Preface |
|
xvii | |
Acknowledgements |
|
xx | |
|
Principles of Probability |
|
|
1 | (26) |
|
Principles of Probability Are the Foundations of Entropy |
|
|
1 | (1) |
|
|
2 | (1) |
|
|
3 | (4) |
|
Correlated Events/Conditional Probabilities |
|
|
7 | (2) |
|
|
9 | (4) |
|
|
13 | (4) |
|
Averages, Standard Deviations |
|
|
17 | (4) |
|
|
21 | (3) |
|
|
24 | (2) |
|
|
26 | (1) |
|
Extremum Principles Predict Equilibria |
|
|
27 | (10) |
|
What Are Extremum Principles? |
|
|
27 | (1) |
|
What Is a State of Equilibrium? |
|
|
28 | (2) |
|
|
30 | (1) |
|
|
31 | (4) |
|
|
35 | (1) |
|
|
36 | (1) |
|
|
36 | (1) |
|
|
37 | (12) |
|
Heat Flows to Maximize Entropy |
|
|
37 | (1) |
|
|
37 | (3) |
|
Heat Was Thought to Be a Fluid |
|
|
40 | (2) |
|
Atoms and Molecules Have Energies |
|
|
42 | (2) |
|
|
44 | (2) |
|
|
46 | (2) |
|
|
48 | (1) |
|
|
48 | (1) |
|
Math Tools: Series and Approximation |
|
|
49 | (12) |
|
Physical Modelling Involves Series Expansions |
|
|
49 | (4) |
|
Making Approximations Involves Truncating Series' |
|
|
53 | (4) |
|
Gaussian Distribution/Random Walk |
|
|
57 | (2) |
|
|
59 | (1) |
|
|
60 | (1) |
|
|
60 | (1) |
|
|
61 | (20) |
|
Functions of Multiple Variables |
|
|
61 | (1) |
|
|
62 | (3) |
|
Extrema of Multivariate Functions |
|
|
65 | (8) |
|
Integrating Multivariate Functions |
|
|
73 | (4) |
|
|
77 | (1) |
|
Rearranging Dependent and Independent Variables |
|
|
78 | (1) |
|
|
79 | (1) |
|
|
80 | (1) |
|
|
80 | (1) |
|
Entropy & the Boltzmann Distribution Law |
|
|
81 | (24) |
|
|
81 | (4) |
|
Flat Distributions if there Are No Constraints |
|
|
85 | (1) |
|
Exponential Distributions if there Are Constraints |
|
|
86 | (3) |
|
Principle of Fair Apportionment |
|
|
89 | (10) |
|
Philosophical Foundations |
|
|
99 | (2) |
|
|
101 | (1) |
|
|
102 | (1) |
|
|
103 | (2) |
|
Thermodynamic Driving Forces |
|
|
105 | (26) |
|
Thermodynamics Is Two Laws |
|
|
105 | (2) |
|
The Fundamental Thermodynamic Equations |
|
|
107 | (1) |
|
Defining the Thermodynamic Driving Forces |
|
|
108 | (3) |
|
|
111 | (1) |
|
Thermal, Mechanical, and Chemical Equilibria |
|
|
111 | (8) |
|
|
119 | (3) |
|
The First Law Interrelates Heat, Work, and Energy |
|
|
122 | (4) |
|
Why Is There an Absolute Temperature Scale? |
|
|
126 | (1) |
|
Other Statements of the Second Law |
|
|
127 | (1) |
|
|
127 | (1) |
|
|
128 | (1) |
|
|
128 | (3) |
|
|
131 | (22) |
|
Switching from Entropy to Free Energy |
|
|
131 | (1) |
|
Free Energy Defines Another Extremum Principle |
|
|
132 | (10) |
|
|
142 | (4) |
|
Using Thermodynamic Cycles |
|
|
146 | (4) |
|
|
150 | (1) |
|
|
151 | (1) |
|
|
152 | (1) |
|
Maxwell's Relations & Mixtures |
|
|
153 | (18) |
|
Predicting Unmeasurable Quantities |
|
|
153 | (2) |
|
Maxwells Relations Interrelate Partial Derivatives |
|
|
155 | (8) |
|
Multicomponent Systems/Partial Molar Quantities |
|
|
163 | (3) |
|
|
166 | (2) |
|
|
168 | (1) |
