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

THE 30 sec VERSION

There is a game

We are all in the game

No one can opt out ! B A D N E WS : You can’t win the game

GOOD NEWS: You can break even

LIMITATION: But only on a very cold day

B A D N E WS : It never gets that cold !

A fundamental realisation simplified

THERMO DYNAMICS

Relating to heat Relating to change/movementNo one cou l d have

guessed that the study of heat would reveal l aws and p r i n c ip l e s pertinent to all systems in general - biological - chemical - physical and man made

The closest we have come to a‘one theory fits all’ - a unifiedset of observations - a generallyapplicable law, & comprehensiveunderstandings

RANKING

Across the ent ire spectrum of phys ics , E inste in l iked Genera l Relat iv i ty and Thermodynamics best because they are both der ived from fundamenta l cons iderat ions of how the universe works ; the ir ‘completeness’ and as fundamenta l ly emergent propert ies

THE NATURE OF HEATA complete mystery for mil lennia

Used and exploited with rules of thumb based on fee l , co lour, me l t ing po int o f meta l s and malleability etc

ASSOCIATED WITH THE GODSAncient 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

A TOOL FOR PEACE AND WARAncient 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“

INDUSTRIAL REVOLUTION 1Water 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 ?

CONCATENATED MILLSQuickly 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

Water transport & limited green energy ~1770D I G G I N G I N T O T H E D E T A I LExperiments, 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 optimumflow even at part load

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

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 adaptat ions 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

COAL, FIRE, WATER, STEAM, BELTA long path to understanding and efficiency realisation

~300bhp @ < 20%

Efficiency

~100kbhp @ >95%

Efficiency

~200 bhp @ < 15%

Efficiency

COAL, FIRE, WATER, STEAM, BELTA long path to understanding and efficiency realisation

~200bhp @ < 20%

Efficiency

~100kbhp @ >95%

Efficiency

~30 bhp @ < 15%

Efficiency

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

SCIENCE COMES TO THE RESCUEDeep 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

THE RUN UPPerspective 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

ForceMotionInert iaMomentum

1) A body is at rest or in linear motionuntil acted upon by some external force

2) Force is the time rate of change ofmomentum

3) For every action in nature there isalways an equal and opposite reaction

VolumePressureTemperature

Volume and Pressureare inversely relatedwhen Temperature isconstant

T H E R U N U PThinking on machines

THE RUN UPStep by step thinking

~1850 Rudolf Clausius

William Thomson (Lord Kelvin)

Max Plank

All proved and stated The First and Second Laws ofThermodynamics:

- 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 tolecture and teach the subject

Entropy from the Greek En = enérgeia + tropos = turning point

THEORY FORMULATIONI t a l l s tarts with the nature of heat

The phys ics o f and understanding of heat… fo l lowed by a rea l i sat ion of a genera l and universa l appl icabi l i ty…

Biology Systems Chemistry Cosmology Information Communications Artificial Intelligence +++++ almost everything else…with each d i sc ip l ine tak ing a d i f ferentroute , apply ing a d i f ferent emphas i s ,in terpretat ion and appl icat ion set

Sad to say the conservationists, sustainability enthusiasts, and politicians still have to discover thermodynamics and entropy!

I N I T I A L F O R M U L A T I O NDerived 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, tr ials , observations repeated mult iple t imes and ways by hundreds of teams across the planet over many l i fet imes.

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 overmil lennia…

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

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

A S F A R A S W E K N O WThe 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

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

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 surroundingsthe heat flow sees entropy fall in the mug and rise in the environment

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!

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

LAW 2: EntropyOrder/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

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.

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

LAW 2 : Times ArrowDoesn’t do reverse gear

Order from disorder isn’t simple

Entropy never decreases

LAW 2 : Times ArrowDoesn’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

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

ENTROPY : Basic System Form

Energy

Sink

Engine transformsthe form of energy

EngineEnergy

Source

Work Output movement

chemical reaction temperature change

ENTROPY : Impossibilities

EngineEnergy

Source

No Work Output

Energy

SinkEngineEngine

There are no perpetual motion machines - and there will never be any

- 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

ENTROPY : Basic System Form

Energy

Sink

Engine transformsthe form of energy

EngineEnergy

Source

Work Output ⇒ Energy Output = E1 - E2 = ∆E ∝T1 -T2 movement

chemical reaction temperature change

Energy Suppled = E1Energy 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 ava i lab le to do use fu l work in a thermodynamic process

ENTROPY : Heat v Statistica l V iew

∆S ≈ ∆ERelative change in Entropy

Many formulation variants - some more convenient or easier to deal with thanothers depending on educational background/mode of thinking distribution butthe outcome/form is always the same and so are all the conclusions - there areno conflicts or exceptrions…

T }Integrating over the entire space/system is then trivial:

S = k log KT∂S ≈ ∂ET∫∫ S = kß log W

Relative change system energyat a given temperature

GENERAL FORMULATIONDerived from the kinetic theory of gases

Historical ly; Thermodynamics and nearly a l l t he ea r l y t h i nk ing emerged f rom considerations of a number a number of i n d u s t r i a l p ro b l e m s r e l a t e d t o h e a t generation, f low and exploitation in the transformation into motion

Development; It was soon real ised and shown that al l the laws could be derived from the study of molecular movement at an individual and fundamental level - and therefore, be based on a statist ical 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

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 ≈ ∂ET∫∫ S = kß log W

T

∂S ≈k ∂TT∫

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

∫

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/componentsNi = The individual molecules/components

N!N

Ni !∏iW = Total number of positions of total population

Total number of individual positions/molecule

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 citedin engineering and information science…and there are many similar forms including Shannon’s Bound

S = ⎲⎲ipi log pi-kß

Iff all the probabilities are equal, then this reduces to:

S = kß log W

ENTROPY : Commonly cited forms

The springboard for information theory

and info systemsunderstanding

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.

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

LAW 3: Entropy > 0 as T > 0 KThe 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

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{

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

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)…..

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?

M O R E E X P L A N A T I O N S / V I E W SNeed 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 Twohttps://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

“It can be argued that civilisation and its technology enabler IS the sustainability problem”

This axiom has a brilliant/controversial thermodynamic proof by Tim 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

cochrane.org.uk

Any further questions

or thoughts ??