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Across the entire spectrum of physics, Einstein liked General Relativity and Thermodynamics best because they are derived from the most fundamental of considerations and see a general applicability

Unfortunately, both appear to be taught badly at high school and students often arrive at college and university with a partial, and/or confused picture of the mechanisms at work, the basic principles, mathematical formulations, and practical applicability. And so they are easily confounded by the books, papers and web pages that go into the necessary depth for their new studies and chosen field of work.

So, this ‘out of hours’ tutorial session has been configured for those students, staff, local industry, school students and others struggling with Thermodynamics. It fully embraces the tutorial style of close interaction with numerous demonstrations and examples in the form of embedded videos and real-time bench experiments.

The mathematical formulations are approached from many different angles to aid rapid assimilation and deep understanding, and to demonstrate specific advantages in different fields of application.

Apart from correcting the earlier failure mechanisms of student-teacher and the school system, my primary objective here is to get students to ‘first base’ so they may pick up books, papers and comb through web pages with confidence. BUT the key here is for attendees realise what a generally powerful and applicable tool Thermodynamics is - to understand fully - and be able to apply it in their future work on systems of all kinds.

Only time will tell if I have succeeded!

Peter Cochrane

This tutorial is one in a series specifically tailored in support of my wider lecture program spanning technology, engineering, and management theory and practice for undergrad and postgrad students the new University of Suffolk UK https://www.uos.ac.uk/

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- 1. Everything you wanted to know about THERMODYNAMICS & ENTROPY …but were afraid to ask ! An open lunch time tutorial for students, staff, industry and anyone studying, or with an interest in, the systems and that power and control our lives, society and the universe by Prof Peter Cochrane cochrane.org.uk
- 2. THE 30 sec VERSION There is a game We are all in the game No one can opt out ! B AD NEWS: You can’t win the game GOOD NEWS: You can break even LIMITATION: But only on a very cold day B AD NEWS: It never gets that cold ! A fundamental realisation simplified
- 3. THERMO DYNAMICS Relating to heat Relating to change/movement No one could have guessed that the study of heat would reveal laws and principles pertinent to all systems in general - biological - chemical - physical and man made The closest we have come to a ‘one theory fits all’ - a unified set of observations - a generally applicable law, & comprehensive understandings
- 4. RANKING Across the entire spectrum of physics, Einstein liked General Relativity and Thermodynamics best because they are both derived from fundamental considerations of how the universe works; their ‘completeness’ and as fundamentally emergent properties
- 5. THE NATURE OF HEAT A complete mystery for millennia Used and exploited with rules of thumb based on feel, colour, melting point of metals and malleability etc
- 6. ASSOCIATED WITH THE GODS Ancient Egyptians related heat to mythology Component of “primordial forces”, from which all was formed and elements of chaos, that existed before the creation of the sun
- 7. A TOOL FOR PEACE AND WAR Ancient Greeks created an early flame thrower First theory Heraclitus ~500 BC: Elements in nature; ﬁre, earth, & water "All things are ﬂowing - and an exchange for ﬁre“
- 8. INDUSTRIAL REVOLUTION 1 Water transport & limited green energy ~1770 Water and water ﬂow sufﬁciently understood and characterised by Archimedes, and adaptations to Newtonian Mechanics ~5 bhp @ <10% Efﬁciency of energy extraction BIG Unknowns How big a wheel ? What shape the blades ? Overﬂow or underﬂow of water ? How high the head and volume of water ?
