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Chapter

Cover Introductory Statistical Mechanics

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

Cover Introductory Statistical Mechanics

Systems with variable numbers of particles  

This chapter explains that a system can have a variable number of particles when particles can enter or leave or because a reaction takes place inside the system. It cites a sealed vessel containing a pure substance with both liquid and gas phases present as an example that demonstrates the presence of a meniscus separating the gas from the liquid. This meniscus allows for determining which atoms to exist in the gas phase and in the liquid phase. The chapter also discusses how gas atoms can condense into liquid or how liquid can evaporate into gas. The chapter highlights the application of mathematical language to reactions of elementary particles or reactions that occurred in the early stages of the universe. It outlines the subject of reactions that occur frequently in science, such as solid-state physics, chemistry, and phase equilibrium.

Chapter

Cover Introductory Statistical Mechanics

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.