The chapter illustrates ensemble as the crucial concept needed in the treatment of
systems of interacting particles. It notes the requirements to set up an ensemble: a
closed system of specified volume, composition, and temperature. Thus, an imaginary
collection of replications of the actual system with a common temperature is called
the canonical ensemble. While the canonical distribution provides the most probable
number of members of the ensemble with a specified total energy, the mean energy of
the members of the ensemble can be calculated from the canonical partition function.
The chapter notes the variation of the energy with volume.
Chapter
The canonical ensemble
Chapter
The canonical ensemble
This chapter describes the canonical ensemble, which is an ensemble of systems that are all prepared in the same way with the same number of particles, volume, shape, magnetic field, and electric field. However, the energy of each system fluctuates. The chapter details experiments that involve condensed matter wherein a system is placed in contact with a heat bath that eventually reaches thermal equilibrium. It also clarifies how the system being studied together with the heat bath or combined system is thermally isolated so that its total energy is constant. The chapter illustrates a Boltzmann probability distribution, wherein probabilities are drawn along the horizontal axis and the energies along the vertical. It highlights the use of the Boltzmann probability distribution on systems that are in contact with a heat bath, granted the number of particles in the system is constant.
Chapter
Fermi and Bose particles
This chapter reviews the techniques of the grand canonical ensemble to give an exact treatment for both Bose and Fermi particles. It looks at the results of Maxwell-Boltzmann statistics for the average number of particles in sufficiently high temperatures and in a single-particle state for both fermions and bosons. It also examines the exclusion principle in Fermi particles, which means that there cannot be two particles in the same single-particle state, while there is no such restriction for Bose particles. The chapter clarifies that the resulting formulae for the average number of particles in a single-particle state are different at low temperatures. It describes Fermi particles at low temperatures that have a large kinetic energy, an energy which can be much larger than the interaction between particles.
