energy: mysterious and amazing, conserved and conserving r. stephen berry the university of chicago...
TRANSCRIPT
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Energy: Mysterious and Amazing, Conserved and
ConservingR. Stephen Berry
The University of Chicago
Nerenberg LectureThe University of Western Ontario21 March 2006
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An Outline
• The mystery and history of energy
• Thermodynamics: Not quite what we were taught it is, in unusual regimes
• Going beyond, to more efficient ways to use energy
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Easy Question: What is Energy?
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Easy Question? Oh, is it?
What is Energy?
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Can you say, tersely, what energy is?
• Energy is one of the most incredible concepts to emerge from the human mind
• Is it a discovery or an invention?
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Energy is an abstract concept that ties together a remarkable
range of dissimilar human experiences
• And does it in a way with astounding quantitative predictability!
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It seems an obvious concept, even to science students today
• But it wasn’t obvious at all for a long, long time
• Bacon, Galileo: heat is motion• Rumford: mechanical work
converts into heat• But is heat a fluid, “caloric,” or is
it matter in motion?
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Commonality of heat and light
• Scheele (1777) identified “radiant heat” to establish an equivalence between heat and light
• But he recognized two kinds of transfer, essentially radiation and convection
• Lavoisier & Laplace (1783): whether caloric or motion, there is a “conservation of heat”
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An indication of the problems: A controversy
• What is the ‘measure of motion’?• Is it mass x velocity, or
mass x (velocity)2 ?• This was the conflict between
the Leibnitzians and Cartesians• At that time, it was inconceivable
that both could be valid!
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How to account for heat that doesn’t change temperature• Recognize latent heats of phase
changes, and role of heat in changing densities
• Rumford: heat has no weight• Young: heat and light are related• Leslie (1804): distinguishes
conduction, convection and radiation and uses the term “energy” without defining it
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Fourier: Quantifies Heat
• Heat capacity
• Internal conductivity
• External conductivity (radiation, convection)
• Quantification of heat flow and transfer, with differential eqns.
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The Steam Engine: Watt
• The external condenser• The direct measure of pressure
as a function of volume, to determine efficiency (the Indicator Diagram, p vs. V)
• The use of high pressures and therefore of high temperatures
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Carnot: The Breakthrough, stimulated by applications
• Heat is ‘motive power’ that has changed its form
• “The quantity of motive power in nature is invariable”
• In effect, Energy is conserved!
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More from Carnot
• The invention of the reversible engine and the demonstration that it is the most efficient engine possible
• The determination of that maximum efficiency, and that no engine can do better
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Aha! Conservation of Energy!
• J. R. Mayer (1842-48) stated the principle explicitly, and included energy from gravitational acceleration
• Quantified the mechanical equivalent of heat
• Included living organisms
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Joule, of course! (1840’s,’50’s)
• Brought electromagnetic energy into the picture
• Measured mechanical equivalent of heat
• Showed that expansion of a gas into a vacuum does no work
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Creation of Thermodynamics
• Motivation: How little fuel must I burn, in order to pump the water out of my tin mine?
• Carnot confronted and solved this problem, but the great generalization came later
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The First Law• Two kinds of variables: State
variables, e.g. pressure p, volume V, temperature T
• Process variables, energy transferred either as heat Q, or as work W.
• The Law: the change of energy, E = Q – W, whatever the path
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This law states conservation of energy
• Whatever the path, only the end points determine the energy change
• If the final and initial states are the same, the energy of the system is unchanged
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The Second Law• The randomness--or entropy--or the
number of microstates the system can explore--never decreases spontaneously
• Decreasing entropy requires input of work
• Corollary: Max efficiency is (Thigh–Tlow)/Thigh
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The Third Law
• There is an absolute zero of temperature, 0o K or –273o C
• You can never get there; it is as unreachable as infinitely high temperature
• But we can now get pretty cold, as low as 10–8 o K
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Einstein: Thermodynamics is, among all sciences, the one most likely to be valid
• Hence we can think of thermodynamics as the epitome of general scientific law
• But we sometimes lose sight of what is truly general and what is applicable for only certain kinds of systems or conditions
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A common, elegant presentation
• Thermodynamics has two kinds of state variables:
• Intensive, independent of amount, e.g. Temperature, pressure
• Extensive, directly proportional to amount, e.g. mass, volume
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Also two kinds of relations
• General laws, the Laws of Thermodynamics
• Relations for specific systems, e.g. equations of state, such as the ideal gas law, pV = nRT, giving a third quantity if two are known (Remember that one?)
