Energy in Thermal Physics

The behavior of energy in bulk-matter systems is subtle. We observe that energy flows spontaneously from high to low temperature; we refer to this flowing energy as heat; and we distinguish heat from work, the transfer of energy through mechanical or other means unrelated to temperature. On the other hand, simple models of gases and solids strongly suggest that at the molecular level all energy is purely mechanical. This introductory chapter surveys these basic concepts of thermal physics, illustrates them with a wide variety of familiar examples, and sets the stage for developing a deeper understanding.

Engines and Refrigerators

The laws of energy conservation and entropy increase put limits on the efficiency of any heat engine and any refrigeration device working over a given temperature range. The limits are independent of the details of how these machines operate, so this chapter first explains them by considering only energy and entropy flows. The detailed mechanisms are still interesting, however, so the chapter ends with descriptions of a variety of engine and refrigeration mechanisms, including methods of reaching temperatures near absolute zero.

Boltzmann Statistics

When a system is held at a fixed temperature, its higher-energy states are less probable than its lower energy states by an amount that depends on how the energy compares to the temperature. The formula that quantifies this idea is called the Boltzmann distribution. This chapter derives the Boltzmann distribution and shows how to use it to predict the thermal behavior of any system whose microscopic states we can enumerate. The examples go beyond the three simple model systems studied already in Chapters 2 and 3 to include detailed properties of gases, stellar spectra, and paramagnetic materials.

Interactions and Implications

Although the law of entropy increase governs the direction in which things change, we don’t observe entropy directly. Instead we observe three quantities—temperature, pressure, and chemical potential—that tell us how the entropy of a system changes as it interacts in three different ways with its surroundings. This chapter shows how these three quantities are mathematically related to a system’s entropy, energy, volume, and number of particles. These relations complete the foundation of macroscopic thermodynamics. Moreover, for the three model systems whose entropies are calculated explicitly in the previous chapter, these relations lead to detailed testable predictions of thermal behavior.

Quantum Statistics

This chapter begins by extending the Boltzmann distribution to the case of a system that exchanges particles with its environment. This idea finds direct applications ranging from hemoglobin adsorption to ionization of atoms in stars. But the main applications are to dense “gases” in which the quantum behavior of identical particles comes into play. Examples include conduction electrons in metals and semiconductors; white dwarf and neutron stars; photon gases and thermal radiation from incandescent objects; neutrino and electron-positron production in the early universe; quasiparticles associated with vibrations and magnetic excitations in solids; and Bose-Einstein condensation of ultracold clouds of atoms.

Systems of Interacting Particles

This chapter presents two examples of the application of Boltzmann statistics to systems with nontrivial interactions between particles. The first example is a nonideal gas, treated approximately using a series expansion that we can visualize in terms of simple diagrams. The second example is a model of a ferromagnet as a collection of two-state particles interacting with their nearest neighbors. It is easy to solve this model exactly in one dimension, and to gain a semi-quantitative understanding of why the system magnetizes below a critical temperature in two or three dimensions. The most powerful tool for studying this model, however, is numerical simulation on a computer using a random-sampling algorithm based on the Boltzmann distribution.

The Second Law

Why are so many large-scale processes irreversible, happening in one direction but not the other as time passes? This chapter answers that question using three simple model systems: a collection of two-state particles such as flipped coins or elementary magnetic dipoles; the Einstein model of a solid as a collection of identical quantum oscillators; and a monatomic ideal gas such as helium or argon. For each system we learn to calculate the multiplicity: the number of possible microscopic arrangements. Taking the logarithm of the multiplicity gives the entropy. And the laws of probability then imply the second law of thermodynamics: Entropy tends to increase.

Free Energy and Chemical Thermodynamics

When a system is held at constant temperature (and sometimes constant pressure) through interactions with its surroundings, its thermodynamic behavior is governed by a combination of energy and entropy, called free energy. This chapter defines free energy and interprets it in two ways: as available work, and as a force toward equilibrium. Extensive applications follow: electrochemistry, phase transformations, mixtures, and chemical equilibrium. The worked examples and problems explore many specific applications including muscle contraction, cloud formation, geochemistry, metallurgy, and gas ionization.