Looking across the entire span of human understanding there are very few things that are derived from, proven, and supported by the most fundamental of considerations and observations spanning the infinitely small to the infinite vast Even Relativity and Quantum Mechanics stand alone in their abilities to deal with the big and the small. 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/

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

30. 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

31. 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.

32. 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

33. LAW 2 : Times Arrow
Doesn’t do reverse gear
Order from disorder isn’t simple
Entropy never decreases

34. 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

37. 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

38. ENTROPY : Basic System Form
Energy
Sink
Engine transforms
the form of energy
Engine
Energy
Source
Work Output
movement
chemical reaction
temperature change

39. ENTROPY : Impossibilities
Engine
Energy
Source
No Work Output
Energy
SinkEngineEngine
There are no perpetual motion machines - and there will never be any

40. - 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

41. 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

42. 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

43. 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

46. 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
∫

47. 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

48. 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

49. ENTROPY : Commonly cited forms
The springboard for
information theory
and info systems
understanding

50. 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.

51. 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

52. 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

53. 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
{

54. 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

55. 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)…..

56. 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?

57. 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

58. “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

59. cochrane.org.uk
Any further questions
or thoughts ??