely reversible
7.10.5. some forms of heat or energy are more useful or available than others
7.10.6. energy is degraded in quality during transformations
7.10.7. heat cannot be completely transformed into work
7.10.8. can only break even at absolute zero7.11. Third Law
7.11.1. entropy would be zero at absolute zero
7.11.2. gives another method to define absolute temperature
7.11.3. atoms would stop moving at absolute zero
7.11.4. Can't get to absolute zero7.11.4.1. can be deduced from zeroth law
7.11.4.2. heat cannot flow unless there is a difference of temperature
7.11.4.3. absolute zero is the absence of heat
7.11.4.4. in the same way that you cannot remove all of the air from a jar without a perfect vacuum7.11.5. Cooling to absolute zero would require
7.11.5.1. a reservoir below absolute zero (not possible by definition)
7.11.5.2. an infinitely large reservoir at absolute zero (not possible either)7.11.6. Modern techniques can approach very close
7.11.6.1. on single atoms or small groups of atoms
7.11.6.2. to 1 x 10-6 K
7.11.6.3. near absolute zero matter displays strange properties
7.11.6.4. superconductivity, Bose-Einstein condensates
8.4.1. Narrative
8.4.1.1. TH = 400K, TC = 300 K
8.4.1.2. Efficiency = 0.25
8.4.1.3. Work = .25 x 1200 J = 300 J
8.4.1.4. QH = 1200J, QC = 900
8.4.1.5.DS = 0 at maximum efficiency
8.4.1.6. no additional work can be extracted because entropy change would be negative
8.4.1.7. second law is limiting factor: entropy change must be nonnegative
9.1.1. Because there are more ways for something to go wrong than to go right
9.5.1. the room gets messy
9.6.1. it takes work to clean up your room
9.7.1. spilled jar of beans is more disorderly than when in the jar
9.7.2. gases diffuse to fill available space thereby increasing disorder
9.7.3. A room becomes cluttered unless an effort is made to keep it in order
9.8.1. there are more places to be out of place than in the proper place
9.8.2. in many cases there is only one right place and an infinite number of wrong ones
9.8.3. it is extremely unlikely that an object will spontaneously find the proper place
10.8.1. S = k log W
10.8.2. W = number of accessible states10.8.2.1. if there are only two accessible states it is an orderly system
10.8.3. k = Boltzman constant
10.8.4. same as constant in ideal gas equation, PV = kT10.8.4.1. note that k = PV/T has the same units as entropy (Joule/Kelvin)
11.5.1. no physical law prevents molecules of air from collecting in one corner of the room leaving a vacuum everywhere else
11.5.2. why doesn't it happen?
12.4.1. "How" of relationships is not difficult
12.4.1.1. Entropy is simply defined
12.4.1.2. Mathematics of thermodynamics is simple ratios
12.4.1.3. Relationships are quantitatively sound, qualitatively logical, and agree with observations12.4.2. "Why" of relationships is difficult
12.4.2.1. philosophically deep
12.4.2.2. the mystery of our time
12.4.2.3. similar to the inverse square central force question in Newton's time
12.4.2.4. not at all clear why these things should be related in this way
12.4.2.5. not at all clear what the relationships are
12.5.1. has generated much discussion
12.5.2. has spawned several new areas of study
12.5.3. has provided new explanations for the behavior of the universe
12.5.4. has allowed linkages between diverse areas of study
13.1.1. is there such a thing as pure randomness?
13.1.2. if so, how would you recognize it?
13.1.3. can we define patterns of pseudo randomness?
13.1.4. what does it take to recognize a pattern?