|
|
169 | (1) |
|
|
169 | (2) |
|
Boltzmann Distribution Law |
|
|
171 | (22) |
|
Probability Distributions for Atoms and Molecules |
|
|
171 | (2) |
|
The Boltzmann Law Describes Equilibria |
|
|
173 | (4) |
|
What Does a Partition Function Tell You? |
|
|
177 | (6) |
|
Thermodynamic Properties from Partition Functions |
|
|
183 | (5) |
|
|
188 | (1) |
|
|
189 | (1) |
|
|
190 | (1) |
|
|
191 | (2) |
|
Statistical Mechanics of Simple Gases and Solids |
|
|
193 | (28) |
|
Macroscopic Properties from Atomic Structures |
|
|
193 | (2) |
|
|
195 | (6) |
|
Harmonic Oscillator Model |
|
|
201 | (2) |
|
|
203 | (3) |
|
|
206 | (6) |
|
The Equipartition Theorem |
|
|
212 | (4) |
|
|
216 | (1) |
|
|
217 | (2) |
|
|
219 | (2) |
|
Temperature, Heat Capacity |
|
|
221 | (14) |
|
A Microscopic Perspective |
|
|
221 | (4) |
|
A Graphical Procedure, from S to Cv |
|
|
225 | (2) |
|
What Drives Heat Exchange? |
|
|
227 | (1) |
|
The Heat Capacity Reflects Energy Fluctuations |
|
|
228 | (4) |
|
|
232 | (1) |
|
|
233 | (1) |
|
|
234 | (1) |
|
|
235 | (16) |
|
Chemical Equilibria from Atomic Structures |
|
|
235 | (8) |
|
|
243 | (1) |
|
Temperature Dependence of Equilibrium |
|
|
244 | (4) |
|
|
248 | (1) |
|
|
249 | (1) |
|
|
249 | (2) |
|
Equilibria Between Liquids, Solids, and Gases |
|
|
251 | (16) |
|
|
251 | (5) |
|
|
256 | (3) |
|
How Do Refrigerators and Heat Pumps Work? |
|
|
259 | (3) |
|
|
262 | (2) |
|
|
264 | (1) |
|
|
265 | (1) |
|
|
265 | (2) |
|
|
267 | (12) |
|
A Lattice Model Describes Mixtures |
|
|
267 | (6) |
|
|
273 | (2) |
|
|
275 | (1) |
|
|
276 | (1) |
|
|
277 | (1) |
|
|
277 | (2) |
|
Solvation and Transfers of Molecules Between Phases |
|
|
279 | (22) |
|
|
279 | (1) |
|
|
280 | (2) |
|
Activity and Activity Coefficient |
|
|
282 | (3) |
|
|
285 | (3) |
|
Freezing Point Depression |
|
|
288 | (1) |
|
|
289 | (2) |
|
Solutes Can Transfer and Partition |
|
|
291 | (3) |
|
|
294 | (3) |
|
|
297 | (1) |
|
|
298 | (3) |
|
|
301 | (14) |
|
Vectors Describe Forces and Flows |
|
|
301 | (1) |
|
Vectors Add and Subtract by Components |
|
|
301 | (1) |
|
|
302 | (1) |
|
|
303 | (5) |
|
The Flux of a Vector Field |
|
|
308 | (2) |
|
|
310 | (1) |
|
|
311 | (3) |
|
|
314 | (1) |
|
|
315 | (26) |
|
Forces Drive Molecules to Flow |
|
|
315 | (1) |
|
Linear Laws Relate Forces to Flows |
|
|
316 | (2) |
|
|
318 | (6) |
|
Sources and Sinks: Examples from Population Biology |
|
|
324 | (2) |
|
|
326 | (1) |
|
The Einstein-Smoluchowski Equation |
|
|
327 | (3) |
|
|
330 | (3) |
|
The Fluctuation-Dissipation Theorem |
|
|
333 | (2) |
|
Onsager Reciprocal Relations Describe Coupled Flows |
|
|
335 | (2) |
|
|
337 | (1) |
|
|
338 | (1) |
|
|
339 | (2) |
|
Chemical Kinetics & Transition States |
|
|
341 | (28) |
|
Rates Depend on Temperature |
|
|
341 | (1) |
|
Rates Are Proportional to Concentrations |
|
|
341 | (1) |
|
At Equilibrium, Rates Obey Detailed Balance |
|
