Physics of Matter: Manchester Physics Series

George King is Emeritus Professor of Physics in the School of Physics & Astronomy at the University of Manchester and Fellow of the Institute of Physics. His research interests are the study of atoms and molecules using synchrotron radiation and electron impact excitation, and he is the author of over 200 published papers describing these studies. He has over 40 years teaching experience that includes lecturing a wide range of undergraduate and postgraduate courses.

Editors' preface to the Manchester Physics Series xv Author's preface xvii 1 Atoms, the constituents of matter 1 1.1 The mass of an atom 1 1.1.1 Atomic masses 4 1.2 The size of an atom 6 1.2.1 Scanning probe microscopy 7 1.3 Atomic structure 11 1.3.1 The Bohr model of the hydrogen atom 12 1.3.2 The Schrodinger equation 17 1.3.3 The Schrodinger equation and the hydrogen atom 25 1.3.4 Multi-electron atoms 36 Problems 1 41 2 The forces that bind atoms together 43 2.1 General characteristics of interatomic forces 43 2.1.1 The range of a force 44 2.1.2 Repulsive and attractive forces 44 2.1.3 Oscillations about the equilibrium separation 46 2.2 Interatomic potential energy 47 2.2.1 The Lennard-Jones 6-12 potential 48 2.3 Types of interatomic bonding 51 2.3.1 van der Waals bonding 51 2.3.2 Repulsive forces between atoms 54 2.3.3 Binding energy and latent heat 54 2.3.4 Ionic bonding 55 2.3.5 The Madelung constant and the Lattice energy 56 2.3.6 Covalent bonding 59 2.3.7 Vibrational motion of a diatomic molecule 61 2.3.8 Metallic bonding 64 2.4 Why gases, liquids, and solids 65 Problems 2 67 3 Thermal energy of atoms and molecules 69 3.1 Temperature and the translational kinetic energy of a molecule 69 3.1.1 The ideal gas equation 71 3.2 Probability distributions and mean values 72 3.2.1 The normal or Gaussian distribution 78 3.3 The Maxwell-Boltzmann speed distribution 80 3.3.1 The kinetic energy distribution 84 3.4 Boltzmann's law 86 3.4.1 General form of Boltzmann's law 86 3.4.2 The probability distribution for a single component of molecular velocity 87 3.4.3 Doppler broadening of spectral lines 89 3.5 The isothermal atmosphere 91 3.5.1 Potential energy distribution of the molecules 92 3.5.2 Velocity distribution of the molecules 94 3.6 Derivation of the Maxwell-Boltzmann speed distribution 96 3.6.1 Two-dimensional gas 96 3.6.2 Three-dimensional gas 99 3.7 Equipartition of energy 100 3.7.1 Rotational motion of a diatomic molecule 100 3.7.2 Vibrational motion of a diatomic molecule 102 3.7.3 The equipartition theorem applied to macroscopic bodies 104 3.8 Specific heats of gases 106 3.8.1 C V , Specific Heat of One Mole of An Ideal Gas at Constant Volume 107 3.8.2 c P , specific heat of one mole of an ideal gas at constant pressure 108 3.8.3 Ratio of specific heats gamma 108 3.8.4 The breakdown of the classical theory 108 3.8.5 Boltzmann's law and discrete energy levels 110 Problems 3 112 4 Kinetic theory of gases: transport processes 117 4.1 Kinetic theory of gases 117 4.2 Molecular collisions and the mean free path 118 4.3 The distribution of free paths 122 4.4 Diffusion 125 4.4.1 Fink's law of diffusion 125 4.4.2 Taylor's theorem 128 4.4.3 The diffusion equation 128 4.4.4 The kinetic theory of diffusion 132 4.5 Thermal conduction 134 4.5.1 Predictions for the thermal