13.2.1. to recognize patterns and communicate information requires order
13.2.2. signal vs. noise
13.3.1. nonlinear systems have feedback
13.3.2. "The Butterfly Effect": An extremely small cause can have very large effects. A butterfly flapping its wings in Asia affect the weather worldwide.13.3.2.1. Lorenz's weather machine
13.3.2.2. rounded divergence
13.3.2.3. folklore 1For want of a nail, the shoe was loss
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost;
For want of a battle, the kingdom was lost.13.3.3. systems have many variations depending on initial conditions
13.4.1. non-equilibrium systems
13.4.1.1. how does order arise if entropy must increase
13.4.1.2. thermodynamics equation are valid for systems near equilibrium
13.4.1.3. in general the further out of equilibrium the more likely there will be ordered structures13.4.1.3.1. pouring water from a bottle
13.4.1.3.2. tornadoes and hurricanes13.4.2. state variables in dynamic systems are constrained by interrelationships
13.4.2.1. act as feedback mechanisms that keep certain systems restrained
13.4.3. attractors
13.4.4. values of functions can bifurcate and attain different states from tiny differences in values
13.4.4.1. The Lorenzian Waterwheel
13.4.4.1.1. simple device proves capable of surprisingly complicated behavior
13.4.4.1.2. long term behavior depends on how hard the driving force is, ie. on the intensity of the energy gradient
13.4.4.1.3. show on graph that Force is the slope of an energy vs. displacement graph
13.4.4.1.4. water pours into top bucket at steady rate
13.4.4.1.5. too slow --> top bucket doesn't fill enough to overcome friction so the wheel never turns
13.4.4.1.6. initial direction is extremely sensitive to initial position of top bucket13.4.4.1.6.1. try balancing a credit card (not the budget) by standing it on end
13.4.4.1.7. If flow rate is faster the weight of the top bucket sets the wheel in motion. It can settle into an equilibrium, steady rotation rate
13.4.4.1.8. change in speed or change in water flow rate causes nonlinear effects
13.4.4.1.9. how much the buckets fill depends on the flow rate and the rate of spin
13.4.4.1.10. slow flow rate means that the buckets take a longer time to fill and buckets start up the other side before they have time to empty
13.4.4.1.11. a rapid spinning rate allows too little time for the buckets to fill
13.4.4.1.12. heavy buckets going uphill slow the wheel and eventually reverse it
13.4.4.1.13. Lorenz discovered that the spin will reverse itself many time, never settles down to a steady rate, never repeating itself in any as yet predictable pattern.
13.4.4.1.14. similar to butterfly effect13.4.4.2. The compound pendulum (Video Demo)
13.4.4.2.1. complex behavior generated from two simple laws
13.4.4.2.2. unpredictable yet predictable
13.4.4.2.3. exact path vs. containment field of paths13.4.5. The Mandelbrot Set and Fractals
13.4.5.1. See illustrations in "Chaos: Making a New Science", by James Gleick
13.4.5.2. the most complex mathematical structure known13.4.5.2.1. a recursive fractal
13.4.5.2.2. reveals infinitely fine structure through series of magnifications
13.4.5.2.3. length of perimeter depends on scale
13.4.5.2.4. number of dimension is somewhere between two and three.
13.4.5.2.5. take complex number and square it, add the original number,repeat13.4.5.3. ((((((A2+A)2+A)2+A)2+A)2+A)2+A)2 . . .
In the figures below, each picture represents an enlargement of the white frame in the pircute before it.
13.4.5.3.1. Mandelbrot 1
13.4.5.3.2. Mandelbrot 2
13.4.5.3.3. Mandelbrot 3
13.4.5.3.4. Mandelbrot 4
13.4.5.3.5. Mandelbrot 5
13.4.5.3.6. Mandelbrot 6
13.4.5.3.7. Mandelbrot 7
13.4.5.3.8. Mandelbrot 8
This last picture is "pixelated" to save time. In reality the set can be "magnified" indefinitely with no loss of clarity.
13.4.5.4. fractal folklore
Turtle upon turtle upon turtle.
13.5.1. under some conditions rapid and catastrophic changes occur
13.5.2. dams burst, beams collapse, floods flash, eg.
13.6.1. why does time flow from the past to the present?
13.6.2. the fact that some kinds of processes can only happen in one direction is related to the flow of time
13.6.3. if all events were equally reversible, like Lorenz's waterwheel, there would be no flow of time
13.7.1.Steven Hawking's analysis of energy leaking from black holes is a theory that not everyone agrees with, but asks some interesting questions.
13.7.2. combines quantum principles with thermodynamic principles
14.4.1. Zeroth. There is a strong incentive to play the game
14.4.2. First: You can't win, you can at best break even
14.4.3. Second: You can only break even at absolute zero
14.4.4. Third: You can't get to absolute zero
14.5.1. a whole new area of study
14.5.2. wide range of applicability in diversity of areas
14.5.3. limits the precision of predictions for complex systems
14.5.4 Suggests that there is a limit to the "knowability" of certain systems.