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Degrees of freedom• How many variables can we
control? For a pure substance, we can change three, e.g. pressure, temperature and amount of stuff
• Fix the amount and we can vary only two
• The equation of state tells us everything else
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But Equations of State are usually not simple
• The equation of state for steam, used daily by engineers concerned with real machines, requires several pages to write in the form they use it!
• Not at all like pV=nRT!
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Generalize to find optimal performances
• Thermodynamic Potentials are the quantities that tell us the most efficient possible energy use for specific kinds of processes, different potential for different processes
• All use the infinitely slow limit, as Carnot did, to do best
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Some jargon
• Names for some thermodynamic potentials are “free energy,” “availability,” “enthalpy,” “exergy,” and energy itself;
• The change in the appropriate potential is the minimum work we must do, or the maximum we can extract, for that process
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The subtle profundity of thermodynamics
• The Gibbs phase rule: relates the number of degrees of freedom, f, to the number of components c (kinds of stuff) and the number of phases present in equilibrium, p:
• f = c – p + 2, the simplest equation in thermodynamics, perhaps in all science
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A simple relation
• The amount of each component can be varied at will
• Each phase, e.g. liquid water, ice or water vapor, has its own equation of state, implying a constraint for each phase
• One substance, one phase, yields two degrees of freedom, as we saw
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Water vapor: any T or p is okay
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But look now, if there is liquid also:
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What’s profound about the Gibbs phase rule?
• The f comes by definition• The c is obviously our choice• The p is the number of constraints• Hence all these are easy and obvious
• It’s the 2 that is profound! Only experience with nature tells us what that number is!
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The real generality of thermodynamics
• Very big systems--galaxy clusters--and very small systems--atomic clusters--should all be describable by thermodynamics
• What’s the predominant energy of a galaxy cluster? Gravitation, of course
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What’s the gravitational energy of two objects?
• Inversely proportional to distance of the objects,
• Directly proportional to the product of their masses, m1 x m2 !
• This is not linear in the mass!• Astronomers created
nonextensive thermodynamics to deal with this.
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Another case where thermodynamics holds, but not as it’s usually taught
• Very small systems, e.g. nanoscale materials, composed of thousands or even just hundreds of atoms
• The distinction between component and phase can be lost, so the Gibbs phase rule loses meaning
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With very small systems,• Two phases may coexist over a
band of pressures and temperatures, not just along a single coexistence curve
• More than two phases can exist in equilibrium over a band of conditions
• Phase changes are gradual, not sharp
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Can we do thermodynamics away from equilibrium?
• Close to equilibrium, Lars Onsager showed a fine way to do it, back in the 1930’s
• Further away from equilibrium, one needs more variables to describe the system
• Can we guess what variables to use? Sometimes, not always
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Create a thermodynamics for processes that must
operate in finite time • We can, for many kinds of finite-time
processes, define quantities like traditional thermodynamic potentials, whose changes give the most efficient or effective possible use of the energy for those processes
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Finite-time potentials
• It is possible to define and evaluate these, for specific processes, to learn how well a process can possibly perform
• It is then possible to identify how, in practice, we can design processes to approach the limits that are those ‘best performances’
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Example: the automobile engine
• The gas-air mix burns, the heat expands the gas, driving the piston down, so the pistons go up and down
• The connecting rod links piston with driveshaft, changing up-down motion into rotation
• Does the piston, in an ordinary engine, follow the best path to maximize work or power? NO!
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So how can we do better?• Change the time path to make the
piston move fastest when the gas is at its highest temperature!
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Changing the mechanical link would improve performance
about 15% • Red: conventional time path of piston;
black: ideal, given a maximum piston speed
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One other example
• Distillation, a very energy-wasteful process
• But make the temperature profile along the column a control variable and the energy waste goes way down
• One such column is going up now, in Mexico
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So what have we seen?
• Energy is an amazing concept, subtle, powerful, elegant, general,
• Isn’t it incredible that we found it!
• Its quantitative, predictive power is perhaps the epitome of what science is about!
• It is important for all its aspects, from the most basic to the most practical and applied
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Thank you!