Thermodynamics: Basic Principles and Engineering Applications

328 Pages·2019·12.726 MB·English

by  Alan M. Whitman

Mechanical Engineering Series
Alan M. Whitman
Thermodynamics:
Basic Principles
and Engineering
Applications
Mechanical Engineering Series
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Francis A. Kulacki, Department of Mechanical Engineering, University of
Minnesota, Minneapolis, MN, USA
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Alan M. Whitman
Thermodynamics: Basic
Principles and Engineering
Applications
123
AlanM. Whitman
Department ofMechanical Engineering
VillanovaUniversity
Villanova, PA,USA
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ISSN 0941-5122 ISSN 2192-063X (electronic)
MechanicalEngineering Series
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To my wife Rella and to
Karen, Phyllis, Roy, and Noam
Preface
In this text, I have presented thermodynamics as mechanics, fluid mechanics, and
heat transfer are presented, by casting the discussion in terms of familiar mathe-
matical concepts that students have learned previously in three semesters of cal-
culus. I have adopted an axiomatic presentation and have introduced the two laws
of thermodynamics as differential equations for each newly defined variable,
internalenergy,andentropy(inthecaseofentropytwoaxiomsareusedtosimplify
the presentation). Although this approach differs from the inductive manner in
whichthesubjectdevelopedhistoricallyandwhichisthepresentationusedinmost
existingtextbooks,Ibelieveithasmanypedagogicaladvantages;forexample,itis
simpler, discussion of the Maxwell relations and other important thermodynamic
resultsoccurnaturallyinthedevelopmentoftheentropicequationofstate,heating,
and power bounds for special systems including the impossibility of perpetual
motion of the second kind and Carnot's result for heat engines, follow deductively
fromthetwolaws,and,mostimportantly,itmakesthermodynamicsmorepalatable
for students, by making learning it like learning all their other engineering science
courses.
Althoughthetreatmentisdeductiveandtendstobemathematical,Ihavetriedto
make the text student friendly by minimizing the level of abstraction, and by
motivating new concepts by relating them to older, more familiar, ones. In dis-
cussing the properties pressure and temperature, I have included material on their
kinetic theory expressions in order to enhance physical intuition. Further on when
introducing new properties of internal energy and entropy, I have also included
kinetic theory material; in these cases, there is even more benefit since these
properties lack the familiarity of the previous ones. I have used a format for
organizing problem statement data that makes clear whether a problem is properly
stated,andhowtoproceedtowardasolution.Thisformatisapplicabletoallchange
of state problems encountered in thermodynamics including those involving both
open and closed systems. This problem-solving methodology is described initially
in Chap. 2 and is continued throughout the text. Every example in the book is
solved using the same format,the idea being that the repetition will make students
comfortable with the process, and better able to use it on their own. Repetition is
vii
viii Preface
also used in discussing equations of state. In Chap. 2, the mechanical equation of
state is written as a differential equation by differentiating vðtÞ¼v½TðtÞ;pðtÞ(cid:2) and
notingthatthepartialderivativesofspecificvolumewithrespecttotemperatureand
pressure are va and (cid:3)vb respectively; the quantity a is the coefficient of thermal
expansion and b is the isothermal compressibility, each of these being an experi-
mentally determinable quantity defined and discussed in Chap. 1. The equation of
state for specific volume is then found by integrating, which results in integrals
whoseintegrandsareknownquantities.InChap.4,thesameapproachisappliedto
the energetic equation of state uðtÞ¼u½TðtÞ;vðtÞ(cid:2), in this case, the partial deriva-
tivesarec andðc (cid:3)c Þ=ðvaÞrespectively;thequantitiesc andc arethespecific
v p v v p
heats at constant volume and at constant pressure, each of these being an experi-
mentally determinable quantity defined and discussed in Chap. 3. The equation of
state for specific internal energy is then obtained in terms of integrals whose
integrands are likewise known quantities. The enthalpic equation of state is also
treated here in the same way. Finally, in Chap. 5, the same approach is again
applied, this time to the entropic equation of state. In all these instances, the
integrals are evaluated in the special cases of liquids and solids, and ideal and
perfect gases, so that all the simple equations of state are derived from first prin-
ciplesusingrelativelysimplemathematicsthathasbeenlearnedinpreviouscourses
andreviewedinChap.2.Thistacticprovidesacommonthreadthattiestogetherthe
various new concepts that are introduced, as well as a familiar framework into
whichtheyareincorporated.Ihavealsousedamatrixformatforthepropertytables
ofsteamandR-12thathelpsstudentsvisualizethisdata.Thisis,especially,truefor
compressed liquid states. In addition, it makes interpolation near the saturation
curve easier to comprehend and to do.
Itisnecessarytomentionafewthingsaboutnotation.Intheattempttoprovidea
good notation, one is always faced with the dilemma of having it convey more
information,andriskingitbeingconfusingbecauseitconveystoomuch,orhaving
it convey less information, and risking it being confusing because it conveys too
little.Withthisinmind,Ihaveendeavoredtomakesymbolsthatrepresentdifferent
things different. The most important case of this is in distinguishing gauge quan-
tities from absolute ones. Thus, gauge pressure is denoted by p while absolute
g
pressure is denoted by p. Although this is unremarkable, I have also distinguished
the gauge temperatures Fahrenheit, T , and Celsius, T , from each other because
f c
they have different zero points, and distinguished them both from absolute tem-
perature, T, as well. Although most texts do not make these distinctions in tem-
perature measures, I believe they are useful for several reasons; first, when using
them, the same conversion equations apply among these quantities as apply to all
other relative quantities such as location and time, (e.g., T ¼T þ32(cid:4)F) and
f c
second,usingthemminimizesthecommonstudenterrorofusingaT orT valuein
f c
an equation written for T, such as the ideal gas law. I use the same philosophy at
otherplacesinthetext,forexample,QA=B denotestheheattransfertobodyAfrom
bodyB;however,inproblemsinvolvingonlyonebody,wherethereislittlechance
for confusion, I simply use Q to denote the heat transfer to it.
Preface ix
Thebasicstructureofthetext hasbeenheavilyinfluenced by readingworkson
thermodynamics by C. Truesdale, J. Serrin, C. L. Ericksen, and their colleagues.
AlthoughthisbookisbynomeansatextonRationalThermodynamics,Ifoundthat
many of my pedagogical concerns had been already addressed by those authors,
and I believe that I was able to cast much of their thought into a form which is
suitable for a one-semester undergraduate course. Naturally, the responsibility for
using this particular form of presentation is mine alone.
Villanova, PA, USA Alan M. Whitman
April 2019
Contents
1 Measurement and Properties of Matter . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Dimensions and Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Fundamental and Derived Dimensions. . . . . . . . . . . . . . . 6
1.2.2 Absolute and Relative Quantities . . . . . . . . . . . . . . . . . . 9
1.3 Properties of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 Weight and Mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.3 Density and Specific Volume . . . . . . . . . . . . . . . . . . . . . 14
1.3.4 Velocity and Acceleration. . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.5 Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.6 Impulse and Momentum. . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3.7 Work and Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.8 Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3.9 Heating, Hotness, and Temperature. . . . . . . . . . . . . . . . . 32
1.3.10 Coefficient of Thermal Expansion . . . . . . . . . . . . . . . . . . 41
1.3.11 Compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2 Thermostatics of Pure Fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3 The State Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3.1 The Geometry of Curves . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.2 The Geometry of Surfaces . . . . . . . . . . . . . . . . . . . . . . . 55
2.3.3 Thermostatic and Thermodynamic Problems . . . . . . . . . . 60
xi