THE NATURE OF THERMODYNAMICS

By EMMA JACKSON

CONTENTS INTRODUCTION CLASSICAL THERMODYNAMICS AND ITS CHALLENGES GEOMETRIC VERSUS ALGEBRAIC APPROACHES THE FOCUS OF THE BOOK THE ROADMAP FOR THE BOOK THE SEQUENCES OF PROPOSITIONS STATES AND PROCESSES THE CLASSI?CATION OF THERMODYNAMIC VARIABLES GLOBAL AND LOCAL VARIABLES, AND EQUILIBRIUM THERMAL, DEFORMATION AND MASS VARIABLES EXTENSIVE AND INTENSIVE VARIABLES, AND SCALING CONTROLLED AND UNCONTROLLED VARIABLES CONJUGATE VARIABLES AND EQUATIONS OF STATE VARIABLES AND STATES THE COMPOSITION OF SYSTEMS SYSTEMS, FAMILIES AND SCALING SCALING AND EXTENSIVITY COMPOSITION AND SCALING FAMILIES OF SYSTEMS ONE-DIMENSIONAL SYSTEMS PROCESSES: CONTROLLABILITY AND ACHIEVABILITY PROCESSES AND ACCESSIBILITY: AXIOMS A–I TO A–VI EQUILIBRIUM PROCESSES AND REVERSIBILITY QUALI?ED ACCESSIBILITY STRICT EQUILIBRIUM PROCESSES DEMARCATED EQUILIBRIUM PROCESSES COMPARISON OF DEMARCATED AND DELIMITED EQUILIBRIUM PROCESSES THE ROLE OF CURVES ACCESSIBILITY AND RECOVERABILITY ADIABATIC PROCESSES AND THE FIRST LAW EXPLICATING ADIABATIC PROCESSES ADIABATIC ACCESSIBILITY: AXIOMS AA–I TO AA–VII THE FIRST LAW: WORK AND INTERNAL ENERGY THE ADIABATIC WORK FUNCTION INTERNAL ENERGY NON-ADIABATIC PROCESSES CARATHÉODORY’S PRINCIPLE AND THE SECOND LAW: ADIABATIC COMPARABILITY AND IRRECOVERABILITY CARATHÉODORY’S STATEMENT OF THE SECOND LAW FORWARD SECTORS AND THE ADIABATIC-ACCESSIBILITY AXIOMS CONSEQUENCES OF CARATHÉODORY’S PRINCIPLE CONSEQUENCES OF THE ADIABATIC-ACCESSIBILITY AXIOMS ADIABATIC COMPARABILITY AND IRRECOVERABILITY THE NON-TRIVIALITY OF FORWARD SECTORS THE SITUATION AT THIS POINT: WHAT HAS BEEN ACHIEVED? SIMPLE SYSTEMS THE SIMPLE-SYSTEM AXIOMS AND THE SECOND LAW THE QUESTION OF SYSTEMS OF VARYING MASS PHILOSOPHICAL RAMI?CATIONS POSITIVE-SIMPLE AND NEGATIVE-SIMPLE SYSTEMS THERMAL EQUILIBRIUM AND THE ZEROTH LAW THERMAL PROPERTIES THERMAL JOINING AND EQUILIBRATION THERMAL SPLITTING THE THERMAL AXIOMS T–I TO T–V THERMAL SPLITTINGS AND ISOTHERMS THE STATES XLX, XUX ??[M ] SINGLE-SYSTEM ENTROPY THE STATES XL, XU ??[M ] THE PRE-ENTROPY FUNCTION ?(X) THE LIEB–YNGVASON MACHINE PROPERTIES THE SINGLE-SYSTEM ENTROPY FUNCTIONS ENTROPY ENTROPY CALIBRATION THE ENTROPY FUNCTIONS S(±)(X) DE?NITIONS, UNIQUENESS AND EXTENSITIVITY EXISTENCE ADIABATS THE EXISTENCE OF CALIBRATION STATES FOR PAIRS OF SYSTEMS PRACTICAL MATTERS ACHIEVING CONSISTENCY FOR ENTROPY FINDING ENTROPY CALIBRATION STATES TEMPERATURE THE EXISTENCE OF TEMPERATURE A CLASSI?CATION OF SYSTEMS THE PROPERTIES OF TEMPERATURE