Reflections on Real (Thermodynamic) Entropy, Disorder and

Report
Reflections on Real (Thermodynamic)
Entropy, Disorder and
Statistical Information Entropy – (Lecture IV)
Institute of Engineering Thermophysics
Tsinghua University
Beijing, China, June 20, 2013
Prof. M. Kostic
Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
www.kostic.niu.edu
Slide 1
Some Challenges in Thermoscience Research
and Application Potentials
Energy Ecology Economy
Tsinghua University, XJTU, and HUST
China 2013: Beijing, Xi’an, Wuhan, June 14-28, 2013
Prof. M. Kostic
Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
www.kostic.niu.edu
Slide 2
Hello:
Thank you for the opportunity
to present a holistic, phenomenological
reasoning of some challenging issues
in Thermo-science.
Discussions are informal and not finalized yet.
Thus, respectful, open-minded arguments, and
brainstorming are desired for better
comprehension of tacit and often elusive
thermal phenomena.
www.kostic.niu.edu
3
Slide 3
Among distinguished invites were five keynote
speakers from China and seven international
keynote speakers: three from the USA and one
each from Japan, United Kingdom, Singapore,
and Spain; including four Academicians and
six university Presidents/vice-presidents.
It has been my great pleasure and
honor to meet Prof. ZY Guo and
other distinguished colleagues,
and even more so to visit
again and meet friends now!
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Slide 4
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Slide 5
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Slide 6
Qcal=Qrev+Wloss=Qrev+Qdiss
Entropy, the thermal displacement
property, dS=dQrev/T (or dQcal/T) with J/K unit,
is “a measure” of thermal dynamic-disorder
or thermal randomness, and may be expressed as
being related to logarithm of number of “all
thermal, dynamic-microstates”, or to their
logarithmic-probability or uncertainty, that
corresponds, or are consistent with the given
thermodynamic macrostate. Note that the
meanings of all relevant adjectives are deeply
important to reflect reality and as such it has
metaphoric description for real systems.
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Slide 7
Persistent misconceptions:
Persistent misconceptions existing for many years in
different fields of science. They are sometimes
encountered in the scientific and especially, the
popular-science literature.
The Entropy (2nd) Law misconceptions are:
1. The first misconception:
Entropy is a measure of any disorder.
2. The second misconception:
Entropy (2nd) Law is valid only for closed systems.
3. The third misconception:
Entropy (2nd) Law is valid for inanimate,
not for living (animate) systems.
© M. Kostic
2009 January 10-12
Slide 8
The Boltzmann constant is a
dimensionless conversion factor:
Temperature is (random kinetic) thermal-energy of a representative (microthermal) particle (with Boltzmann constant being the conversion factor between
micro-thermal energy and macro-temperature),
… thus entropy is ratio between macro (multi-particle) thermal energy and a
representative particle thermal-energy, thus dimensionless. For average
(representative) thermal- particle, the unit for the Boltzmann constant, kB, is:
 =
ℎ  [/particle]
_
   []
_
_
ℎ 
=
_


