Slide 1 www.kostic.niu.edu Reflections on Thermal Energy,
Reversible and Caloric Processes, Exergy and Entransy (Lecture II)
Prof. M. Kostic Mechanical Engineering NORTHERN ILLINOIS UNIVERSITY
Institute of Engineering Thermophysics Tsinghua University Tsinghua
University Beijing, China, June 18, 2013 Beijing, China, June 18,
2013
Slide 2
Slide 2 www.kostic.niu.edu Some Challenges in Thermoscience
Research and Application Potentials Energy Ecology Economy Prof. M.
Kostic Mechanical Engineering NORTHERN ILLINOIS UNIVERSITY Tsinghua
University, XJTU, and HUST China 2013: Beijing, Xian, Wuhan, June
14-28, 2013
Slide 3
Slide 3 www.kostic.niu.edu 3 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.
Slide 4
Slide 4 www.kostic.niu.edu 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.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,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!and even more so to visit again and meet
friends now!
Slide 5
Slide 5 www.kostic.niu.edu
Slide 6
Slide 6 www.kostic.niu.edu
Slide 7
Slide 7 www.kostic.niu.edu What is Energy ? If one could expel
all energy out of a physical system then empty, nothing will be
left If one could expel all energy out of a physical system then
empty, nothing will be left so ENERGY is EVERYTHING E=mc 2 so
ENERGY is EVERYTHING E=mc 2 Mass (m) and energy (E) are
manifestation of each other and are equivalent; they have a
holistic meaning of mass-energy More important than what it appears
to beMore important than what it appears to be
Slide 8
Slide 8 www.kostic.niu.edu What is Energy ? From the Sovereign
Sun to the deluge of photons out of the astounding compaction and
increase of power-density in computer chips From the Sovereign Sun
to the deluge of photons out of the astounding compaction and
increase of power-density in computer chips Mass-Energy represents
motion of a system structure, i.e., its representative particles at
different space and time scales, and ultimately motion of photons.
Where the Thermal Energy fits in?
Slide 9
Slide 9 Energy Carriers & Underlying Energy Carriers
Fundamental or Underlying energy carriers are the FOUR fundamental
forces/interactions (and related particles) in physics: 1.Strong
nuclear 2.Weak nuclear 3.Electro-magnetic (EM), and 4.Gravitational
Underlying carriers for electro-chemical and thermo-mechanical
energy are photons (EM), And massive (convective) carriers may be
electrons (or electron shells) and bulk matter, including crystal
shell (phonons) www.kostic.niu.edu
Slide 10
Slide 10 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. 2009 January 10-12 M.
Kostic 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
bio- medical applications.
Slide 12 Heat Is Transfer of Thermal Energy Philosophically,
you cannot transfer something that does not exist. For example, you
cannot transfer water unless you have water. You cannot transfer
energy (type) without having it somewhere (stored) to transfer and
store it somewhere else. In the process (while transferring) you
may convert/reprocess (modify the "original structure") while
conserving the underlying substructure (true elementary particles):
existential conservationism. Some deny existence of thermal energy.
It is the same as denying existence of its (heat) transfer! 041115
M. Kostic thus Q=U in_transfer
Slide 13
Slide 13 Interchangeability of heat and work? heatworkheatwork
I have reservation about accuracy of "Heat and Work Example" and
Thermal Energy in: http:// hyperphysics.
phy-astr.gsu.edu/hbase/thermo/heat.htmlI have reservation about
accuracy of "Heat and Work Example" and Thermal Energy in: http://
hyperphysics. phy-astr.gsu.edu/hbase/thermo/heat.html http://
hyperphysics. phy-astr.gsu.edu/hbase/thermo/heat.html http://
hyperphysics. phy-astr.gsu.edu/hbase/thermo/heat.html "This example
of the interchangeability of heat and work as agents for adding
energy to a system can help to dispel some misconceptions about
heat."This example of the interchangeability of heat and work as
agents for adding energy to a system can help to dispel some
misconceptions about heat.heatworkheatwork ? ? ?
www.kostic.niu.edu
Slide 14
Slide 14 Useful Energy: Work potential, Exergy (and Entransy)
concept(s) Two systems in non-equilibrium have potential of
extracting work (useful energy). The maximum work potential is if
they are reversibly brought to mutual equilibrium while the work is
extracted (thus re-arranging the non- equilibrium: entropy is
conserved, thus over-all isentropic), otherwise part or in-whole
that work potential (i.e., non-equilibrium) will dissipate via heat
to thermal energy and generate entropy. If one system is fixed (an
infinite thermal reservoir) and taken as a reference (like
environment at T o & P o ), then that maximum work potential
depends on the other system state, i.e., it is independent of the
process path, thus, could be considerred the system property,
called Exergy. Note that there will be a need to reversibly
exchange heat (and entropy) at the reference temperature or
reversibly regenerate heat internally, except for isentropic
processes. www.kostic.niu.edu
Slide 15
Slide 15 Work Potential NOT path dependent (very important!)