conductivity 136 4.5.2 The heat equation 137 4.6 Viscosity 140 4.6.1 Predictions for the coefficient of viscosity 142 4.7 Comparison of transport properties 142 4.7.1 Estimation of Avogadro's number 143 4.8 Effusion 144 4.8.1 Isotope separation 146 4.9 The random walk 149 4.9.1 Probability distribution P[x]dx for displacement of the particle 152 4.9.2 The random walk and molecular diffusion 153 Problems 4 155 5 Real gases 157 5.1 The van der Waals equation 158 5.1.1 The finite size of molecules 160 5.1.2 The intermolecular force of attraction 161 5.2 P-V isotherms for a real gas 163 5.2.1 the Critical Points, T C , P C , and V C 165 5.3 The virial equation 166 5.3.1 Relationship between the van der Waals constants a and b and the virial coefficients B and c 168 5.4 Internal energy and specific heats of a van der Waals gas 169 5.4.1 The molar specific heats at constant volume and constant pressure 170 5.5 Phase diagrams 171 Problems 5 175 6 The First Law of Thermodynamics 177 6.1 Thermodynamic equilibrium 178 6.1.1 The equation of state 179 6.2 Temperature 180 6.2.1 The zeroth law of thermodynamics 181 6.2.2 The measurement of temperature 181 6.2.3 Definition of the kelvin 184 6.3 Heat 185 6.3.1 The measurement of heat 185 6.4 Internal energy 186 6.4.1 Internal energy; a function of state 187 6.4.2 Internal energy of an ideal gas 187 6.5 Work and Joule's paddle wheel experiment 188 6.6 First law of thermodynamics 191 6.6.1 Paths between thermodynamic states 191 6.6.2 Thermodynamic definitions of internal energy and heat 193 6.7 Work done during volume changes 194 6.8 Reversible processes 196 6.8.1 Quasistatic processes 197 6.8.2 Idealised reversible process 197 6.8.3 The effect of frictional forces 199 6.8.4 Practical realization of a reversible process 200 6.9 Expansion of gases and the first law of thermodynamics 202 6.10 The Joule effect; the free expansion of an ideal gas 203 6.11 Molar specific heats of an ideal gas 205 6.11.1 Molar Specific Heat at Constant Volume, C V 205 6.11.2 the Difference in Molar Specific Heats, C P C V 206 6.11.3 Reversible adiabatic expansion of an ideal gas 207 6.12 Enthalpy 210 6.12.1 Specific heat at constant pressure, C P 211 6.13 The Joule-Kelvin effect 212 6.13.1 Joule-Kelvin effect and intermolecular forces 216 6.14 Thermochemistry 217 6.14.1 The enthalpy of vaporization 218 6.14.2 Heats of reaction 218 Problems 6 219 7 The second law of thermodynamics 223 7.1 Introduction 223 7.2 Heat engines 224 7.2.1 The steam turbine 225 7.2.2 Refrigerators and heat pumps 227 7.3 The Carnot cycle 229 7.3.1 Stages of the Carnot cycle 230 7.3.2 Thermal efficiency of a Carnot engine 232 7.3.3 The Kelvin or absolute temperature scale 234 7.4 Entropy 235 7.4.1 The measurement of changes in entropy 236 7.4.2 Entropy as a state function 237 7.5 Entropy changes in reversible processes 238 7.5.1 Reversible processes in an ideal gas 238 7.5.2 Water and ice mixture 238 7.5.3 The Carnot cycle 239 7.6 Entropy changes in irreversible processes 241 7.6.1 Free expansion of an ideal gas 242 7.6.2 Temperature equalisation 242 7.6.3 Heating water 243 7.7 Entropy and the second law 245 7.8 The fundamental thermodynamic relationship 246 7.9 Phase changes and the Clausius-Clapeyron equation 247 7.10 Gibbs free energy 252 7.10.1 Physical interpretation of Gibbs free energy 252 