  
_
= [J/(K particle)]
=[J/J]=[1]
_
The thermal-energy used for entropy is without its ‘useful’ part or work potential, thus
include pressure-volume influence. In that regard, a single particle entropy without
thermal-interactions is zero (no random-thermal motion), but also infinity (as if in
infinite volume, taking forever to thermally interact).
© M. Kostic
2009 January 10-12
Slide 9
2
…thus thermal & mechanical
energies are coupled
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Slide 10
Importance of Sadi Carnot's treatise of reversible heatengine cycles for Entropy and the 2nd Law definitions:
Carnot's ingenious reasoning of limiting, reversible engine
cycles allowed others to prove that entropy is conserved
in ideal cycles (Clausius Equality - definition of
entropy), that entropy cannot be destroyed since it will
imply supper-ideal cycles, more efficient than reversible
ones, but is always irreversibly generated (overall
increased) due to dissipation of any work potential to
heat (Clausius Inequality) in irreversible cycles.
These are easily expanded for all reversible and
irreversible processes and generalization of the 2nd Law of
Thermodynamics.
www.kostic.niu.edu
Slide 11
Thermal energy versus Internal energy
concepts in Thermodynamics:
The entropy is related to internal thermal energy
(obvious for incompressible substances), but is
more subtle for compressible gases due to
coupling of internal thermal energy (transferred as
heat TdS) and internal elastic-mechanical energy
(transferred as work PdV). Entropy is NOT related
to any other internal energy type, but thermal
(unless the former is converted/dissipated to
thermal in a process).
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Slide 12
Disorder versus Spreading/Dispersal as
statistical metaphorical-concepts of entropy:
The three terms are qualitative and metaphorical
concepts related to each other and have to relate to the
random, complex thermal motion and complex thermal
interactions of material structure, like its thermal heat
capacity and temperature, among others.
Only for simple ideal gases (with all internal energy
consisting of random thermal motion and elastic
collisions), entropy could be correlated with statistical and
probabilistic modeling, but has to be and is measured for
any and all real substances (regardless of its structure)
as phenomenologically defined by Clausius
(dS=dQrev/Tabs). Thus entropy and the Second Law are
well defined in classical Thermodynamics
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Slide 13
Disorder versus Spreading/Dispersal as
statistical metaphorical-concepts of entropy:
The simplified simulations (analytical, statistical,
numerical, etc.) should not take precedence over
phenomenological reality and reliable observations, but to
the contrary:
Substance is more important than formalism!
‘Extreme’ judgments based on simulations are usually
risky, particularly if detached from reality-checks or with
attempt to suppress reality.
www.kostic.niu.edu
Slide 14
A system form and/or functional
order/disorder:
A system form and/or function related order or disorder is
not thermal-energy order/disorder, and the former is not
the latter, thus not related to Thermodynamic entropy.
Entropy is always generated (due to ‘energy dissipation’)
during production of form/function order or disorder,
including information, i.e., during any process of creating
or destroying, i.e., transforming any material structure.
Expanding entropy to any disorder type or information is
unjustified, misleading and plain wrong.
www.kostic.niu.edu
Slide 15
Disorder versus Spreading/Dispersal as
statistical metaphorical-concepts of entropy:
There is a "strange propensity” of some authors involved
with simplified statistical interpretation of complex, random
natural phenomena, to make unjustified statements that
their analyses are true descriptions of natural phenomena
and that the phenomenological definitions are deficient
and misleading, or even worse, that the natural
phenomena are a subset of more general statistical
theory, for example, that information entropy is more
general than thermodynamic entropy, the latter being a
subset of the former. For example, some “promoters” of
statistical descriptions of entropy become so detached
from physical reality as if not aware of the reality.
www.kostic.niu.edu
Slide 16
Entropy and Disorder …
S=S(T,V) not of other type of disorder:
If Tleft=Tright and Vleft=Vright  Sleft=Sright
Entropy refers to dynamic thermal-disorder of its micro
structure (which give rise to temperature, heat capacity, entropy
and thermal energy. It does not refer to form-nor functionaldisorder of macro-structure: For example, the same
ordered or piled bricks (see above) at the same temperature
have the same entropy (the same Thermodynamic state)!
www.kostic.niu.edu
Slide 17
Disorder versus Spreading/Dispersal as
statistical metaphorical-concepts of entropy:
Since entropy is directly related to the random thermal
motion of a system micro (atomic and molecular)
structure, it is suitable to statistical analysis, particularly
of simple system structures, like ideal gases, consisting of
completely randomized particle motion in thermal
equilibrium, without any other particle interactions, but
elastic, random collisions of material point-like particles.
For more complex, thus all real systems, the thermal
motion and interactions are much more complex, thus the
statistical analysis is metaphorical only and cannot be
quantitatively reduced to physical entropy, the latter welldefined and measured in laboratory for all substances
of practical interest.
www.kostic.niu.edu
Slide 18
Entropy Generation (Production)
Sgen
Entropy Generation (Production) is always irreversible in
one direction only, occurring during a process within a system
and stored as entropy property. Entropy cannot be destroyed
under any circumstances, since it will imply spontaneous
heat transfer from lower to higher temperature, or imply higher
efficiency than the ideal Carnot cycle engine
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Slide 19
Dissecting The Second Law of Thermodynamics:
It Could Be Challenged But Not Violated
Carnot
Clausius
1824
Heat Engine
Reversibility
Kelvin-Planck
1850 NO Heat
from cold to hot
1865 Entropy
1848 Abs. Temperature
1865 NO Work
from single reservoir
Gibbs
1870’s Entropy,
Chem.Potential
Phys.Chemistry
… with some updates
Presented at:
Royal Institute of Technology - KTH
KTH Department of Energy Technology, Stockholm, Sweden, 22 May 2012
Prof. M. Kostic
Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
www.kostic.niu.edu
Slide 20
Sadi Carnot’s far-reaching treatise of heat
engines was not noticed at his time
and even not fully recognized nowadays
In 1824 Carnot gave a full and
accurate reasoning of heat engine
limitations almost two decades
before equivalency between work
and heat was experimentally
established by Joules in 1843
Sadi Carnot laid ingenious foundations for the Second
Law of Thermodynamics before the Fist Law of energy
conservation was known and long before Thermodynamic
concepts were established.
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Slide 21
Fig. 1: Similarity between an ideal
heat engine (HE) and a water wheel (WW)
(instead oh heat, entropy is conserved).
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Slide 22
Carnot Efficiency …
W  W netOUT  Q IN  f c (T H , T L )
 Ct 
W netOUT
Q IN
 f c (T H , T L )
 