www.kostic.niu.edu Or any path Also for any 1-2 states
(non-isentropic)
Slide 16
Slide 16 www.kostic.niu.edu reversible processes are over-all
isentropic All reversible processes are over-all isentropic
(entropy conserved)! Exergy analysis to minimize and optimize
irreversibility Entransy analysis to maximize and optimize heat
transfer
Slide 17
Slide 17 www.kostic.niu.edu Engineering Thermodynamics 7 th Ed.
By Moran et al, Wiley But not ALWAYS true: Irreversible work will
increase entropy thus resulting in different state with the same
internal energy as reversible work. It is, though, true if ALL work
is irreversibly converted to heat and stored as thermal energy, as
in isohoric processes (V=constant) with solids and liquids (as in
the Jules experiments). BUT so is E 2 -E 1 =Q in, if W=0 NOT
true!
Slide 18
Slide 18 www.kostic.niu.edu Howard DeVoe, Thermodynamics and
Chemistry (electronic) textbook: www2.chem.umd.edu/thermobook/
www2.chem.umd.edu/thermobook/ on 11 April 2013
Slide 19
Slide 19 Mechanical and Thermal Energies Are Distinguishable
Within Internal Energy! U 12s = U 12v U 2s =U 2v U=U th +U
mech(elastic) T 2s =T 2v (for Ideal Gas) BUT! 2s2v P s >P v ; S
s U mech,v Ex s >Ex v etc. 2009 January 10-12 M. Kostic or HEAT
applied FORCE applied
Slide 20
Slide 20 Thermal and Mechanical energies 041115 M. Kostic 1 kJ
heating is NOT the SAME as 1 kJ compressing! Thermal and Mechanical
energies are distinguishable, NOT the same Internal energy (as
argued by some)!
Slide 21
Slide 21 2009 January 10-12 M. Kostic Mechanical and Thermal
Energies Are Distinguishable Within Internal Energy! or HEAT
applied FORCE applied
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Slide 22 www.kostic.niu.edu
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Slide 23 www.kostic.niu.edu
Slide 24
041115 M. Kostic Prof. M. Kostic Mechanical Engineering
Mechanical Engineering NORTHERN ILLINOIS UNIVERSITY IRREVERSIBILITY
AND REVERSIBLE HEAT TRANSFER: The Quest and Nature of Energy and
Entropy
Slide 25
041115 M. Kostic Focus and Goal : Focuses on philosophical and
practical aspects of energy and entropy, with emphasis on
reversibility and irreversibility, and goal to establish the
concept of reversible heat transfer, regardless that heat transfer
is a typical irreversible process.
Slide 26
041115 M. Kostic Objective : to emphasize known, but not so
well-recognized issues about entropy, irreversibility and
reversibility, as well as to put certain physical and philosophical
concepts in perspective, as well as to put certain physical and
philosophical concepts in perspective, and initiate discussion and
arguments about the paper theme.
Slide 27
041115 M. Kostic Heat Transfer : Heat transfer like any other
energy transfer, may be achieved from any-to-any temperature level,
and in limit be reversible, if temperature of an intermediary
cyclic substance is adjusted as needed, using isentropic
compression and expansion
Slide 28
041115 M. Kostic This is practically demonstrated This is
practically demonstrated in refrigeration and heat pump devices,
and enables further increase in energy efficiency. A dual
power-and-heat-pump cycle is introduced and analyzed here, to
provide for reversible heat transfer. It may be considered as a
reversible heat-transfer transformer, from-any-to-any temperature
levels.
Slide 29
041115 M. Kostic Limits and Practical Potentials : The
reversible heat transfer limits are the most efficient and
demonstrate limiting potentials for practical heat transfer
processes.
Slide 30
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) 2009 January 10-12 M.
Kostic
Slide 31
Local-Instant & Quasi-Equilibrium: At instant (frozen)
time, a locality around a point in space may be considered as
instant-equilibrium (including inertial forces) with instantaneous
local-properties 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 net-zero energy exchange. 2009 January
10-12 M. Kostic
Slide 32
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; it could be
put/reversed back), 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. 2009 January 10-12
M. Kostic
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. 2009 January 10-12 M. Kostic
Slide 34
041115 M. Kostic 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.
However, the source entropy will decrease to a smaller extent over
higher potential, thus resulting in overall entropy generation for
the two interacting systems.