7.10.2 The example of a lead acid battery 253 7.10.3 Gibbs free energy and spontaneous processes 254 7.11 Thermodynamic identities 255 7.11.1 Maxwell's relations 257 7.12 A statistical approach to the second law of thermodynamics 259 7.12.1 Permutations and combinations 260 7.12.2 Probability and entropy; Boltzmann's equation 265 Problems 7 268 8 Solids 271 8.1 Types of solids 271 8.2 Crystal structure 273 8.2.1 Close packing of atoms in a crystal 273 8.2.2 Some common crystal structures 275 8.2.3 Ionic crystals 278 8.3 The crystal lattice, unit cell, and basis 282 8.3.1 Types of crystal lattice and the unit cell 283 8.3.2 The basis 286 8.3.3 Graphene 287 8.3.4 The three-dimensional lattice 288 8.4 X-ray crystallography 290 8.4.1 The Bragg law 291 8.4.2 Crystal planes 292 8.5 Experimental techniques of X-ray crystallography 294 8.5.1 X-ray sources 295 8.5.2 Collection and analysis of diffraction patterns 298 8.6 Neutron scattering 298 8.7 Interatomic forces in solids 299 8.7.1 Heat of sublimation 299 8.7.2 Surface energy of a crystal 300 8.8 Vibrations in crystals 301 8.8.1 Thermal expansion 305 Problems 8 306 9 The elastic properties of solids 309 9.1 Stress, strain, and elastic moduli 309 9.1.1 Tensile and compressional stress and strain 310 9.1.2 Strength of solid materials 312 9.1.3 Shear stress and strain 313 9.1.4 Bulk stress and strain 314 9.2 Poisson's ratio 315 9.3 The velocity of sound in a thin wire 320 9.4 Torsional stress and strain 322 9.5 Elastic moduli and interatomic forces and potential energies 325 9.5.1 Young's modulus 327 9.5.2 Bulk modulus 330 9.6 The inelastic behaviour of solids 332 9.6.1 Slip 334 Problems 9 336 10 Thermal and transport properties of solids 339 10.1 Molar specific heats of solids 339 10.1.1 The Einstein model 341 10.1.2 The Debye model 346 10.2 Thermal conductivity of solids 350 10.3 Diffusion in solids 353 10.3.1 The diffusion coefficient 354 10.4 Electrical and thermal conductivities of metals 356 10.4.1 Thermal conductivity of metals 359 10.4.2 Successes and failures of the classical free electron model 360 Problems 10 360 11 Liquids 363 11.1 The structure of liquids 363 11.1.1 The radial distribution function 364 11.2 Physical properties of liquids 366 11.2.1 Latent heats of vapourisation and fusion 366 11.2.2 Vapour pressure 366 11.2.3 Surface energy and surface tension 369 11.2.4 Capillarity 370 11.2.5 Diffusion 373 11.3 The flow of liquids 374 11.3.1 The continuity equation 375 11.3.2 Bernoulli's equation 376 11.4 The flow of real liquids 380 11.4.1 Viscosity of liquids 380 11.4.2 Viscous flow through a pipe 381 Problems 11 383 12 Liquid crystals 387 12.1 Liquid crystal phases 388 12.2 Thermotropic liquid crystal phases 389 12.2.1 Nematic phase 390 12.2.2 Smectic phase 391 12.2.3 Chiral liquid crystal phases 392 12.2.4 Molecular order and temperature 394 12.2.5 Molecular structure of liquid crystals 395 12.3 Polarised light 396 12.4 Optical properties of liquid crystals 402 12.4.1 Birefringence 402 12.4.2 Selective reflection 405 12.4.3 Waveguide regime 407 12.4.4 Optical polarising microscopy 409 12.5 Liquid crystal displays 410 12.5.1 Reorientation of liquid crystals in an electric field 410 12.5.2 The twisted nematic liquid crystal display 411 12.6 Liquid crystals in nature 415 Problems 12 415 Solutions to problems 417 Index 437