slide 1 reflections on thermal energy, reversible and caloric processes, exergy and entransy –...

Download Slide 1  Reflections on Thermal Energy, Reversible and Caloric Processes, Exergy and Entransy – (Lecture II) Prof. M. Kostic Mechanical

If you can't read please download the document

Upload: byron-doyle

Post on 17-Dec-2015

215 views

Category:

Documents


1 download

TRANSCRIPT

  • Slide 1
  • 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 11
  • Slide 11 www.kostic.niu.edu thus thermal & mechanical energies are coupled 2
  • Slide 12
  • 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
  • Slide 22
  • Slide 22 www.kostic.niu.edu
  • Slide 23
  • 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