- 9. CONCATENATED MILLS Quickly ran out of energy as more built ****** Water and water ﬂow sufﬁciently understood and characterised by Archimedes, and adaptations to Newtonian Mechanics The ﬁght for efﬁciency was driven by building mill after mill along rivers only to run out of energy….a victory for science, engineering, innovation… and a foundation for the rationale of thermodynamics A story to be repeated with the steam engine and the belt drive… with energy distribution, friction and efﬁciency…the next big hurdles
- 10. Water transport & limited green energy ~1770 D I G G I N G I N T O T H E D E T A I L Experiments, intuition, guessing, theory, understanding Mathematician Leonhard Euler and son Albert (1750s) experimented with/characterised waterwheels Mathematician Jean-Victor Poncelet (1862) proposed inward-ﬂowing radial turbine - modern turbine precursor Engineer Samuel B. Howd (1838) patented enclosed vertical spindle & curved blades. Hydraulic Engineer James B. Francis (1892) added guide vanes and shaped the blades to the correct angle Francis turbine is still the most widely used for medium-high heads/pressure Engineer James Thomson, added pivoted curved guide vanes to assure optimum ﬂow even at part load
- 11. INDUSTRIAL REVOLUTION 2 Steam power and ‘engine design’ were very rudimentary with many accidents and huge inefﬁciencies apparent due to the lack of scientiﬁc knowledge and sound engineering principles Steam transport & energy from coal ~1850 BIG Unknowns What fuel ? What ﬂuid ? What pressure ? What size piston ? How efﬁcient the design ? ~30 bhp @ < 15% Efficiency
- 12. THE LEARNING EXPERIENCE Big accidents People get hurt/killed Understanding is essential Without knowledge and understanding…… Water and water ﬂow sufﬁciently understood and characterised by Archimedes, and adaptations to Any fool can build a water mill and/or a steam engine, but it takes science and engineering to build a good/efﬁcient/safe machine ~500 bhp @ < 20% Efficiency
- 13. COAL, FIRE, WATER, STEAM, BELT A long path to understanding and efficiency realisation ~300bhp @ < 20% Efficiency ~100kbhp @ >95% Efficiency ~200 bhp @ < 15% Efficiency
- 14. COAL, FIRE, WATER, STEAM, BELT A long path to understanding and efficiency realisation ~200bhp @ < 20% Efficiency ~100kbhp @ >95% Efficiency ~30 bhp @ < 15% Efficiency
- 15. TITANIC ~50,000 bhp Engines x 2 ~ 50k bhp Total Speed ~ 22 knots Coal ~ 825 Tons/day Engines = 2 Boiler Rooms = 6 Boilers = 24 Furnaces = 72
- 16. SCIENCE COMES TO THE RESCUE Deep knowledge & understanding creates acceleration All our transport, energy, industrial, civil, military, information & network systems hinge on this knowledge Riding a horse to walking on the moon < 200 years Riding on a train to riding on a rocket <100 years
- 17. THE RUN UP Perspective thinking ~1662 Robert Boyle Gas Law ~1666 Issac Newton Laws of Motion P.V = k P.V = mRT F = d(mv) dt s = ut + ft2 Force Motion Inertia Momentum 1) A body is at rest or in linear motion until acted upon by some external force 2) Force is the time rate of change of momentum 3) For every action in nature there is always an equal and opposite reaction Volume Pressure Temperature Volume and Pressure are inversely related when Temperature is constant
- 18. T H E R U N U P Thinking on machines
- 19. THE RUN UP Step by step thinking ~1850 Rudolf Clausius William Thomson (Lord Kelvin) Max Plank All proved and stated The First and Second Laws of Thermodynamics: - the total heat in a closed system is conserved - there really is no free lunch - 100% efficiency can never be realised - perpetual motion machines are impossible [Heat converted to work analysis Work converted to heat analysis Gave ‘Entropy’ its name and the ﬁrst to lecture and teach the subject Entropy from the Greek En = enérgeia + tropos = turning point
- 20. THEORY FORMULATION It all starts with the nature of heat The physics of and understanding of heat…followed by a realisation of a general and universal applicability… Biology Systems Chemistry Cosmology Information Communications Artiﬁcial Intelligence +++++ almost everything else …with each discipline taking a different route, applying a different emphasis, interpretation and application set Sad to say the conservationists, sustainability enthusiasts, and politicians still have to discover thermodynamics and entropy!