TEMPERATURE BOUNDS ADIABATS AND ISOTHERMS REVISITED ENTROPY, TEMPERATURE AND MUTUAL THERMAL EQUILIBRIUM THERMOMETERS AND RESERVOIRS A SINGLE THERMOMETER THE ENTROPY OF THERMOMETERS ENTROPY WITHOUT THE TRANSVERSALITY AXIOM T–IV CYCLES AND COMPARISONS OF VERSIONS OF THE SECOND LAW VERSIONS OF THE SECOND LAW THE RELATIONSHIP BETWEEN THE KELVIN–PLANCK VERSION OF THE SECOND LAW AND THOSE DUE TO CARATHÉODORY PROCESSES INVOLVING IT-RESERVOIRS AN EQUILIBRATION PROCESS AN ISOTHERMAL PROCESS COMPLETING THE CYCLE REVISITING THE KELVIN–PLANCK AND CLAUSIUS VERSIONS OF THE SECOND LAW MODI?CATIONS OF THE KELVIN–PLANCK AND CLAUSIUS VERSIONS OF THE SECOND LAW POSITIVE AND NEGATIVE TEMPERATURES POSITIVE AND NEGATIVE TEMPERATURES, NON-INCREASING AND NON-DECREASING ENTROPY THE RELATIONSHIP BETWEEN THE MODI?ED KELVIN–PLANCK VERSION OF THE SECOND LAW AND THAT DUE TO CARATHÉODORY PROCESSES BETWEEN POSITIVE AND NEGATIVE TEMPERATURES A GEOMETRIC ROUTE TO ENTROPY AND TEMPERATURE THE FIRST LAW REVISITED THE SECOND LAW AND EMPIRICAL ENTROPY THE ROLES OF CTH?I AND CTH?II THE LOCAL NATURE OF CARATHÉODORY’S THEOREM BOYLING’S DERIVATION OF A GLOBAL INTEGRAL OF THE HEAT FORM THE ZEROTH LAW AND EMPIRICAL TEMPERATURE THE EMPIRICAL NATURE OF EMPIRICAL TEMPERATURE THE DERIVATION OF ENTROPY AND TEMPERATURE ENERGY AND ENTROPY CHANGES IN ADIABATIC PROCESSES APPROACH I: TREATING ENTROPY S AS AN INDEPENDENT VARIABLE APPROACH II: TREATING INTERNAL ENERGY U AS AN INDEPENDENT VARIABLE THE EXTENSIVITY OF THERMODYNAMIC FUNCTIONS CONCLUSIONS AND COMPARISONS PHASE TRANSITIONS AND CRITICAL PHENOMENA THE CLASSI?CATION OF PHASE TRANSITIONS UNIVERSALITY SIZE SCALING AND DENSITIES THE GEOMETRY OF PHASE TRANSITIONS A TWO-DIMENSIONAL PHASE SPACE CLASSICAL METHODS CRITICAL POINT AND COEXISTENCE CURVE CRITICAL EXPONENTS AND INEQUALITIES LANDAU EXPANSIONS SCALING THEORY A CRITICAL CURVE A CRITICAL POINT AND COEXISTENCE CURVE: SCALING LAWS CLASSICAL EXPONENTS AT A CRITICAL POINT SCALING AND UNIVERSALITY NON-EQUILIBRIUM THEORY THE LIEB AND YNGVASON ACCOUNT THE EXTENSION OF ?[M ] TO NON-EQUILIBRIUM STATES THE CONTINUOUS FLUID MODEL IN CIT A NOTE ON DIMENSIONS THE RATE OF CHANGE OF SPECI?C VOLUME THE RATE OF CHANGE OF INTERNAL ENERGY THE RATE OF CHANGE OF ENTROPY AND THE LOCAL EQUILIBRIUM HYPOTHESIS THE PHENOMENOLOGICAL ASSUMPTION THE DETERMINATION OF NON-EQUILIBRIUM STATES THE RELATIONSHIP BETWEEN THE APPROACHES OF LIEB AND YNGVASON AND CIT ADIABATIC PROCESSES REVISITED THE POSSIBILITY OF A UNIQUE NON-EQUILIBRIUM ENTROPY IN THE LIEB–YNGVASON APPROACH