Slide 35
041115 M. Kostic It is possible to obtain work from the equal
amount of disorganized thermal energy or heat, if such process is
reversible. For eample: j reversible expansion at constant internal
energy, e.g. isothermal ideal-gas expansion, (dW=dQ), see Fig. 1a,
and j reversible adiabatic expansion (dW=-dU). j Work potential is
lost during unrestricted expansion (Fig. 1b)
Slide 36
041115 M. Kostic Heat Transfer and Irreversibility: ENTROPY
RANSFER AND GENERATION
Slide 37
041115 M. Kostic Entropy We could consider a system internal
thermal energy and entropy, as being accumulated from absolute zero
level, by disorganization of organized or higher level energy
potential with the corresponding entropy generation. Thus entropy
as system property is associated with its thermal energy. Thus
entropy as system property is associated with its thermal
energy.
Slide 38
041115 M. Kostic Entropy Primer: entropy could be transferred
in reversible processes along with heat transfer, and additionally
generated if any work potential (including thermal energys) are
disorganized at the lower thermal potential during irreversible
processes. Once a process completes, any generated entropy due to
irreversibility becomes (permanent) system property and cannot be
reversed/destroyed by any process in nature (thus, a permanent
change).
Slide 39
041115 M. Kostic Entropy Primer (2): Thus, entropy transfer is
due to reversible heat transfer and could be ether positive or
negative, while entropy generation is always positive and always
due to irreversibility.
Slide 40
041115 M. Kostic Reversible Heat Transfer and Practical
Potentials: Dual Power-Heat Pump cycle
Slide 41
041115 M. Kostic Coefficients of Performance for Three Typical
Cases of Reversible Heat Transfer the most efficient reversible
heat transfer from system H at higher temperature T H to system L
at lower temperature T L as presented on Fig. 3b may be obtained
(as limiting case) by using a dual power-and-heat-pump cycle (PHP),
which is governed by the following conditions (W PC = W HPC )
Slide 42
041115 M. Kostic Conclusion j j Energy is a fundamental concept
indivisible from matter and space, and energy exchanges or
transfers are associated with all processes (or changes), thus
indivisible from time. j j Energy is the building block and
fundamental property of matter and space, thus fundamental property
of existence. For a given matter (system) and space (volume) energy
defines the system equilibrium state, and vice versa. j j For a
given system state (structure and phase) addition of energy will
tend (spontaneously) to randomly distribute (disorganize) over the
system microstructure and space it occupies, called internal
thermal energy, increasing energy-potential (temperature) and/or
energy-displacement (entropy), and vice versa.
Slide 43
041115 M. Kostic Conclusion (2): j j Energy and mass are
conserved within interacting systems (all of which may be
considered as a combined isolated system not interacting with
others surrounding systems), and energy transfer (in time) is
irreversible (in one direction) from higher to lower potential
only, which then results in continuous generation (increase) of
energy-displacement, called entropy generation, which is a
fundamental measure of irreversibility, or permanent changes, the
latter also measured with the passing time. j j Reversible energy
transfer is only possible as limiting case of irreversible energy
transfer at infinitesimally small energy- potential differences,
thus in quasiequilibrium processes, with conservation of entropy.
Since such changes are reversible, they are not permanent (could be
reversed without leaving any relevant effect on the surroundings)
and, along with time, irrelevant (NOT permanent).
Slide 44
041115 M. Kostic Conclusion (3): j j Entropy may be transferred
from system to system by reversible heat transfer and also
generated due to irreversibility of heat and work transfer. j j
Heat transfer, like any other energy transfer, may be achieved from
any-to-any temperature level (performed in real power and
refrigeration cycles), and in limit be reversible, if temperature
of an intermediary cyclic substance is adjusted as needed, using
isentropic compression and expansion. The reversible heat transfer
limits are the most efficient and demonstrate limiting potentials
for practical heat transfer processes.
Slide 45
041115 M. Kostic Conclusion (4): j j The Dual Power-Heat Pump
Cycle, introduced here, may be considered as a reversible
heat-transfer transformer, from-any-to-any temperature levels. j j
The simple analysis of this dual, combined cycle (Eq. 4. and Fig.
3b), to achieve reversible heat transfer only (from higher to lower
temperature system) and without any net- work produced or utilized,
j j Presented emphasis (with analysis) of underlying physical
phenomena, including several hypothesis, is intended contribution
of this paper.
