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Energy: Mysterious and Amazing, Conserved and Conserving

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Title: Energy: Mysterious and Amazing, Conserved and Conserving


1
Energy Mysterious and Amazing, Conserved and
Conserving
  • R. Stephen Berry
  • The University of Chicago
  • Nerenberg Lecture
  • The University of Western Ontario
  • 21 March 2006

2
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

3
Easy Question What is Energy?
4
Easy Question? Oh, is it? What is Energy?
5
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?

6
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!

7
It seems an obvious concept, even to science
students today
  • But it wasnt 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?

8
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

9
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!

10
How to account for heat that doesnt 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

11
Fourier Quantifies Heat
  • Heat capacity
  • Internal conductivity
  • External conductivity (radiation, convection)
  • Quantification of heat flow and transfer, with
    differential eqns.

12
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

13
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!

14
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

15
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

16
Joule, of course! (1840s,50s)
  • Brought electromagnetic energy into the picture
  • Measured mechanical equivalent of heat
  • Showed that expansion of a gas into a vacuum does
    no work

17
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

18
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

19
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

20
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
    (ThighTlow)/Thigh

21
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 108 o K

22
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

23
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

24
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?)

25
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

26
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 pVnRT!

27
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

28
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

29
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

30
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

31
Water vapor any T or p is okay
32
But look now, if there is liquid also
33
Whats 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
  • Its the 2 that is profound! Only experience with
    nature tells us what that number is!

34
The real generality of thermodynamics
  • Very big systems--galaxy clusters--and very small
    systems--atomic clusters--should all be
    describable by thermodynamics
  • Whats the predominant energy of a galaxy
    cluster? Gravitation, of course

35
Whats 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.

36
Another case where thermodynamics holds, but not
as its 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

37
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

38
Can we do thermodynamics away from equilibrium?
  • Close to equilibrium, Lars Onsager showed a fine
    way to do it, back in the 1930s
  • Further away from equilibrium, one needs more
    variables to describe the system
  • Can we guess what variables to use? Sometimes,
    not always

39
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

40
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

41
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!

42
So how can we do better?
  • Change the time path to make the piston move
    fastest when the gas is at its highest
    temperature!

43
Changing the mechanical link would improve
performance about 15
  • Red conventional time path of piston black
    ideal, given a maximum piston speed

44
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

45
So what have we seen?
  • Energy is an amazing concept, subtle, powerful,
    elegant, general,
  • Isnt 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

46
Thank you!
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