Max
Qualitativ e function
Rev .
“The motive power of heat is independent of the
agents employed to realize it; its quantity is fired
solely by the temperatures of the bodies between
which is effected, finally, the transfer of the caloric.”
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Slide 23
Fig. 2: Heat-engine ideal Carnot cycle:
Note thermal and mechanical expansions and compressions
(the former is needed for net-work out, while the latter is needed to
provide reversible heat transfer).
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Slide 24
Q H , Q L , W C 


 Q H ,  Q L , W C 
(2)
IF REVERESED
Fig. 3: Reversible Heat-engine (solid lines) and Refrigeration Carnot
cycle (dashed lines, reversed directions).
Note, WH =WL=0 if heat transfer with phase change (compare Fig.2).
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Slide 25
Q (T1|T
Any
)
Q (T 2 | H )
T=TAny
`

Q Ref  f (T1|T
Any
)
Q Ref  f (T 2 | H )

f (T1 )
f (T 2 )

f (T )   T
T1
T2

Q 1|T
Any
Q 2|H
The Carnot ratio equality
above , is much more important
than what it appears at first.
Actually it is probably
the most important equation in
Thermodynamics and among the
most important equations in natural
sciences.
Fig. 5: For a fixed TH, TRref, QH, and QRef, the Q(T) is proportional to QRef
(efficiency is intensive property) and an increasing (positive) function of T
for a given TRef (thus absolute temperature).
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Slide 26
“Definition” of Temperature, Mass, etc…
Q (T1 )
Q (T 2 )

Q Ref  f (T1 )
Q Ref  f (T 2 )



d
F 
f ( m )V
dt

f (T1 )
f (T 2 )


f ( T )   T

f ( m ) m
d
dt
T1 , A ny
T 2 , Ref

mV



Q 1 , A ny
 f (T )  T
Q 2 , Ref
 f (m )  m
The Carnot
ratio equality above , defines Temperature vs. Heat-flux
correlation, the way the Newton Law defines Force vs. Momentum-flux
correlation. The two simplest non-zero positive-definite functionals are
chosen, however the others are also possible. Similarly, the Einstein’s
theory of relativity concept could have been correlated with similar, but
different functional, resulting to similar and equally coherent theory!
www.kostic.niu.edu
Slide 27
Clausius (In)Equality
W

dQ
T
Irr
Irr
   Q Irr  
  Q
Rev
 W Rev

 dQ

dQ
  
 0  or 
  S Gen  0
T Re v
T   
 


  

Any Cycle
Eq . ( 10 )