- 21. I N I T I A L F O R M U L A T I O N Derived from the kinetic theory of gases Law 0: If two systems are in thermal equilibrium with a third then all are in equilibrium Law 1: Conservation - energy cannot be created or destroyed in an isolated system Law 2: Celestial Ratchet - entropy of any isolated system always increases Law 3: System Entropy - approaches a constant as temperature approaches absolute zero …theories, experiments, trials, observations repeated multiple times and ways by hundreds of teams across the planet over many lifetimes. The most complete view of the way (our) universe works and why! All based on what we observer, what we can test, what we can prove: the ‘truths’ established by standing on the shoulders of giants over millennia…
- 22. If two systems are in thermal equilibrium with a third then all are in equilibrium LAW 0 Defines temperature and heat flow Cold Water + Hot Water + Dish }All want to be at the same temperature Flow is hot to cold and never the reverse direction
- 23. LAW 1: Conservation of Energy Energy cannot be created or destroyed in an isolated system Energy can only change in form potential, kinetic, heat Perhaps obvious from Einstein E = mc2 In a universe, or system, of constant mass the energy is also constant But this is partially a circular argument Internal Energy = +Heat Input +Work Done by System ∆u = Q + W Internal Energy = Heat Output -Work Done on System ∆u = -Q - W
- 24. A S F A R A S W E K N O W The total mass/energy of the universe is constant Dark Energy ? Quantum Dynamics ? Black Holes ? String Theory ? Worm Holes ? Multi-Dimensionality ? Relativity Quantum Mechanics Experiments Observations ExperiencesMeasurements Theories
- 25. LAW 2: Full energy and state accounting Celestial Ratchet - entropy of any isolated system always increases Entropy can be thought of in terms of order and disorder All systems tend toward a disordered state One way processes Drop a cup and it smashes, but the reverse never happens A battery always discharges it never decides to recharge itself We live and then die and not the other way round - there are no zombies The more energy is dispersed - the greater the entropy
- 26. LAW 2: Full energy and state accounting Celestial Ratchet - entropy of any isolated system always increases Entropy can be thought of in terms of order and disorder All systems tend toward a disordered state One way processes Drop a cup and it smashes, but the reverse never happens A battery always discharges it never decides to recharge itself We live and then die and not the other way round - there are no zombies The more energy is dispersed - the greater the entropy Hot coffee in a mug is concentrated - but as the heat dissipates into the surroundings the heat ﬂow sees entropy fall in the mug and rise in the environment
- 27. LAW 2: Entropy - Turbo charger and turbo booster in an internal combustion cycle - Activation energy necessary to initiate a chemical reaction - Photosynthesis as a form of energy transformation - Energy conversion of aviation fuel in a jet engine - Chlorophyll as a mechanism of energy storage - Spread of heat from the sun across the earth - Efﬁciency of a modern power station - After burner cycle of a jet turbine The nature of heat/energy ﬂow/spread/dissipation The ‘purists’ always ‘retreat’ to this founding conceptualisation/formulation applicable to: These, and many more, are the ‘qualiﬁed/recognised’ boundaries of the science founded on heat, energy, and reactions. Here, formulations are directly related to the original roots of thermodynamics without abstraction, modiﬁcation or mutation!
