Entropy for Biologists (eBook)

Front Cover 1
Entropy for Biologists: An Introduction 
4 
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 12
CHAPTER I. TEMPERATURE 18
A. INTRODUCTION 18
B. PHYSIOLOGICAL TEMPERATURE 20
C. EMPIRICAL THERMOMETERS 20
D. GAS-LAW THERMOMETERS 21
PROBLEMS 23
CHAPTER II. ENERGY 24
A. MECHANICAL ENERGY 25
B. CONSERVATION OF ENERGY 26
C. THERMAL ENERGY 30
PROBLEMS 31
CHAPTER III. INTRODUCTION TO KINETIC THEORY 32
PROBLEMS 40
CHAPTER IV. TOTAL ENERGY 42
A. THE MEASURABILITY OF ENERGY 42
B. THE FIRST LAW OF THERMODYNAMICS 44
PROBLEMS 47
CHAPTER V. THE SECOND LAW OF THERMODYNAMICS 48
A. HEAT ENGINES AND REFRIGERATORS 49
B. STATEMENTS OF THE SECOND LAW 50
C. CARNOT CYCLES 52
D. CARNOT THEOREMS 56
E. THE THERMODYNAMIC TEMPERATURE SCALE 58
PROBLEMS 61
CHAPTER VI. THE ENTROPY FUNCTION 62
A. STATE FUNCTIONS 62
B. INTEGRALS OF dQ 65
C. PROPERTIES OF THE ENTROPY FUNCTION 66
D. THE MEASURABILITY OF ENTROPY 73
E. THE THIRD LAW OF THERMODYNAMICS 74
F. ENTROPY AND CHEMICAL REACTIONS 74
PROBLEMS 77
CHAPTER VII. PROBABILITY AND INFORMATION 78
A. PROBABILITY 78
B. INFORMATION THEORY 83
PROBLEMS 88
CHAPTER VIII. INTRODUCTION TO STATISTICAL MECHANICS 90
A. THE STATISTICAL POINT OF VIEW 90
B. THE QUANTUM MECHANICAL DESCRIPTION OF SYSTEMS 94
C. THE ENSEMBLE APPROACH 98
D. THE MOST PROBABLE DISTRIBUTION 99
E. THE MAXWELL-BOLTZMANN DISTRIBUTION 102
PROBLEMS 105
CHAPTER IX. THE RELATION BETWEEN STATISTICAL MECHANICS AND THERMODYNAMICS 106
A. EQUIVALENT FORMULATIONS 106
B. THE PARTITION FUNCTION 110
C. HELMHOLTZ FREE ENERGY 110
D. CLASSICAL STATISTICAL MECHANICS 111
E. VELOCITY DISTRIBUTION FUNCTION 113
F. INTERNAL DEGREES OF FREEDOM 116
PROBLEMS 120
CHAPTER .. ENTROPY, INFORMATION, AND ENERGY 122
A. INFORMATION AND FNTROPY 122
., MAXWELL'S DEMON 125
PROBLEMS 128
CHAPTER XI. FREE-ENERGY FUNCTIONS 130
A. GIBBS FREE ENERGY 130
B. HELMHOLTZ FREE ENERGY 132
C. GENERALIZED ENERGY FUNCTION 133
D. ENTHALPY AND STANDARD STATES 135
E. THE EULER EQUATION 137
F. ACTIVITY 139
G. THE USE OF ALTERNATIVE METHODS 145
PROBLEMS 148
CHAPTER XII. THERMAL ENERGY 150
A. ORDER AND DISORDER 150
B. DIFFUSION 152
C. BROWNIAN MOTION 158
PROBLEMS 160
CHAPTER XIII. APPLICATIONS OF THE GIBBS FREE ENERGY AND THE GIBBS CHEMICAL POTENTIAL 162
A. ELECTROCHEMISTRY 162
B. SURFACE CHEMISTRY 166
C. THE PHASE RULE 169
D. OSMOTIC PRESSURE 170
PROBLEMS 172
CHAPTER XIV. MEASUREMENT IN THERMAL PHYSICS 174
CHAPTER XV. ENTROPY AND BIOLOGY 182
Appendix I: CONSERVATION OF MECHANICAL ENERGY: GENERAL TREATMENT 188
Appendix II: THE PROOF OF THE EQUIVALENCE OF THE PERFECT-GAS TEMPERATURE SCALE AND THE ABSOLUTE THERMODYNAMIC TEMPERATURE SCALE 194
Appendix III: ENTROPY OF A PERFECT GAS 202
Appendix IV: STIRLING'S APPROXIMATION 204
Appendix V: EVALUATION OF THE PARTITION FUNCTION OF A PERFECT GAS 206
INDEX 208