Clausius Inequality
dQ
 S Gen  0
 T  
Any Cycle
Clausius Inequality
Note :
S Gen ( Cycle )  S out  S in  0 , but  S cycle   S in  S Gen   S out  0
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( any cycle )
Slide 28
Fig. 7: Heat engine ideal Carnot cycle between two different temperature heat-reservoirs (TH>TL and W>0)
(left), and with a single temperature heat-reservoirs (TH=TL and W=0, ideal reversible cycle) (right).
Low-temperature thermal compression is needed (critical), not the mechanical (isentropic)
compression, to realize work potential between the two different temperature heat-reservoirs,
due to internal thermal energy transfer via heat (W=QH-QL>0). The isentropic expansion and
compression are needed to provide temperature for reversible heat transfer, while net thermal expansioncompression provides for the net-work out of the cycle.
www.kostic.niu.edu
Slide 29
Therefore, …
... the so called
“waste cooling-heat” in power cycles
(like in thermal power plants)
is not waste but very useful heat,
necessary for thermal compression of cycling
medium (steam-into-condensate, for example),
without which it will not be possible to
produce mechanical work from heat
(i.e., from thermal energy).
www.kostic.niu.edu
Slide 30
Fig. 8: Significance of the Carnot’s
reasoning of reversible cycles is in many
ways comparable with the Einstein’s relativity
theory in modern times. The Carnot Ratio
Equality is much more important than what it
appears at first. It is probably
the most important equation in
Thermodynamics and among the most
important equations in natural
sciences.
www.kostic.niu.edu
Slide 31
Heat Transfer Is Unique and Universal:
 Heat transfer is a spontaneous irreversible process where all
organized (structural) energies are disorganized or dissipated
as thermal energy with irreversible loss of energy potential
(from high to low temperature) and overall entropy increase.
Thus, heat transfer and thermal energy are
unique and universal manifestation of all natural
and artificial (man-made) processes,
… and thus … are vital for more efficient cooling and heating
in new and critical applications, including energy production
and utilization, environmental control and cleanup, and biomedical applications.
© M. Kostic
2009 January 10-12
Slide 32
REVERSIBILITY AND
IRREVERSIBILITY:
ENERGY TRANSFER AND DISORGANIZATION,
RATE AND TIME, AND ENTROPY GENERATION
Net-energy transfer is in one direction only, from higher
to lower potential (energy-forcing-potential), and the
process cannot be reversed.
Thus all real processes are irreversible in the direction
of decreasing energy-forcing-potential, like pressure and
temperature (forced displacement of mass-energy)
© M. Kostic
2009 January 10-12
Slide 33
Quasi-equilibrium Process :
in limit, energy transfer process with infinitesimal potential
difference (still from higher to infinitesimally lower
potential, P).
Then, if infinitesimal change of potential difference direction
is reversed
P+dP → P-dP
with infinitesimally small external energy, since dP→0,
the process will be reversed too, which is characterized
with infinitesimal entropy generation,
and in limit, without energy degradation (no further energy
disorganization) and no entropy generation
thus achieving a limiting reversible process.
© M. Kostic
2009 January 10-12
Slide 34
Local-Instant & Quasi-Equilibrium:
At instant (frozen) time, a locality around a point in space
may be considered as ‘instant-local equilibrium’
(including inertial forces) with instantaneous localproperties well-defined, regardless of non- uniformity.
Quasi-equilibrium is due to very small energy fluxes due
to very small gradients and/or very high impedances,
so that changes are infinitely slow, for all practical
purposes appearing as equilibrium with virtually netzero energy exchange.
© M. Kostic
2009 January 10-12
Slide 35
REVERSIBILITY –Relativity of Time:
Therefore, the changes are ‘fully reversible,’ and along with
their rate of change and time, totally irrelevant (no
irreversible-permanent change), as if nothing is
effectively changing (no permanent-effect to the
surroundings or universe)
The time is irrelevant as if it does not exist, since it could
be reversed or forwarded at will and at no ‘cost’ (no
permanent change) and, thus, relativity of time.
Real time cannot be reversed,
it is a measure of permanent changes, like irreversibility, which is
in turn measured by entropy generation.
In this regard the time and entropy generation of the universe have to
be related.
© M. Kostic
2009 January 10-12
Slide 36
The 2nd Law Definition …
Non-equilibrium cannot be spontaneously created.
All natural spontaneous, or over-all processes (proceeding
by itself and without interaction with the rest of the
surroundings) between systems in non-equilibrium have
irreversible, forced tendency towards common
equilibrium and thus irreversible loss of the original work
potential (measure of non-equilibrium), by converting
(dissipating) other energy forms into the thermal energy (and
degrading the latter to lower temperature) accompanied with
increase of entropy (randomized equi-partition of energy
per absolute temperature level).
The 2nd Law is more than thermo-mechanical (heat-work)
energy conversion, but about energy processes in general:
Forcing due to non-equilibrium has tendency towards equilibrium.
www.kostic.niu.edu
Slide 37
The 2nd Law “Short” Definition:
• The useful-energy (non-equilibrium work
potential) cannot be created from within
equilibrium alone or otherwise, it only can be
forcefully transferred between systems
(ideally conserved) and irreversibly dissipated
towards equilibrium into thermal energy
thus generating entropy.
The 2nd Law is more than thermo-mechanical (heat-work)
energy conversion, but about energy processes in general:
Forcing due to non-equilibrium has tendency towards equilibrium.
Force or Forcing is a process of exchanging useful-energy
(forced displacement) with net-zero exchange at forced equilibrium.
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Slide 38
Issues and Confusions …
• There are many puzzling issues surrounding the Second
Law and other concepts in Thermodynamics, including
subtle definitions and ambiguous meaning of very
fundamental concepts.
• Further confusions are produced by attempts to
generalize some of those concepts with similar but not
the same concepts in other disciplines, like
Thermodynamic entropy versus other types of (quasi &
statistical) entropies.
Thermodynamic ENTROPY [J/K] is related to thermal energy transfer &
generation per absolute temperature; it is a physical concept not a statistical
construct (which is only a limited ‘description’ tool) as argued by some.
www.kostic.niu.edu
Slide 39
Local Creation of Non-equilibrium …
… It should not be confused with local
increase/decrease of non-equilibrium and/or
‘organized structures’ on expense of ‘over-all’
non-equilibrium transferred from elsewhere. Nonequilibrium is always “destroyed” by spontaneous
and irreversible conversion (dissipation) of other
energy forms into the thermal energy, always and
everywhere accompanied with entropy generation.
(randomized
of energy per absolute
 W 
 S
  Q equi-partition
 

