Concepts in Thermal Physics

by Blundell, Stephen; Blundell, Katherine

• ISBN13: 9780198567707
• ISBN10: 0198567707
• Format: Paperback
• Copyright: 2006-10-12
• Publisher: Oxford University Press

Summary

An understanding of thermal physics is crucial to much of modern physics, chemistry and engineering. This book provides a modern introduction to the main principles that are foundational to thermal physics, thermodynamics and statistical mechanics. The key concepts are carefully presented in a clear way, and new ideas are illustrated with copious worked examples as well as a description of the historical background to their discovery. Applications are presented to subjects as diverse as stellar astrophysics, information and communication theory, condensed matter physics and climate change. Each chapter concludes with detailed exercises.

Author Biography

Professor Stephen J. Blundell
Department of Physics
Clarendon Laboratory
University of Oxford
Parks Road
Oxford OX1 3PU Stephen Blundell did his undergraduate degree in Physics and Theoretical Physics at Peterhouse, Cambridge and his Ph. D. in the Cavendish Laboratory at Cambridge. He moved to the Clarendon Laboratory at Oxford to take up an SERC research fellowship, followed by a Junior Research Fellowship at Merton College, where he began research in organic magnets and superconductors using muon-spin rotation. In 1997 he was appointed to a University Lectureship in the Physics Department and a Tutorial Fellowship at Mansfield College, Oxford, and was subsequently promoted to Reader and then Professor. He was a joint winner of the Daiwa-Adrian Prize in 1999 for his work on organic magnets.
Dr Katherine Blundell
Department of Astrophysics
Keble Road
Oxford
OX1 3RH Katherine Blundell did her undergraduate degree in Physics and Theoretical Physics at New Hall College, Cambridge and her Ph. D. in the Cavendish Laboratory at Cambridge. She moved to Oxford University Astrophysics department, holding a Junior Research Fellowship at Balliol College, an 1851 Research Fellowship, before taking up a Royal Society University Research Fellowship. Her research concentrates on radio galaxies and quasars. In 2005 she won a Leverhulme prize for her research.