Slide 46
041115 M. Kostic
Slide 47
041114 M. Kostic Compressed Liquid water enthalpy corrections :
It is custom to approximate solid and liquid properties as being
function of temperature only, since they are virtually
incompressible: j Pdv compression work may be neglected. j For
isothermal compression processes: j correction for liquid enthalpy
approximation pumping work, vdP j Analysis of water real properties
shows that such a correction is unnecessary for intermediate
pressures and temperatures, and it is even erroneous for higher
temperatures and pressures, and thus counterproductive and
misleading.
Slide 48
041114 M. Kostic Compressed Liquid water enthalpy corrections
(2) : However, enthalpy is unique, since it is explicitly defined
as a function of pressure: Even enthalpy Solids and liquids are
virtually incompressible, thus compression work, Pdv, could be
neglected, and properties will not be function of pressure but
temperature only :
Slide 49
041114 M. Kostic REAL fluid enthalpy CORRECTIONS However, REAL
fluid enthalpy CORRECTIONS are not only due to change of pressure
(cor.C), but also to change of internal energy (cor.A), and volume
(cor.B): In all engineering references, and Thermodynamics
textbooks [1, 2]: or
Slide 50
041114 M. Kostic Isothermal vs. Isentropic compression of sat.
liquid water For isentropic compression (q=0): u=q+w comp = Pdv 0,
increase of internal energy and temperature (for 12 o C, from 260 o
C to 272 o C, see last row in Table I). To maintain constant
temperature in isothermal compression, there must be some cooling
(q out), thus internal energy decrease (corr.A).
Slide 51
041114 M. Kostic Recommended enthalpy correction in the
literature for isothermal compression Recommended enthalpy
correction in the literature is more appropriate for the isentropic
than for isothermal processes, due to erroneous assumption that
internal energy is not, and enthalpy is, dependent on pressure. It
is exactly opposite in Table I, see how the corresponding values (u
& h) change with pressure at constant temperature of 260 o
C.
Slide 52
041114 M. Kostic Compressed Liquid water properties and
relevant enthalpy corrections Corr.B small may be neglected. BUT
Corr.A & B are comparable and opposite sign. So, take both or
none, since it is more erroneous to take one (corr.C) only !
Slide 53
041114 M. Kostic Compressed liquid enthalpies at different
temperatures and pressures more in error for higher temperature and
pressure than the corresponding saturated values about the same for
the intermediate temperatures
Slide 54
041114 M. Kostic Conclusion j j Recommendations in the
literature for improvement of enthalpy calculation of compressed
liquids, by accounting for pressure dependence, are not generally
valid. j j Those recommendations may be erroneous and thus
counterproductive and misleading, as is the case for liquid water
at higher temperatures and pressures. j j For intermediate
pressures and temperatures, the recommended enthalpy corrections
are unnecessary, since the errors are about the same in magnitude
(but opposite in sign) as the corresponding saturated enthalpy
values without any corrections. j j The recommended enthalpy
corrections are only useful for smaller temperatures and
pressures.
Slide 55
The Concept of "Entransy" May Be More Important Than What It
Appears at First but it has to be "properly" related to existing
concepts of Thermal energy (not precisely defined yet, see
elsewhere), Exergy and Entropy, as well as irreversibility and
reversibility. but it has to be "properly" related to existing
concepts of Thermal energy (not precisely defined yet, see
elsewhere), Exergy and Entropy, as well as irreversibility and
reversibility. Entransy concept and analysis have some unique
advantages over other approaches. There is a need to define
Entransy as a property (how it relates to other thermodynamic
properties) and as process energy flux (how it relates to heat
& work transfer and entropy transfer & generation). We also
could advance and synergize your "Thermomass" concept with my work
in that area. Entransy concept and analysis have some unique
advantages over other approaches. There is a need to define
Entransy as a property (how it relates to other thermodynamic
properties) and as process energy flux (how it relates to heat
& work transfer and entropy transfer & generation). We also
could advance and synergize your "Thermomass" concept with my work
in that area. www.kostic.niu.edu
Slide 56
Stretching the mind further Mass may be a special tensor-like
quantity due to "over-all- isotropic in all-directions" motion of
elementary particles (that make up its structure) and thus give
rise to inertia if accelerated in any direction, i.e., resisting
change of motion in any and all directions with equal components
(the isotropic mass inertia). There may be anisotropic masses, with
bulk linear or rotational motion, being the extreme cases. Note
that fundamental particles (without inertial mass, like photons and
similar, but with relativistic masses E/c^2) has to always move
with ultimate speed of light in vacuum, and such particles (some
yet to be discovered) might be moving (orbiting with twisting,
string- like vibration and rotation) within virtually infinitesimal
spaces and thus making-up other "massive" so-called elementary
particles www.kostic.niu.edu
Slide 57
Deterministic vs. Probabilistic All interactions in nature are
physical and based on simple cause-and-effect conservation laws,
thus deterministic and should be without any exceptional
phenomenon. Due to diversity and complexity of large systems, we
would never be able to observe deterministic phenomena with full
details but have to use holistic and probabilistic approach for
observation; therefore, our observation methodology is holistic and
probabilistic, but phenomena have to be deterministic, not
miraculous nor probabilistic www.kostic.niu.edu
Slide 58
Elementary Particles: Electron? There is no proof that an
electron, or any other elementary particle, has or does not have a
structure. The concept of elementary particle is intrinsically
problematic (just because we cannot observe or reason a structure
which exhibits certain phenomena, does not mean it does not exist).