 0 , local entropy generation rate


temperature
 t  m  t T  level).
m  K  kg 
Gen
Over - all entropy increases without exception
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on any time and space scales
Slide 40
Definition of Entropy
"Entropy is ‘an integral measure’ of (random) thermal
energy redistribution (stored as property, due to heat transfer
or irreversible heat generation) within a system mass and/or
space (during system expansion), per absolute temperature
level. Entropy is increasing from orderly crystalline structure
at zero absolute temperature (zero reference) during
reversible heating (entropy transfer) and entropy generation
during irreversible energy conversion, i.e. energy
degradation or random equi-partition within system material
structure and space." (by M. Kostic)
Thermodynamic ENTROPY [J/K]
is THE specific thermo-physical concept,
NOT a statistical concept, i.e., the S=k log(W) is ONLY a
SIMPLIFIED/very-limited ‘construct’ not to be extrapolated …
© M. Kostic
2009 January 10-12
Slide 41
Entropy …
… entropy of a system for a given state is
the same, regardless whether it is reached by reversible
heat transfer or irreversible heat or irreversible work
transfer (entropy is a state function, while entropy generation is
process dependent). Once generated it cannot be destroyed
(irreversible change), but transferred only.
dS 
Q

 Q rev   Q gen
T
or
T
S 

Q
T
 S ref
However, the source entropy will decrease to a smaller
extent over higher potential, thus resulting in overall
entropy generation for the two interacting systems.
Note :  Q Irr   Q gen   W Loss
 W Loss(W) ( i.e., V ol  Punristr. | throtll. )

 
  W Loss(Q )  S Area dT Irr  T ref  S gen (Vol)
Irr
© M. Kostic
2009 January 10-12
Slide 42
Note :
Q Irr  Q Gen   W Loss  T Ref S Gen ( any )
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Slide 43
… Entropy …
We could consider a system internal thermal energy
and entropy, as being accumulated from absolute
zero level, by disorganization of organized/structural
or higher level energy potential with the
corresponding entropy generation.
Thus entropy as system property is associated with
its thermal energy and temperature.
(but also space, since mechanical & thermal energies are
coupled and equi-partitioned for I.G. (PV=NkBT): unrestricted
expansion is work-potential loss to thermal energy, as is the
heat-transfer at finite temperature difference).
…thus thermal & mechanical
energies are coupled
© M. Kostic
2009 January 10-12
Slide 44
Entropy Summary
Thus, entropy transfer is
due to reversible heat transfer and could be ether
positive or negative (thus entropy is over-all
conserved while reversibly transferred).
However, entropy generation is always positive
and always due to irreversibility. Thus entropy
is Over-ALL increased (The Second Law):
  Q Gen  W 
 


