A Treatise Of Heat And Energy

312 Pages·2020·6.822 MB·English

by  Lin-Shu Wang

Mechanical Engineering Series
Lin-Shu Wang
A Treatise
of Heat and
Energy
Mechanical Engineering Series
Series Editor
Francis A. Kulacki, Department of Mechanical Engineering,
University of Minnesota, Minneapolis, MN, USA
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Lin-Shu Wang
A Treatise of Heat
and Energy
123
Lin-Shu Wang
StonyBrookUniversity
StonyBrook, NY,USA
ISSN 0941-5122 ISSN 2192-063X (electronic)
MechanicalEngineering Series
ISBN978-3-030-05745-9 ISBN978-3-030-05746-6 (eBook)
https://doi.org/10.1007/978-3-030-05746-6
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HeatandworkflowforaCarnotcycle,whichisanexampleofextractingfromtheheatsink
reservoir“heatoftheamount,QH(cid:1)QC”,(thatwouldhavebeenlostinaspontaneousheattransfer
process)fortheproductionofwork,W=QH(cid:1)QC.
To Ming
Preface
Thermodynamic understanding of heat and energy is based on the mechanical
theory of heat (MTH), which resulted from the synthesis, by Kelvin and Clausius,
of Carnot’s theory of heat and the Mayer–Joule principle. Yet, there are no good
definitionsforheatorenergyinthecurrentliteratureonthermodynamics.Itisnoted
that the advent of the entropy principle created the scientific stream of thermody-
namics(anewstreambranchedofffromitsoriginalsource,theengineeringstream)
and led to, in quick succession, the successful formulation of equilibrium ther-
modynamics. Here, I make the case that the impression of the Kelvin–Clausius
synthesis’ success is formed from its success in producing a coherent system of
equilibrium thermodynamics, not in resulting in a coherent system of engineering
stream of thermodynamics—the failure of which is reflected in the fact that engi-
neering thermodynamics cannot even talk about heat and energy without
self-contradictionsaswellasfailtoprovidestudentsofthermodynamicsrealgrasp
on reversibility. This disquisition–essay makes the case that the uneven achieve-
ment of Joule, Kelvin, and Clausius is because they made the classic error of
equating correlation between heat and work to causality between heat and work,
and, as a result, prevented the (later) formulation of the entropy principle from
realizingitsfullpower.Whilethiserrorhasbeenpointedoutinanumberofpapers,
the authors of those papers advocated, for removing the error, a return to Carnot’s
theoryasacalorictheoryofheat.Thatwasclearlyamistake:itisarguedherethat
Carnot’stheoryisarelationaltheoryofheatnotanontologicaltheoryand,infact,it
can be made to incorporate with, ontologically, either the caloric theory or MTH.
This disquisition essay presents a relational, i.e., predicative, theory of heat
embracing fully MTH’s ontology for an updated understanding of heat, sponta-
neous energy conversion, and reversible-like processes.
Stony Brook, USA Lin-Shu Wang
ix
Contents
1 Introduction: Temperature and Some Comment on Work . . . . . . . 1
1.1 Heat, Its Two Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thermal Equilibrium and Temperature. . . . . . . . . . . . . . . . . . . 4
1.3 Thermodynamic Systems and the General Concept
of Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Nonequilibrium and Irreversibility. . . . . . . . . . . . . . . . 8
1.4 Dimension and Unit of Temperature . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Universal Constants: Dimensionless Conversion
Factors and Dimensional Universal Constants . . . . . . . 10
1.5 Thermal Equation of State for Ideal Gases . . . . . . . . . . . . . . . . 11
1.6 Mixtures of Ideal Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 Work . . . . . . .R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 Calculation of pdV for “Quasi-static Processes”. . . . . . . . . . . 17
1.9 Difference Between a Mass Body and a Thermodynamic
System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.9.1 Quasi-static Process and Work Reservoir. . . . . . . . . . . 20
1.9.2 A Mass Body and a Thermodynamic System:
No Thermodynamic System is an Island . . . . . . . . . . . 21
1.10 Quantity of Heat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Calorimetry and the Caloric Theory of Heat, the Measurement
of Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 Theories of Heat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Direct Heating: Sensible Heat and Latent Heat . . . . . . . . . . . . . 27
2.3 The Doctrine of Latent and Sensible Heats in an Internally
Reversible Medium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Adiabatic Heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
xi
xii Contents
3 The First Law: The Production of Heat and the Principle
of Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Adiabatic Work and Internal Energy . . . . . . . . . . . . . . . . . . . . 38
3.3 Heat Exchange and the First Law of Thermodynamics . . . . . . . 42
3.4 Energy Conservation in a Reversible Universe . . . . . . . . . . . . . 46
3.5 Irreversible Universe: Heat versus Heat . . . . . . . . . . . . . . . . . . 46
3.6 Enthalpy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.7 Heat Capacity and Molar Heat Capacity. . . . . . . . . . . . . . . . . . 48
3.8 Joule’s Law (Joule Free Expansion): The Caloric Equation
of State for Ideal Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.9 Quasi-static Heating and the Adiabatic Transformation
of a Gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.9.1 Isochoric processes. . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.9.2 Isobaric processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.9.3 Adiabatic Transformation of an Ideal Gas . . . . . . . . . . 53
3.10 Energy Analyses of Processes in Open Systems . . . . . . . . . . . . 56
3.11 The Story of Heat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Carnot’s Theory of Heat, and Kelvin’s Adoption
of Which in Terms of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1 Unidirectional Nature of Processes and the Production
of Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 The Carnot Cycle and Carnot’s Principle . . . . . . . . . . . . . . . . . 64
4.3 The Absolute Thermodynamic Temperature . . . . . . . . . . . . . . . 67
4.3.1 Carnot’s Reversible Efficiency. . . . . . . . . . . . . . . . . . . 70
4.4 Carnot’s Function and Kelvin’s Resolution of the Conflict
Between MEH and Carnot’s Principle . . . . . . . . . . . . . . . . . . . 70
4.5 Falling of Caloric in Reversible Processes . . . . . . . . . . . . . . . . 74
4.5.1 Absolute Thermodynamic Temperature
and the Ideal-Gas Thermometric Temperature . . . . . . . 74
4.5.2 Falling of Caloric. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5.3 The Carnot Formula and the Kelvin Formula. . . . . . . . 79
4.5.4 Caloric or Heat: Interpreted as Both Heat Flow
and “Entropy” Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5.5 Equivalence of the Clausius Statement
and the Kelvin-Planck Statement. . . . . . . . . . . . . . . . . 81
4.6 Limitation in the Amount of Heat to be Converted into
Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81