Table Of ContentSPRINGER BRIEFS IN PHYSICS
Ulf W. Gedde
Essential Classical
Thermodynamics
123
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Ulf W. Gedde
Essential Classical
Thermodynamics
UlfW.Gedde
FibreandPolymerTechnology
SchoolofEngineeringSciencesinChemistry
BiotechnologyandHealth
KTHRoyalInstituteofTechnology
Stockholm,Sweden
ISSN2191-5423 ISSN2191-5431 (electronic)
SpringerBriefsinPhysics
ISBN978-3-030-38284-1 ISBN978-3-030-38285-8 (eBook)
https://doi.org/10.1007/978-3-030-38285-8
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Preface
Even before writing our recent book Fundamental Polymer Science (Springer
Nature (2019)), I realized that a thorough understanding of thermodynamics is
essential if the reader is to be able to capture the content of this specialized field.
At this stage, the plan was to prepare a brief account as a supplementary chapter.
When the polymer science book was delivered, however, in order to reach the
broadestpossible audienceforaconciseandhighlyreadableprimeronthermody-
namics, David Packer of Springer Nature proposed that I should write a separate
book to be included in a series of publications called Springer Brief. At this stage,
I also realized that many other books in chemistry, physics, materials science and
engineeringhadthesame“problem”;aknowledgeaboutbasicclassicalthermody-
namicsisrequiredinordertobeabletoabsorbthematerialinthesetexts.Thereare
many comprehensive books on thermodynamics. Most of them are 500 pages or
longer,and they also havea broader perspective, including kinetics, basic physics,
applied thermodynamics, etc. Concise texts on classical thermodynamics are few,
and many of them are quite old. These short texts are very useful for newcomers,
typically first or second year university students, as a complement to the more
comprehensive books. Ph.D. students, postdocs and engineers in industry and
research institutes have had their basic thermodynamics training 5–10 years back,
and it is possible that some of the thermodynamics is forgotten. This book is
essentially aimed at this group. For the last decade, I have been teaching the
thermodynamics course at KTH Royal Institute of Technology in Stockholm for
students in chemistry and biosciences. This 10-year effort has taught me the prob-
lemswithunderstandingthermodynamics.Ourgraduationhasincreasedbyafactor
of3duringthisperiodsimplybyaddressingtheseissuesandprovidingsecond-and
third-level opportunities during the course. The lesson is that inspiration, concern
and time make most students knowledgeable. I feel relaxed and happy now in
delivering this text to hopefully many readers. Feel free to mail me if you have
questionsandideasconcerningthebook.
v
vi Preface
Thisbookhasveryfewreferences.Itfocusestoprovideonlytheessentialsforthe
understandingofthesubject.Ihaveincludedquiteafewequationsandderivations
ofimportantexpressions(laws).Thesteptoapplytheformulaetoyourproblemsis
notsofar-reaching.
ProfessorsMikaelHedenqvist,EricTyrodeandFritjofNilsson,allatKTHRoyal
Institute of Technology, Stockholm, Sweden, have provided feedback on the text.
Dr. Anthony Bristow has corrected the English. Bristow is a person with a unique
combinationofsenseoflanguageandfactualknowledgeofscience.DavidPackerof
Springer Nature has provided inspiration and great ideas concerning this book and
therecentpolymersciencebooks.Thankyou,David.
Stockholm,Sweden UlfW.Gedde
October7,2019
Contents
1 AnIntroductiontoThermodynamicsandtheFirstLaw. . . . . . . . . 1
2 TheSecondandThirdLaws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 GibbsandHelmholtzFreeEnergies. . . . . . . . . . . . . . . . . . . . . . . . 21
4 AComprehensiveViewoftheStateFunctionsIncluding
MaxwellRelations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 ChemicalPotentialandPartialMolarProperties. . . . . . . . . . . . . . 29
6 One-ComponentSystems:TransitionsandPhaseDiagrams. . . . . . 35
7 Solutions,Phase-SeparatedSystems,ColligativeProperties
andPhaseDiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
8 ChemicalEquilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
9 ThermodynamicsProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
FirstLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
FirstandSecondLawsCombined. . . . . . . . . . . . . . . . . . . . . . . . . . . 76
GibbsandHelmholtzFreeEnergiesandtheMaxwellRelations. . . . . . 76
ChemicalPotentialandPhaseEquilibria. . . . . . . . . . . . . . . . . . . . . . . 76
ColligativeProperties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
ChemicalEquilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
PhaseDiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
10 SolutionstoProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
11 MathematicsUsefulfortheThermodynamics. . . . . . . . . . . . . . . . . 93
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
vii
Chapter 1
An Introduction to Thermodynamics
and the First Law
Classical thermodynamics is based on several robustly formulated statements,
referred to as the laws of thermodynamics. The words of Albert Einstein say
something important about thermodynamics: “A theory is the more impressive the
greater the simplicity of its premises, the more varied the kinds of things that it
relates and the more extended the area of its applicability. Therefore, classical
thermodynamics has made a deep impression on me. Thermodynamics is the only
science about which I am fairly convinced that, within the framework of the
applicabilityofitsbasicprinciples,itwillneverbeoverthrown”.Anotherrespected
scientist,ArnoldSommerfeld,wrote:“Thermodynamicsisafunnysubject.Thefirst
timeyougothroughthesubject,youdonotunderstanditatall.Thesecondtime,you
thinkyouunderstandit,exceptforoneortwosmallpoints.Thethirdtime,youknow
thatyoudonotunderstandit,butyouaresousedtothesubjectthatitdoesnotbother
youanymore”.