  0 , local entropy generation
 t  m  t T  m  K  kg 
 S
rate
Witho ut exception
for all time and space scales
  

J 


ΔS Over ALL
 ΔS Rev. Tr . ALL  S Gen       dm dt  0
 K   

t  m

 
conserved (  0 )
Over - all change
ALL
© M. Kostic
2009 January 10-12
Slide 45
“The Second Law
of Thermodynamics
is considered one of the central laws of science,
engineering and technology.
For over a century it has been assumed to be
inviolable by the scientific community.
Over the last 10-20 years, however, more than two
dozen challenges to it have appeared in the
physical literature - more than during any other
period in its 150-year history.”
Second Law Conference: Status and Challenges
with Prof. Sheehan in Sun Diego, CA June 2011
Slide 46
© M. Kostic <www.kostic.niu.edu>
The Second Law Symposium has been a unique
gathering of the unorthodox physicist and
inventors (to avoid using a stronger word)
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Slide 47
Living and Complex Systems
Many creationists (including evolutionists and information scientists)
make claims that evolution violates the Second Law.
Although biological and some other systems may and do
create local non-equilibrium and order (BUT only on expense of
elsewhere!), the net change in entropy for all involved
systems is positive (due to its unavoidable irreversible local
generation) and conforms to the Laws of Nature and the
Second Law for non-equilibrium open systems.
It may appear that the created non-equilibrium structures are self-organizing
from nowhere, from within an equilibrium (thus violating the 2nd Law), due to
the lack of proper observations and ‘accounting’ of all mass-energy flows, the
latter maybe in ‘stealth’ form or undetected rate at our state of technology and
comprehension (as the science history has though us many times).
www.kostic.niu.edu
Slide 56
Crystal ‘self-formation’…
It may appear that the created
non-equilibrium structures are
self-organizing from nowhere, from
within an equilibrium (thus violating
the 2nd Law), due to the lack of proper
‘observations’ at our state of
technology and comprehension
(as the science history has though us
many times).
… and Plant Cells growth
www.kostic.niu.edu
Slide 57
Nature often defy our intuition
• Without friction, clock will not work, you could not walk, birds
could not fly, and fish could not swim.
• Friction can make the flow go faster
• Roughening the surface can decrease drag
• Adding heat to a flow may lower its temperature, and removing
heat from a flow may raise its temperature
• Infinitesimally small causes can have large effects (tipping
point)
• Symmetric problems may have non-symmetric solutions
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Slide 58
YES! Miracles are possible !
It may look ‘perpetuum mobile’ but miracles are real too …
Things and Events are both, MORE but also LESS complex
than how they appear and we ‘see’ them -- it is
natural simplicity in real complexity
… we could not comprehend energy conservation
until 1850s:
(mechanical energy was escaping “without being noticed how”)
… we may not comprehend now new energy conversions
and wrongly believe they are not possible:
(“cold fusion” seems impossible for now … ?)
…….Let us keep our eyes
and our minds ‘open’ ………..
www.kostic.niu.edu
Slide 59
YES! Miracles are possible !
… but there is NO
ideal ‘Things and Events’ …
‘Things and Events’ are both, MORE but also LESS complex
than how they appear and we ‘see’ them:
it is natural
simplicity in real complexity
no ideal things
… there are
, no ideal rigid body, no ideal gas,
no perfect elasticity, no adiabatic boundary, no frictionless/reversible process,
no perfect equilibrium, not a steady-state process …
always processes
… there are
- energy in transfer or motion,
all things/everything ARE energy in motion with unavoidable
process irreversibilities, however, in limit, an infinitesimally slow
process with negligible irreversibility ‘appears’ as instant reversible equilibrium –
thus,
everything is relative with regard to different space and time scales
….Let us keep our eyes
and our minds ‘open’ ………..
www.kostic.niu.edu
Slide 60
All processes are transient …
All processes are transient (work and heat transfer, and
entropy production, in time) and degradive/dissipative,
even Eulerian steady-state processes (space-wise) are
transient in Lagrangian form (system-wise, from input to
output),
… but equilibrium processes and even quasi-static (better,
quasi-equilibrium) processes are sustainable/reversible.
The existence in space and transformations in time are manifestations
of perpetual mass-energy forced displacement processes: with net-zero