|
342 | (2) |
|
Mass Action Laws Describe Mechanisms |
|
|
344 | (1) |
|
Reaction Rates Depend on Temperature |
|
|
345 | (3) |
|
Activated Processes and Transition State Theory |
|
|
348 | (8) |
|
Catalysts Speed Up Chemical Reactions |
|
|
356 | (3) |
|
|
359 | (4) |
|
Funnel Landscapes and Diffusional Processes |
|
|
363 | (1) |
|
|
364 | (2) |
|
|
366 | (1) |
|
|
367 | (2) |
|
|
369 | (18) |
|
Charges and Coulomb's Law |
|
|
369 | (1) |
|
Charge Interactions are Long-Ranged |
|
|
370 | (3) |
|
Charge Interactions Are Weaker in Media: Dielectric Constants |
|
|
373 | (2) |
|
Electrostatic Forces Add Like Vectors |
|
|
375 | (1) |
|
What Is an Electrostatic Field? |
|
|
376 | (2) |
|
Electric Fields Have Fluxes |
|
|
378 | (6) |
|
|
384 | (1) |
|
|
385 | (1) |
|
|
385 | (2) |
|
The Electrostatic Potential |
|
|
387 | (22) |
|
Electrostatic Potentials with Electrostatic Fields |
|
|
387 | (5) |
|
Dipoles Are Separated Charges |
|
|
392 | (3) |
|
|
395 | (4) |
|
|
399 | (7) |
|
|
406 | (1) |
|
|
407 | (1) |
|
|
407 | (2) |
|
Electrochemical Equilibria |
|
|
409 | (24) |
|
Electrochemical Potentials in Ionic Solutions |
|
|
409 | (1) |
|
|
410 | (7) |
|
Voltage-Gated Ion Channels |
|
|
417 | (1) |
|
Acid-Base Equilibria Are Shifted by Electrostatic Fields |
|
|
418 | (2) |
|
Electrostatic Gradients Cause Ion Flows |
|
|
420 | (3) |
|
Creating Charge Distribution Costs Free Energy |
|
|
423 | (7) |
|
|
430 | (1) |
|
|
431 | (1) |
|
|
432 | (1) |
|
Salt Ions Shield Charged Objects |
|
|
433 | (16) |
|
Salts Dissociate and Shield Other Charges |
|
|
433 | (7) |
|
Strong and Weak Electrolytes |
|
|
440 | (4) |
|
|
444 | (2) |
|
|
446 | (1) |
|
|
447 | (2) |
|
Intermolecular Interactions |
|
|
449 | (18) |
|
Short-ranged Repulsions and Long-ranged Attractions |
|
|
449 | (1) |
|
Short-ranged Attractions Are Electrostatic |
|
|
450 | (7) |
|
The van der Waals Gas Model |
|
|
457 | (5) |
|
The Lattice Model Contact Energy |
|
|
462 | (1) |
|
|
463 | (1) |
|
|
464 | (1) |
|
|
465 | (2) |
|
|
467 | (26) |
|
Two States Can Be Stable at the Same Time |
|
|
467 | (1) |
|
Liquids or Solids Mix at High Temperatures |
|
|
468 | (3) |
|
Phase Separations Are Driven to Lower the Free Energy |
|
|
471 | (6) |
|
|
477 | (1) |
|
|
478 | (1) |
|
The Principles of Boiling |
|
|
479 | (6) |
|
Boiling a Liquid Mixture Involves Two Transitions |
|
|
485 | (2) |
|
|
487 | (1) |
|
|
488 | (3) |
|
|
491 | (2) |
|
|
493 | (22) |
|
Abrupt Transitions Occur in Many Different Systems |
|
|
493 | (1) |
|
Transitions and Critical Points Are Universal |
|
|
493 | (3) |
|
|
496 | (3) |
|
|
499 | (9) |
|
The Ising Model Describes Magnetization |
|
|
508 | (1) |
|
The Kinetics of Phase Transitions and Nucleation |
|
|
509 | (2) |
|
|
511 | (1) |
|
|
512 | (3) |
|
Adsorption, Binding & Catalysis |
|
|
515 | (18) |
|
Binding and Adsorption Processes Are Saturable |
|
|
515 | (1) |
|
|
515 | (4) |
