Thermodynamics, Gibbs method and statistical physics of electron gases (Q1039199)

Thermodynamics is a phenomenological theory. It studies the physical (mechanical, thermal, magnetic, optical, electrical, etc.) properties of macroscopic bodies and processes, without consideration of the inner physical mechanisms. It generalizes experiments. Statistical physics is a microscopic theory. On the basis of the knowledge of the type of particles a system consists of the nature of the particle interaction, and the laws of motion of these particles, it explains experimental results. It substantiates the laws of thermodynamics and determines the limits of their applicability (see the preface). Chapter 1 of the work starts with the introduction of the basic concepts and postulates of thermodynamics and statistical physics. Different ways of the description of the state of macroscopic systems, consisting of a very large number of particles such as atoms, molecules, ions, electrons, photons, phonons, etc., are adduced. Such concepts as the distribution function over microstates, statistical weight of the preassigned macroscopic state of a system, absolute temperature, and pressure are also introduced. The three basic laws of thermodynamics are explained in Chapter 2. Besides, the method of thermodynamic functions and the finding of general thermodynamic relationships based on them are discussed. Chapter 3 is devoted to the Gibbs method, which is applied to find the function of the free energy, which forms the basis of the canonical distribution. Further, on the basis of the microcanonical distribution, canonical distributions for closed and open systems in a thermostat are found. In Chapter 4, the Gibbs method is applied to an ideal gas. Here the free energy and the entropy of the system are calculated, and thermal and caloric equations of state are found. The exposition of classical and quantum theories of the heat capacity of an ideal gas occupies a large place. A mixture of ideal gases and the Gibbs paradox are considered. Thermodynamic properties of an ideal system of polar molecules in an external electric field as well as an ideal system of magnetic dipoles in an external magnetic field are treated. At the end of the chapter, a simple example of the thermodynamic state of a system with negative absolute temperature is discussed. Chapter 5 is devoted to the application of the Gibbs method to nonideal, that means real, molecular gases. Here, first the equation of state of rarefied gases consisting of weakly interacting molecules is derived in general form. Thereupon, the thermodynamics of a non-ideal gas of the van der Waals type is considered. Finally, a relation for the free energy of a plasma with Debye screening is derived. Non-conducting crystalline solids are treated in Chapter 6. At the beginning of the chapter, the Hamilton function of a vibrating simple crystalline lattice with normal coordinates is described. Further, in the classical and quantum cases, applying the Gibbs method, the free energy, total energy, equation of state, heat capacity and coefficients of thermal expansion of a solid are calculated. Quantum statistics (Fermi-Dirac and Bose-Einstein distribution functions) and the theory of thermodynamic properties of quantum ideal gases are considered in Chapter 7. Here, first the Boltzmann distribution function is discussed, which forms the basis of classical statistics. The main difficulties of classical statistics are explained. Then the principle of indistinguishability of particles is introduced, and the equations of states of Fermi and Bose gases are derived. As applications, the heat capacity of metals and the Pauli paramagnetism are considered. Besides the statistics of charge carriers in semiconductors, the Bose-Einstein condensation, and photon gases are discussed. In Chapter 8, a statistical theory of thermodynamic properties of an electron gas taking into account the energy-spectrum quantization in an external magnetic field is expounded. On the basis of the grand thermodynamic potential, the chemical potential, the thermal equation of state, entropy and heat capacity of an electron gas are found. The Landau diamagnetism is considered. It is shown that all results of the quantum theory in the quasi-classical approximation pass into the known classical ones. In the last chapter, on the basis of the Boltzmann kinetic equation, the electron gas in metals and semiconductors is considered in a nonequilibrium state. Nonequilibrium processes are associated with charge carrier motion in a crystal under external disturbances such as an electric field or a temperature gradient in a magnetic field. They include electric conductivity, thermoelectric, galvanometric, and thermomagnetic effects.