mass-energy transfer in equilibrium (equilibrium process) and non-zero
mass-energy transfer in non-equilibrium (active process) towards
equilibrium.
© M. Kostic
2009 January 10-12
Slide 61
If we are unable to observe …
• If we are unable to measure something it does not mean
it does not exist (it could be sensed or measured with
more precise instruments or in a longer time scale, or in
similar stronger processes (mc2 always!, but often not
measurable).
• So called "self-organizing" appear as entropy increasing
processes, since we are unable to comprehend or to
observe/measure entropy change within or of affecting
boundary environment, for such open processes.
The miracles are until they are comprehended and understood!
© M. Kostic
2009 January 10-12
Slide 62
Simulation and Reality …
• Entropy is a measure of thermal-energy
metaphorical-disorder (with ‘strings’ attached),
not a measure of any-form disorder.
• Einstein is quoted as satted:
“Since mathematicians explained ‘Theory of
Relativity’, I do not understand it any more.”
• Similarly, after statisticians explained ‘Entropy’
I do not understand it any more.
www.kostic.niu.edu
Slide 63
Statistical Interpretation Is
Important as Metaphoric Only
• Again, a statistical interpretation is important as
metaphoric only: The sum of the probabilities
of possible discrete microstates, pi's, that could
occur during the "random fluctuations" of a given
macro-state. The adjective, possible, could
occur, consistent random fluctuations (thus
thermal), and the holistic of the statement have
deep meanings, and could not be evaluated for
any real system, but only scaled for the trivial
one(s).
www.kostic.niu.edu
Slide 64
Granted, there are
some benefits, BUT …
Granted, there are some benefits from simplified statistical
descriptions to better understand the randomness of thermal
motion and related physical quantities, but the limitations
should be stated so the real physics would not be
overlooked, or worse discredited. The phenomenological
thermodynamics has the supremacy due to logical
reasoning based on the fundamental laws and without the
regard to the system complex dynamic structure and even
more complex interactions. The fundamental laws and
physical phenomena could not be caused and governed
by mathematical modeling and calculation outcomes as
suggested by some, but the other way around.
www.kostic.niu.edu
Slide 65
Thank you! Any Questions ?
www.kostic.niu.edu
Slide 66
Appendices
Stretching the mind further …
www.kostic.niu.edu
Slide 67
Entropy Logarithmic Law:
• dS=CthdT/T then S-Sref=Cth*ln(T/Tref), i.e.
proportional to T or thermal motion, or W, number
of thermal microstates (depends on thermal
motion) that are consistent/correspond to a
macrostate.
• Many other processes/phenomena are governed
by CdX/X and thus Logarithmic Law.
• The Cth is thermal capacity of any reversible
heating process or isochoric thermal capacity Cv
otherwise
www.kostic.niu.edu
Slide 68
Entropy and Random Thermal Motion
• Since entropy is directly related to the random
thermal motion of a system micro (atomic and
molecular) structure, it is suitable to statistical
analysis, particularly of simple system structures, like
ideal gases, consisting of completely randomized particle
motion in thermal equilibrium, without any other particle
interactions, but elastic, random collisions of material
point-like particles. For more complex, thus all real
systems, the thermal motion and interactions are much
more complex, thus the statistical analysis is
metaphorical only and cannot be quantitatively reduced
to physical entropy, the latter well-defined and measured
in laboratory for all substances of practical interest.
www.kostic.niu.edu
Slide 69
Just because we could scale entropy …
• Just because we could scale entropy using a statistical
description of statistically random thermal motion of
simple system particulate structure, the latter related to
both, the thermal energy and thermodynamic
temperature, thus entropy, it does not mean that
entropy is a simple statistical concept and not physical
quantity of its own right. Actually, the statistical
representation is so simple and so limited, that without
knowing the result upfront, the scaling would be
impossible but for trivially simple and fully randomized
mono-atomic ideal gas structure.
www.kostic.niu.edu
Slide 70
statistical analysis is ‘going so far’
• The interpretation of the statistical analysis is
going so far as to forget about the phenomena
it is trying to describe, and presenting it as
spatial particle arrangement, and or simplified
statistics of position and momenta of particles