Past and recent history proved us to be wrong every time.
Particularly problematic is the current theory which requires
elementary particle annihilation/creation (miraculous creationism)
while using conservation laws. At the very least (in
phenomenological view) the elementary particles should be conserved
and be the building structure for other particles and systems. Note
that many concepts (in modern physics) are "virtual" entities that
are part of the mathematical theory, but are not directly
observable. www.kostic.niu.edu
Slide 59
Boundary Forces There is no such thing as a unidirectional
force or a force that acts on only one body (no imaginary boundary
vector- forces). Put it very simply: a forcing (force-flux
cause-and-effect phenomena) acts between an interface of pair of
objects (forced interaction: action-reaction, including
process-inertial forces), and not on a single object. The Newton
Laws and the Laws of Thermodynamics imply that all forces are mass-
energy interactions (forced displacements with momentum and energy
transfer and conservation) between different particulate bodies due
to non-equilibrium (available energy or work potential, cause of
forcing) towards the equilibrium. www.kostic.niu.edu
Slide 60
No Perfect Rigidity All matter must be somewhat elastic (can be
compressed or stretched). If bodies could be perfectly rigid we'd
have infinite forces acting with infinite speeds for infinitesimal
times (if you pushed on one end of a perfectly rigid stick, the
other end would move instantaneously). System components (bodies)
that exert forces have to be massive (2nd Newton Law) and with
accompanying reaction forces (3rd Newton Law).
www.kostic.niu.edu
Slide 61
Energy is bound by forced motion Energy is possessed (thus
equilibrium property) by material systems and redistributed
(transferred) between and within system(s), due to systems'
non-equilibrium, via forced- displacement interactions (process)
towards the equilibrium (equi-partition of energy over mass and
space); thus energy is conserved (the 1st Law) but degraded (the
2nd Law). Effects are consequences of Causes except at Equilibrium
they are equal (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.
System components (particles and bodies) that exert forces have to
be massive (2nd Newton Law) and with accompanying reaction forces
(3rd Newton Law). www.kostic.niu.edu
Slide 62
Force and Forcing Force or Forcing is a process of exchanging
useful-energy (forced displacement) with net- zero exchange at
forced equilibrium. The Second Law provides conditions and limits
for process forcing (energy exchange direction Force or Forcing is
a process of exchanging useful-energy (forced displacement) with
net- zero exchange at forced equilibrium. The Second Law provides
conditions and limits for process forcing (energy exchange
direction Second Law Second Law www.kostic.niu.edu
Slide 63
Processes Miracles "Nothing occurs locally nor in the universe
without mass-energy exchange/conversion and irreversible entropy
production. "Nothing occurs locally nor in the universe without
mass-energy exchange/conversion and irreversible entropy
production. It is crystal-clear (to me) that all confusions related
to the far-reaching fundamental Laws of Thermodynamics, and
especially the Second Law (Abstract), are due to the lack of their
genuine and subtle comprehension." It is crystal-clear (to me) that
all confusions related to the far-reaching fundamental Laws of
Thermodynamics, and especially the Second Law (Abstract), are due
to the lack of their genuine and subtle comprehension." to meSecond
LawAbstractto meSecond LawAbstract The miracles are until they are
comprehended and understood. www.kostic.niu.edu
Slide 64
041115 M. Kostic For further Info you may contact Prof. Kostic
at: [email protected] or on the Web: www.kostic.niu.edu Prof. M.
Kostic Mechanical Engineering Mechanical Engineering NORTHERN
ILLINOIS UNIVERSITY