|
Binding and Saturation in Solution |
|
|
519 | (2) |
|
The Principle of Adsorption Chromatography |
|
|
521 | (1) |
|
|
522 | (5) |
|
Sabatier's Principle for Stabilizing Transition States |
|
|
527 | (2) |
|
|
529 | (1) |
|
|
530 | (1) |
|
|
531 | (2) |
|
Multi-site Cooperative Ligand Binding |
|
|
533 | (30) |
|
|
534 | (2) |
|
The Two-site Model of Binding Cooperativity |
|
|
536 | (3) |
|
Binding Intermediate States |
|
|
539 | (2) |
|
Constructing Binding Polynomials from Rules of Probability |
|
|
541 | (5) |
|
Oxygen Binding to Hemoglobin |
|
|
546 | (4) |
|
|
550 | (2) |
|
Model of McGhee and von Hippel |
|
|
552 | (4) |
|
Rates Can Often Be Treated by Using Binding Polynomials |
|
|
556 | (1) |
|
|
556 | (2) |
|
|
558 | (1) |
|
|
559 | (3) |
|
|
562 | (1) |
|
|
563 | (14) |
|
Water Is an Unusual Liquid |
|
|
563 | (1) |
|
Water Has Hydrogen Bonded Structure |
|
|
563 | (5) |
|
Pure Water Has Anomalous Properties |
|
|
568 | (7) |
|
|
575 | (1) |
|
|
576 | (1) |
|
|
576 | (1) |
|
|
577 | (16) |
|
Oil and Water Don't Mix: The Hydrophobic Effect |
|
|
577 | (1) |
|
Signature of Hydrophobicity: Its Temperature Dependence |
|
|
578 | (4) |
|
Water Is Structured Near Cavities and Planar Surfaces |
|
|
582 | (3) |
|
Alcohols Constrict the Volumes of Aqueous Mixtures |
|
|
585 | (1) |
|
Ions Can Make or Break Water Structure |
|
|
586 | (2) |
|
|
588 | (1) |
|
|
589 | (1) |
|
|
590 | (1) |
|
|
591 | (2) |
|
|
593 | (16) |
|
Polymers Are Governed by Statistics |
|
|
593 | (1) |
|
Polymers Have Distributions of Conformations |
|
|
593 | (1) |
|
Polymer Solutions Differ from Small Molecule Solutions |
|
|
594 | (2) |
|
|
596 | (5) |
|
Nonideal Colligative Properties |
|
|
601 | (1) |
|
The Phase Behavior of Polymers |
|
|
601 | (4) |
|
Dilution Entropy Drives Solute Partitioning into Polymers |
|
|
605 | (1) |
|
|
606 | (1) |
|
|
607 | (1) |
|
|
608 | (1) |
|
|
609 | (20) |
|
Polymeric Materials Are Elastic |
|
|
609 | (4) |
|
Random-flight Chains Are Gaussian |
|
|
613 | (1) |
|
Polymer Elasticity Follows Hooke's Law |
|
|
614 | (5) |
|
Elasticity of Rubbery Materials |
|
|
619 | (2) |
|
Polymer Collapse and Expansion |
|
|
621 | (5) |
|
|
626 | (1) |
|
|
627 | (1) |
|
|
627 | (2) |
|
Polymers Resist Confinement & Deformation |
|
|
629 | (16) |
|
|
629 | (2) |
|
Chain Conformations Are Perturbed Near Surfaces |
|
|
631 | (3) |
|
Polymer Conformations by a Diffusion Equation Method |
|
|
634 | (2) |
|
Polymers Tend to Avoid Confined Spaces |
|
|
636 | (2) |
|
The Rouse-Zimm Model of Polymer Dynamics |
|
|
638 | (2) |
|
|
640 | (2) |
|
|
642 | (1) |
|
|
643 | (1) |
|
|
643 | (2) |
Appendix A Table of Constants |
|
645 | (1) |
Appendix B Table of Units |
|
646 | (1) |
Appendix C Useful Taylor Series Expansions |
|
647 | (1) |
Appendix D Useful Integrals |
|
648 | (1) |
Appendix E Multiples of Units, Their Names, and Symbols |
|
649 | (2) |
Index |
|
651 | |