Table of Contents

I. Preliminaries	1	(44)
Introduction	2	(11)
What is a mole?	3	(1)
The thermodynamic limit	4	(2)
The ideal gas	6	(1)
Combinatorial problems	7	(2)
Plan of the book	9	(4)
Exercises	12	(1)
Heat	13	(5)
A definition of heat	13	(1)
Heat capacity	14	(4)
Exercises	17	(1)
Probability	18	(12)
Discrete probability distributions	19	(1)
Continuous probability distributions	20	(1)
Linear transformation	21	(1)
Variance	22	(1)
Linear transformation and the variance	23	(1)
Independent variables	24	(6)
Further reading	27	(1)
Exercises	27	(3)
Temperature and the Boltzmann factor	30	(15)
Thermal equilibrium	30	(1)
Thermometers	31	(2)
The microstates and macrostates	33	(1)
A statistical definition of temperature	34	(2)
Ensembles	36	(1)
Canonical ensemble	36	(4)
Applications of the Boltzmann distribution	40	(5)
Further reading	44	(1)
Exercises	44	(1)
II. Kinetic theory of gases	45	(28)
The Maxwell--Boltzmann distribution	46	(8)
The velocity distribution	46	(1)
The speed distribution	47	(2)
(v) and (v2)	48	(1)
The mean kinetic energy of a gas molecule	48	(1)
The maximum of f(v)	49	(1)
Experimental justification	49	(5)
Exercises	52	(2)
Pressure	54	(8)
Molecular distributions	55	(1)
Solid angles	55	(1)
The number of molecules travelling in a certain direction at a certain speed	55	(1)
The number of molecules hitting a wall	56	(1)
The ideal gas law	56	(2)
Dalton's law	58	(4)
Exercises	59	(3)
Molecular effusion	62	(6)
Flux	62	(2)
Effusion	64	(4)
Exercises	67	(1)
The mean free path and collisions	68	(5)
The mean collision time	68	(1)
The collision cross-section	69	(2)
The mean free path	71	(2)
Exercises	72	(1)
III. Transport and thermal diffusion	73	(30)
Transport properties in gases	74	(14)
Viscosity	74	(5)
Thermal conductivity	79	(2)
Diffusion	81	(3)
More-detailed theory	84	(4)
Further reading	86	(1)
Exercises	87	(1)
The thermal diffusion equation	88	(15)
Derivation of the thermal diffusion equation	88	(1)
The one-dimensional thermal diffusion equation	89	(3)
The steady state	92	(1)
The thermal diffusion equation for a sphere	92	(3)
Newton's law of cooling	95	(2)
The Prandtl number	97	(1)
Sources of heat	98	(5)
Exercises	99	(4)
IV. The first law	103	(18)
Energy	104	(10)
Some definitions	104	(2)
A system in thermal equilibrium	104	(1)
Functions of state	104	(2)
The first law of thermodynamics	106	(2)
Heat capacity	108	(6)
Exercises	111	(3)
Isothermal and adiabatic processes	114	(7)
Reversibility	114	(2)
Isothermal expansion of an ideal gas	116	(1)
Adiabatic expansion of an ideal gas	117	(1)
Adiabatic atmosphere	117	(4)
Exercises	119	(2)
V. The second law	121	(42)
Heat engines and the second law	122	(14)
The second law of thermodynamics	122	(1)
The Carnot engine	123	(3)
Carnot's theorem	126	(1)
Equivalence of Clausius and Kelvin statements	127	(1)
Examples of heat engines	127	(2)
Heat engines running backwards	129	(1)
Clausius' theorem	130	(6)
Further reading	133	(1)
Exercises	133	(3)
Entropy	136	(17)
Definition of entropy	136	(1)
Irreversible change	136	(2)
The first law revisited	138	(2)
The Joule expansion	140	(2)
The statistical basis for entropy	142	(1)
The entropy of mixing	143	(2)
Maxwell's demon	145	(1)
Entropy and probability	146	(7)
Exercises	149	(4)
Information theory	153	(10)
Information and Shannon entropy	153	(2)
Information and thermodynamics	155	(1)
Data compression	156	(2)
Quantum information	158	(5)
Further reading	161	(1)
Exercises	161	(2)
VI. Thermodynamics in action	163	(36)
Thermodynamic potentials	164	(18)
Internal energy, U	164	(1)
Enthalpy, H	165	(1)
Helmholtz function, F	166	(1)
Gibbs function, G.	167	(1)
Availability	168	(2)
Maxwell's relations	170	(12)
Exercises	178	(4)
Rods, bubbles and magnets	182	(11)
Elastic rod	182	(3)
Surface tension	185	(1)
Paramagnetism	186	(7)
Exercises	192	(1)
The third law	193	(6)
Different statements of the third law	193	(2)
Consequences of the third law	195	(4)
Exercises	198	(1)
VII. Statistical mechanics	199	(74)
Equipartition of energy	200	(9)
Equipartition theorem	200	(3)
Applications	203	(2)
Translational motion in a monatomic gas	203	(1)
Rotational motion in a diatomic gas	203	(1)
Vibrational motion in a diatomic gas	204	(1)
The heat capacity of a solid	205	(1)
Assumptions made	205	(2)
Brownian motion	207	(2)
Exercises	208	(1)
The partition function	209	(12)
Writing down the partition function	210	(1)
Obtaining the functions of state	211	(7)
The big idea	218	(1)
Combining partition functions	218	(3)
Exercises	219	(2)
Statistical mechanics of an ideal gas	221	(11)
Density of states	221	(2)
Quantum concentration	223	(1)
Distinguishability	224	(1)
Functions of state of the ideal gas	225	(3)
Gibbs paradox	228	(1)
Heat capacity of a diatomic gas	229	(3)
Exercises	230	(2)
