This chapter explains how the Boltzmann distribution has been used to predict the
populations of states in systems at thermal equilibrium. It considers the
calculation of the populations of the energy levels of a system consisting of a
large number of non-interacting molecules. The relative populations of energy
levels, as opposed to states, must take into account the degeneracies of the energy
levels. The chapter mentions that energy levels can be associated with any mode of
motion, such as vibration or rotation. Moreover, the principle of equal a
priori probabilities assumes that all possibilities for the distribution
of energy are equally probable in the sense that the distribution is blind to the
type of motion involved.
Chapter
The Boltzmann distribution
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
Planck's distribution
This chapter considers the distribution of the energy U among N oscillators of frequency ν, noting that an infinite number of distributions are possible if U is viewed as a divisible without limit. It discusses the theory of black-body radiation, which was developed by Max Planck in 1900 and gave birth to quantum physics. It defines a black body as one that absorbs all the radiation incident upon it. No radiation is reflected so that it looks black when it is cold. The chapter explains that objects emit electromagnetic radiation at a rate which varies in relation to their temperature. This radiation cannot be seen because its wavelength is the wrong frequency for the human eye. The chapter states that a body in thermal equilibrium with its surroundings emits and absorbs radiation at exactly the same rate.
Chapter
The Boltzmann distribution
This chapter highlights the Boltzmann distribution, which is used to predict the
populations of states in systems at thermal equilibrium. It considers the Boltzmann
distribution as one of the most important equations in chemistry as it summarizes the
populations of states and provides insight into the nature of temperature. It also reviews
how thermodynamic properties, the temperature dependence of equilibrium constants, and the
rates of chemical reactions can be interpreted in their terms. The chapter recognizes
temperature as the most probable distribution of molecules over the available energy levels
subject to certain restraints. It looks at the concept of the Boltzmann distribution that
underlie all the descriptions of the relation between the individual properties of molecules
and the properties of bulk matter.
Chapter
Fundamentals of thermal radiation
This chapter provides a background on thermal radiation, which is considered as the third mechanism of heat transfer after conduction and convection. It explains that the transfer of heat is a mechanism of energy transfer and is aimed at achieving thermal equilibrium and equal temperatures. It also points out that thermal radiation is an emission of electromagnetic waves which can be transferred between two bodies even if they are separated by a vacuum. The chapter considers thermal radiation as an electromagnetic radiation that is attributed to velocity, frequency, and wavelength. It discusses the radiation emitted and not equally distributed over a wide range of wavelengths, which is referred to as spectral distribution or spectrum.