- 28. LAW 2: Entropy - A measure/number of possible arrangements the atoms in a system can have - Measure of how (dis)organised energy is in a system of atoms or molecules - The level of (dis)organisation of characters on a page or bits in a message - The level of social activity and or physical movement in a crowd - The effectiveness of passwords, coding and encryption - The level of cohesion in a ﬁghting force Order/disorder is a popular visualisation The ‘purists’ tend to wince at this visual perspective as, for many of them, it strays too far from the thermodynamic origins of the property and heat based formulations: The level of ‘bastardisation’ of the original thermodynamic concepts and formulations increases as we come down this list - however, they, and many more, prove to be useful across many ﬁelds - BUT we should note that, as useful as they may be, they are not the same as the original starting point, but can be statistically justiﬁed
- 29. LAW 2: Entropy Order/disorder information Order Disorder . , : ; i if iff I need to talk with you soon The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication" Information
- 30. ENGINEERING MAXIMS : Does it work ? “ Whilst it is permissible for the mathematicians, physicists, chemists and biologists to declare that there is no solution to a problem - WE in engineering enjoy no such luxury and WE always have to ﬁnd an answer” Order/disorder is more than a popular visualisation - it is a useful tool The primary question for engineers is: Does it work ? Reﬁnement, efﬁciency, reliability, resilience, and functionality often have to follow! “Engineers have to drink from the ‘well of human knowledge’ and experience; they are obliged to utilise and/or bend any likely discovery/result to their advantage - and do so without regret or limitation” In this sense engineers and engineering ride the boundary between science and alchemy in the/ir search for practical solutions often ahead of reliable results or any workable science.
- 31. One way processes From order to disorder Entropy always increases This is the universe we live in - our experiences Order disorder LAW 2 : Times Arrow
- 32. LAW 2 : Times Arrow Doesn’t do reverse gear Order from disorder isn’t simple Entropy never decreases
- 33. LAW 2 : Times Arrow Doesn’t do reverse gear Order from disorder isn’t simple Entropy never decreases We have never witnessed any reverse order processes- and whilst theoretically feasible their probability is so close to zero we can say they will never happen….and we have no evidence of time travellers either !! Order disorder
- 34. EXCEPTION ALERT : LIFE!! Time’s arrow isn’t in reverse ! -ve Entropy partly deﬁnes life systems Only possible (and true) in small pockets Life is an insigniﬁcant element of a bigger system Entropy goes negative as order emerges from disorder Does not detract signiﬁcantly from the universal trend toward total disorder WE ALWAYS have to consider any system in the context of the whole environment… ..the Entropy of a closed/isolated/ constrained system can experience/see + or -ve Entropy,. but the whole only ever sees a +ve change
- 35. ENTROPY : Basic System Form Energy Sink Engine transforms the form of energy Engine Energy Source Work Output movement chemical reaction temperature change
- 36. ENTROPY : Impossibilities Engine Energy Source No Work Output Energy SinkEngineEngine There are no perpetual motion machines - and there will never be any
- 37. - No free energy - No free material - No free processes - No perpetual motion machines NOTHING IS FREE : Everything has a cost !! Efﬁciency Always < 100% Energy Out < Energy In
- 38. ENTROPY : Basic System Form Energy Sink Engine transforms the form of energy Engine Energy Source Work Output ⇒ Energy Output = E1 - E2 = ∆E ∝T1 -T2 movement chemical reaction temperature change Energy Suppled = E1 Energy Dissipated = E2 Energy = E1 ∝T1 Energy = E2 ∝T2 NOTICE : The work/energy output is dictated by the temperature differential and the efﬁciency of the machine. For a given efﬁciencey the output = Z( T1 - T2) NOTICE : Entropy deﬁnes the energy available to do useful work in a thermodynamic process
- 39. ENTROPY : Heat v Statistical View ∆S ≈ ∆ERelative change in Entropy Many formulation variants - some more convenient or easier to deal with than others depending on educational background/mode of thinking distribution but the outcome/form is always the same and so are all the conclusions - there are no conﬂicts or exceptrions… T } Integrating over the entire space/system is then trivial: S = k log KT∂S ≈ ∂E T∫∫ S = kß log W Relative change system energy at a given temperature