The history of the establishment of the first law of thermodynamics involved
personsstudyingandthinkingaboutenergyovera60-yearperiod.Severalimportant
experimentswerecarriedoutattheendoftheeighteenthcenturyandthefirsthalfof
the nineteenth century, the most prominent being made by the British American-
bornBenjaminThompson,theBritishHumphryDavy,theGermannaturalscientist
Julius Robert Mayer and the brilliant experimentalist James Prescott Joule
(England). Mayer, working at the time as a doctor on a ship sailing around the
world, noticedtheunusual colourofvenous bloodofshipmen whenstaying inthe
warmequatorialpartsoftheworld.Thisobservationstartedhisobsessioninthinking
aboutenergy,workandheat.Itledultimatelytoascientificpaperpublishedin1842,
in which the first law of thermodynamics was formulated as an idea. It was Joule
who produced the precise experimental evidence, which really established the first
law.Joulepublishedhisfindingsin1843(firstinapreliminaryform),in1847(the
paper was rejected after submission) andfinallyin1849. Thisimportantpaper had
the title “On the mechanical equivalent of heat”. The first law expressed in mathe-
matical terms was delivered in slightly different forms by several scientists,
©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2020 1
U.W.Gedde,EssentialClassicalThermodynamics,SpringerBriefsinPhysics,
https://doi.org/10.1007/978-3-030-38285-8_1
2 1 AnIntroductiontoThermodynamicsandtheFirstLaw
Heat (q) + work (w) Heat (q) + work (w) Heat (q) + work (w)
Matter (mDn) Matter (mDn) Matter (mDn)
Open system Closed system Isolated system
Fig.1.1 Schematicrepresentationofthreedifferentthermodynamicsystems
Hermann von Helmholtz (1847), Rudolf Clausius (1850) and William Rankine
(1850).
The first law states that energy cannot be produced; it can only be transformed
from one form to another or, differently formulated, transferred from or to the
surroundingsof a given system (Fig. 1.1). The energy of the universe, whichis an
isolated system, is constant. Outside the universe nothing exists, and there can
thereforebenotransferofenergytoandfromtheuniverse.
Figure1.1showsthreedifferenttypesofsystem:
(cid:129) Anopensystem(likethebodyofalivinghuman)canexchangeheat(q),work(w)
andmatter(μΔn)withitssurroundings.
(cid:129) A closed system cannot exchange matter but certainly heat and work with the
surroundings.Anexampleofaclosedsystemisatightmetalcontainer.
(cid:129) Anisolatedsystemcannotexchangeenergyinanyofthethreetransferforms.As
already noted, an example is the universe. A perfect thermos flask is another
example.
Thefollowingequationsaremathematicalformulationsofthefirstlaw.Equation
(1.1)describesanopensystem,Eq.(1.2)aclosedsystemandEq.(1.3)theconstant
internalenergyofanisolatedsystem,e.g.theuniverse:
dU ¼dqþdwþμdn;ΔU ¼qþwþμΔn ð1:1Þ
dU ¼dqþdw;ΔU ¼qþw ð1:2Þ
dU ¼0;ΔU ¼0 ð1:3Þ
wheredUisthetotaldifferentialoftheinternalenergy(unit:joule,J),dqanddware
thedifferentialquantitiesofrespectivelyheatandwork(unitofboth:joule,J),μis
the chemical potential (unit: joule per mole, J mol(cid:2)1) and dn is the differential
change in the number of moles of matter. An alternative way of describing these
