This Primer focusses on the statistical physics of classical and quantum systems. The course text explores the three cornerstones of statistical physics which include the Boltzmann, Fermi–Dirac, and Bose–Einstein distribution laws. It also provides a highly useful and in-depth investigation of the thermal properties of paradigmatically important systems such as classical ideal gas, electron gas and phonon gas. The structure of this text is tailored to facilitate the planning of a one-semester course: this volume provides bachelor students with a main teaching tool. More specifically, each part identifies an independent teaching module, while each chapter corresponds to approximately two weeks of lecturing.
Author(s): Luciano Colombo
Publisher: IOP Publishing
Year: 2022
Language: English
Pages: 125
City: Bristol
PRELIMS.pdf
Foreword
Presentation of the ‘Primer series’
Acknowledgements
Author biography
Luciano Colombo
Introduction to:
Acknowledgements
Symbols
CH001.pdf
Chapter 1 The statistical description of a classical system
1.1 Basic concepts
1.2 Equilibrium distribution probability
1.3 The Boltzmann distribution law
1.4 A statistical definition of temperature
1.5 Calculating ensemble averages
1.6 Entropy
1.6.1 Thermodynamical entropy
1.6.2 Boltzmann entropy
1.6.3 Entropy and ignorance
1.7 The ideal monoatomic gas
1.7.1 Partition function
1.7.2 The equation of state
1.7.3 Energy and heat capacity
1.7.4 The Maxwell distribution law
1.7.5 The entropy state function
1.8 On the statistical concept of irreversible process
References
CH002.pdf
Chapter 2 Thermal properties of classical gases
2.1 Thermal properties of polyatomic ideal gases
2.1.1 Rotational energy
2.1.2 Vibrational energy
2.1.3 Molar constant-volume heat capacity
2.1.4 Equipartition of energy
2.2 Real gases
2.2.1 Equation of state
2.2.2 The virial expansion
2.3 Thermal properties under the action of an external field
2.3.1 Paramagnetism
2.3.2 Polarisation
References
CH003.pdf
Chapter 3 The statistical description of a quantum system
3.1 Basic concepts
3.1.1 Symmetric and antisymmetric wavefunctions
3.1.2 Intrinsic probability of a quantum state
3.2 Fermi–Dirac statistics
3.2.1 The equilibrium partition
3.2.2 The chemical potential
3.3 Bose–Einstein statistics
3.4 Quantum statistics revisited
3.4.1 The grand canonical ensemble
3.4.2 Fermi–Dirac and Bose–Einstein distributions
References
CH004.pdf
Chapter 4 Thermal properties of quantum gases
4.1 The electron gas
4.1.1 Electrons in metals
4.1.2 The chemical potential of the free electron gas
4.1.3 Thermal properties of the free electron gas
4.2 The phonon gas
4.2.1 Lattice vibrations
4.2.2 The specific heat of the phonon gas
4.2.3 The thermal conductivity of the phonon gas
References
CH005.pdf
Chapter 5 Other quantum systems and phenomena
5.1 The photon gas
5.2 The quantum ideal gas
5.3 The Bose–Einstein condensation
References
CH006.pdf
Chapter 6 What is missing in this ‘Primer’
APPA.pdf
Chapter
A.2 Lagrange multipliers
A.3 Integrals useful in statistical physics
APPB.pdf
Chapter
APPC.pdf
Chapter
C.1 Thermodynamic parameters
C.2 Thermodynamic potentials
References
APPD.pdf
Chapter
References
APPE.pdf
Chapter
References
APPF.pdf
Chapter
References
APPG.pdf
Chapter
References
APPH.pdf
Chapter
References