- 40. GENERAL FORMULATION Derived from the kinetic theory of gases Historically; Thermodynamics and nearly all the early thinking emerged from considerations of a number a number of i n d u s t r i a l p ro b l e m s re l a t e d t o h e a t generation, flow and exploitation in the transformation into motion Development; It was soon realised and shown that all the laws could be derived from the study of molecular movement at an individual and fundamental level - and therefore, be based on a statistical model c o n c e r n e d w i t h t h e p r o b a b i l i t i e s associated with movement and location
- 41. ENTROPY : Thermal Derivation ~1840 ∆S ≈ ∆E ≈ k∆TRelative change in Entropy Many formulation variants - some more convenient or easier to deal with than others depending on educational background/mode of thinking, but the outcome and form is always the same and so are all the conclusions - there are no conﬂicts or exceptions… T Integrating over the entire space/system is then trivial: ∂S ≈ ∂E T∫∫ S = kß logW T ∂S ≈k ∂T T∫ kß = Boltzman’s Constant = 1.38065 × 10−23 J/K Joules/Kelvin This W nomenclature was ‘standardised’ from later probabalistic derivations Original formulation in 1842 by Boltzmann did not use W =Wahrscheinlichkeit (German for probability) - it was introduced by Max Plank in 1900 ∫
- 42. ENTROPY : Statistical Derivation ~1900 A measure of the number of possible micro-states of a system in thermodynamic equilibrium, consistent with its macro-state A full formulation is rendered impossibly large unless all the micro-states are statistically independent and all the probabilities are the same for the whole macro-state W = Wahrscheinlichkeit (probability) of a macrostate for some probability distribution of microstates - positions and momenta of all molecules - the most general expression of the thermodynamic entropy N = The total number of molecules/components Ni = The individual molecules/components N! N Ni !∏i W = Total number of positions of total population Total number of individual positions/molecule
- 43. ENTROPY : Statistical Thermodynamics In many practical cases a system’s thermodynamic micro-states are not equally probable: eg, high energy states are less probable than low energy at a ﬁxed temperature And so the equal probabilities assumption does not always obtain, but a well established generalisation is given by Gibbs: This formulation is the most useful and most cited in engineering and information science…and there are many similar forms including Shannon’s Bound S = ⎲⎲ i pi log pi-kß Iff all the probabilities are equal, then this reduces to: S = kß logW
- 44. ENTROPY : Commonly cited forms The springboard for information theory and info systems understanding
- 45. EXCEPTION ALERT: New Dimensions Our reality of 4 dimensions appears to be a fraction of an 11 dimensional universe. But all of the above is based on millennia of evidential understanding of our 4D ‘reality’ and the Laws of Physics appear immutable. Though challenged and tested continually they remain steadfast and the foundation of our understandings. There is always room for new discoveries, but unless there is another reality of different and/or more dimensions the Laws of Thermodynamics remains our most complete model, at the core of our base understandings of the universe in which we live.
- 46. POSITIONING: Human knowledge E = mc2 S = kß log W kß = 1.38065 × 10−23 J/K If this is mankind’s most prophetic equation: Then this is a very close second: Profound consequences: Time travel is impossible and nothing lives or lasts forever
- 47. LAW 3: Entropy > 0 as T > 0 K The only law founded on unique measurement trends “The entropy of a perfect crystal at absolute zero is exactly equal to zero” In a sense this law is more hypothetical that any of the other three as it cannot be directly demonstrated - ie we cannot create perfect crystals or a temperature of absolute zero ! “Perfect order and thus zero entropy is only possible at absolute zero” https://arxiv.org/abs/1412.3828
- 48. TO BE AWARE: ENTHALPY A measure of the total energy of a system The internal energy plus that required to create a system Entropy S = Joules/Kelvin - a measure of how energy is distributed in a system Enthalpy H = Joules - A systems internal energy + p.v TO BE CLEAR OTHER TERMS Endothermic = Absorbing Energy Exothermic = Releasing Energy Adiabatic = No Energy Exchange More generally applicable in chemistry and chemical engineering et al and not information systems and theory { Terms commonly employed in many other ﬁelds but not in general use for information systems and theory {
