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

Energy: Mysterious and
Amazing, Conserved and
Conserving
R. Stephen Berry
The University of Chicago
Nerenberg Lecture
The University of Western Ontario
21 March 2006
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
Easy Question:
What is Energy?
Easy Question?
Oh, is it?
What is Energy?
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?
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!
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?
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”
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!
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
Fourier: Quantifies Heat
• Heat capacity
• Internal conductivity
• External conductivity (radiation,
convection)
• Quantification of heat flow and
transfer, with differential eqns.
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
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!
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
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
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
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
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
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
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
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
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
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
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?)
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
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!
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
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
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
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
Water vapor: any T or p is okay
But look now, if there is liquid
also:
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!
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
What’s the gravitational
energy of two objects?
• Inversely proportional to
distance of the objects,
• Directly proportional to the
product of their masses,
m 1 x m2 !
• This is not linear in the mass!
• Astronomers created
nonextensive thermodynamics
to deal with this.
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
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
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
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
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’
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!
So how can we do better?
• Change the time path to make the
piston move fastest when the gas is
at its highest temperature!
Changing the mechanical link
would improve performance
about 15%
• Red: conventional time path of piston;
black: ideal, given a maximum piston speed
One other example
• Distillation, a very energywasteful 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
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
Thank you!