without other realistic interactions. As if entropy
is a measure of statistical randomness without
reference to thermal energy, or reference to
energy in general, both physically inappropriate!
www.kostic.niu.edu
Slide 71
The real entropy, as defined and measured
The real entropy, as defined and measured, is related to the
thermal energy and thermodynamic temperature, dS=dQ/T, not
others internal energies. The Boltzmann's metaphorical entropy
description, S=k*log(W), refers to a logarithmic measure of the
number of possible microscopic states (or microstates), W, of a
system in thermodynamic equilibrium, consistent with its
macroscopic entropy state (thus ‘equivalent’ number of thermal,
dynamic microstates). This is really far-fetched qualitative
description that transfers all real complexity to W (number of
relevant thermal, dynamic microstates) with deep meaning of
relevant adjectives: equivalent number of microstates consistent
with the well-defined macro-state.
www.kostic.niu.edu
Slide 72
not a number of all possible
spatial distributions
• This is not a number of all possible spatial distributions
of micro-particles within the system volume as often
graphically depicted.
• For example, the microstates with all molecules in one
half or one quarter of system volume and similar are
inappropriate to count, since they are not consistent
with the macrostate, nor physically possible to selfforce all molecules in one half volume with vacuum in the
other half. That would be quite different macrostate with
virtually null probability (not equi-probable)!
www.kostic.niu.edu
Slide 73
Randomness is Statistical
The microstate of a very simple, ideal system could be
described by the positions and momenta of all the atoms.
In principle, all the physical properties of the system are
determined by its microstate. The Gibbs or von Neumann
quantum or Shanon or other probabilistic entropy
descriptions are also statistical as Boltzmann's.
Actually they all reduce to the latter for fully randomized
large system in equilibrium, since the logarithmic probability
of all discrete microstates, where, equiprobable pi=1/W,
result in the Boltzmann's logarithmic value, i.e.:
-Sum(pi*log(pi)=log(W)
www.kostic.niu.edu
Slide 74
Statistical Interpretation Is
Important as Metaphoric Only
• Again, a statistical interpretation is important as
metaphoric only: The sum of the probabilities
of possible discrete microstates, pi's, that could
occur during the "random fluctuations" of a given
macro-state. The adjective, possible, could
occur, consistent random fluctuations (thus
thermal), and the holistic of the statement have
deep meanings, and could not be evaluated for
any real system, but only scaled for the trivial
one(s).
www.kostic.niu.edu
Slide 75
Granted, there are
some benefits, BUT …
Granted, there are some benefits from simplified statistical
descriptions to better understand the randomness of thermal
motion and related physical quantities, but the limitations
should be stated so the real physics would not be
overlooked, or worse discredited. The phenomenological
thermodynamics has the supremacy due to logical
reasoning based on the fundamental laws and without the
regard to the system complex dynamic structure and even
more complex interactions. The fundamental laws and
physical phenomena could not be caused and governed
by mathematical modeling and calculation outcomes as
suggested by some, but the other way around.
www.kostic.niu.edu
Slide 76
U,T & S are subtle and elusive,
but …
• The energy, temperature and entropy are subtle
and elusive, but well-defined and precisely
measured as physical quantities, and used as
such. They should be further refined and
explained for what they are and not be
misrepresented as something they are not. Any
new approach should be correlated with existing
knowledge, and limitations clearly and
objectively presented.
www.kostic.niu.edu
Slide 77
To repeat again …
Qcal=Qrev+Wloss=Qrev+Qdiss
Entropy, the thermal displacement
property, dS=dQrev/T (or dQcal/T) with J/K unit,
is a measure of thermal dynamic-disorder or
thermal randomness, and may be expressed as
being related to logarithm of number of “all
thermal, dynamic-microstates”, or to their
logarithmic-probability or uncertainty, that
corresponds, or are consistent with the given
thermodynamic macrostate. Note that the
meanings of all relevant adjectives are deeply
important to reflect reality and as such it has
metaphoric description for real systems.
www.kostic.niu.edu
Slide 78
Thank you! Any Questions ?
www.kostic.niu.edu
Slide 79

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