The chemical potential	232	(15)
A definition of the chemical potential	232	(1)
The meaning of the chemical potential	233	(2)
Grand partition function	235	(1)
Grand potential	236	(2)
Chemical potential as Gibbs function per particle	238	(1)
Many types of particle	238	(1)
Particle number conservation laws	239	(1)
Chemical potential and chemical reactions	240	(7)
Further reading	245	(1)
Exercises	246	(1)
Photons	247	(16)
The classical thermodynamics of electromagnetic radiation	248	(1)
Spectral energy density	249	(1)
Kirchhoff's law	250	(2)
Radiation pressure	252	(1)
The statistical mechanics of the photon gas	253	(1)
Black body distribution	254	(3)
Cosmic Microwave Background radiation	257	(1)
The Einstein A and B coefficients	258	(5)
Further reading	261	(1)
Exercises	262	(1)
Phonons	263	(10)
The Einstein model	263	(2)
The Debye model	265	(3)
Phonon dispersion	268	(5)
Further reading	271	(1)
Exercises	271	(2)
VIII. Beyond the ideal gas	273	(80)
Relativistic gases	274	(6)
Relativistic dispersion relation for massive particles	274	(1)
The ultrarelativistic gas	274	(3)
Adiabatic expansion of an ultrarelativistic gas	277	(3)
Exercises	279	(1)
Real gases	280	(17)
The van der Waals gas	280	(8)
The Dieterici equation	288	(2)
Virial expansion	290	(4)
The law of corresponding states	294	(3)
Exercises	296	(1)
Cooling real gases	297	(8)
The Joule expansion	297	(2)
Isothermal expansion	299	(1)
Joule--Kelvin expansion	300	(2)
Liquefaction of gases	302	(3)
Exercises	304	(1)
Phase transitions	305	(20)
Latent heat	305	(3)
Chemical potential and phase changes	308	(1)
The Clausius--Clapeyron equation	308	(5)
Stability & metastability	313	(3)
The Gibbs phase rule	316	(2)
Colligative properties	318	(2)
Classification of phase transitions	320	(5)
Further reading	323	(1)
Exercises	323	(2)
Bose--Einstein and Fermi--Dirac distributions	325	(12)
Exchange and symmetry	325	(1)
Wave functions of identical particles	326	(3)
The statistics of identical particles	329	(8)
Further reading	332	(1)
Exercises	332	(5)
Quantum gases and condensates	337	(16)
The non-interacting quantum fluid	337	(3)
The Fermi gas	340	(5)
The Bose gas	345	(1)
Bose--Einstein condensation (BEC)	346	(7)
Further reading	351	(1)
Exercises	352	(1)
IX. Special topics	353	(80)
Sound waves	354	(7)
Sound waves under isothermal conditions	355	(1)
Sound waves under adiabatic conditions	355	(1)
Are sound waves in general adiabatic or isothermal?	356	(1)
Derivation of the speed of sound within fluids	357	(4)
Further reading	360	(1)
Exercises	360	(1)
Shock waves	361	(7)
The Mach number	361	(1)
Structure of shock waves	361	(2)
Shock conservation laws	363	(1)
The Rankine--Hugoniot conditions	364	(4)
Further reading	367	(1)
Exercises	367	(1)
Brownian motion and fluctuations	368	(18)
Brownian motion	368	(3)
Johnson noise	371	(1)
Fluctuations	372	(1)
Fluctuations and the availability	373	(2)
Linear response	375	(3)
Correlation functions	378	(8)
Further reading	385	(1)
Exercises	385	(1)
Non-equilibrium thermodynamics	386	(12)
Entropy production	386	(1)
The kinetic coefficients	387	(1)
Proof of the Onsager reciprocal relations	388	(3)
Thermoelectricity	391	(4)
Time reversal and the arrow of time	395	(3)
Further reading	397	(1)
Exercises	397	(1)
Stars	398	(15)
Gravitational interaction	399	(5)
Gravitational collapse and the Jeans criterion	399	(2)
Hydrostatic equilibrium	401	(1)
The virial theorem	402	(2)
Nuclear reactions	404	(1)
Heat transfer	405	(8)
Heat transfer by photon diffusion	405	(2)
Heat transfer by convection	407	(1)
Scaling relations	408	(4)
Further reading	412	(1)
Exercises	412	(1)
Compact objects	413	(11)
Electron degeneracy pressure	413	(2)
White dwarfs	415	(1)
Neutron stars	416	(2)
Black holes	418	(1)
Accretion	419	(1)
Black holes and entropy	420	(1)
Life, the Universe and Entropy	421	(3)
Further reading	423	(1)
Exercises	423	(1)
Earth's atmosphere	424	(9)
Solar energy	424	(1)
The temperature profile in the atmosphere	425	(2)
The greenhouse effect	427	(6)
Further reading	432	(1)
Exercises	432	(1)
A. Fundamental constants	433	(1)
B. Useful formulae	434	(2)
C. Useful mathematics	436	(15)
The factorial integral	436	(1)
The Gaussian integral	436	(3)
Stirling's formula	439	(2)
Riemann zeta function	441	(1)
The polylogarithm	442	(1)
Partial derivatives	443	(1)
Exact differentials	444	(1)
Volume of a hypersphere	445	(1)
Jacobians	445	(2)
The Dirac delta function	447	(1)
Fourier transforms	447	(1)
Solution of the diffusion equation	448	(1)
Lagrange multipliers	449	(2)
D. The electromagnetic spectrum	451	(1)
E. Some thermodynamical definitions	452	(1)
F. Thermodynamic expansion formulae	453	(1)
G. Reduced mass	454	(1)
H. Glossary of main symbols	455	(2)
I. Bibliography	457	(3)
Index	460