- 49. IS HELL ENDOTHERMIC OR EXOTHERMIC ? 1) We postulate that if souls exist, then they must have some mass. If they do; a mole of souls can also have a mass 2) So, at what rate are souls moving into and exiting hell? I think we can safely assume that once in hell souls do not leave 3) Many/most religions state that if you are not a member, then you will go to hell. Since there are so many of these religions and people do not belong to more than one religion, we can project that all people and souls go to hell 4) With birth and death rates as they are, we can expect the number of souls in hell to increase exponentially. 5) NOW; Boyle’s Law states that in order for the temperature and pressure in hell to stay the same, the ratio of the mass of souls and volume needs to stay constant. Two options exist: a)If hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose b)If hell is expanding at a rate faster than the increase of souls in hell, then the temperature and pressure will drop until hell freezes over So which is it? If we accept the quote given to me by Theresa Manyan during Freshman year, "that it will be a cold night in hell before I sleep with you" and take into account the fact that I still have NOT succeeded in having sexual relations with her, then Option 2 cannot be true...Thus, hell is exothermic." A fun read from the internet often falsely attributed to Dr Schambaugh of the Oklahoma School of Chemical Engineering
- 50. TO CONTEMPLATE - THE FRIVOLOUS ? Analysing and making sense of the extreme including the non-sensical 1) How much energy ﬂows down Harry Potters wand when he casts a spell? 2) AND where does that energy come from, and what kind of energy is it? 3) What are the limitations to building a matter transporter - aka Start Trek? 4) Is it possible for any life form to survive in its own waste materials? 5) Does a pregnant mother see an increase or decrease in her entropy? 6) When someone/thing dies, does it’s entropy stop increasing? 7) What is the ultimate limit to our information storage capacity? 8) In the movie ‘The Martian’ would his survival strategy actually work? 9) Where are heaven and hell located and how much energy do they consume? 10)…..
- 51. TO CONTEMPLATE: SERIOUS PROBLEMS Fashion, fad, political and scientiﬁc correctness are almost never in alignment 1) Do our waste recycling programs actually work ? 2) Should we be burning plastic waste instead of recycling? 3) Are electric vehicles really green ? 4) Do wind farms cost in ecologically? 5) Can wave power save us? 6) Is tidal power a better option? 7) Can we actually live ‘off grid’ and beneﬁt the planet? 8) Do solar cells create more pollutants than they save? 9) Can ‘natural farming’ feed the planet? 10)Could we actually freeze technologically driven change?
- 52. M O R E E X P L A N A T I O N S / V I E W S Need to know even more? https://en.wikipedia.org/wiki/History_of_entropy http://entropysimple.oxy.edu/content.htm https://www.khanacademy.org/science/biology/energy-and-enzymes/the-laws-of-thermodynamics/a/ the-laws-of-thermodynamics http://physicsforidiots.com/physics/thermodynamics/ Brian Cox explains why time travels in one direction - Wonders of the Universe - BBC Two https://www.youtube.com/watch?v=uQSoaiubuA0 A derivation (and quantiﬁcation) of the third law of thermodynamics Masanes & Oppenheim (Quantum Physics 11 Dec 2014 (v1), revised 7 Apr 2016) https://arxiv.org/abs/1412.3828
- 53. “It can be argued that civilisation and its technology enabler IS the sustainability problem” This axiom has a brilliant/controversial thermodynamic proof byTim Denton in a 2007/9 paper suggesting tCivilisation itself is a heat engine - producing 9.6 milliwatts of heat for ever dollar of GDP normalised to 1990 value. The insight is quite brilliant, and the implications terrifying. FURTHER FOOD FOR THOUGHT ! Make it your practice to read wider than your lecture notes and printed books. Search out the radical, the deep thinkers, and those who posit the challenging! “you don't solve problems from within the system that created those same problems” Axiom - Einstein
- 54. cochrane.org.uk Any further questions or thoughts ??

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