Chapter 5 explores phase transitions in magnetic systems. We start by defining the basic magnetic phases, such as paramagnetic and ferromagnetic. We show how this relates to the magnetic signatures seen in ocean floors due to seafloor spreading. Next, we introduce the Ising model as a simple theoretical model to help understand magnetic phase transitions. We solve the Ising model with the theoretical method known as mean-field theory, and we show how to use cobwebbing to give numerical solutions to the mean-field equations. Also covered are the critical exponents that show the behavior in the close vicinity of the critical point. We also explore Landau expansions and show how simple considerations of series expansions can give deep insight into phase transitions in magnetic systems. Finally, hysteresis is discussed, and we relate it to both magnetic systems and everyday situations.

Chapter 6 looks at the phase behavior of binary mixtures, as opposed to phases in systems with only a single component. Adding a second component immediately results in a rich variety of phase behavior. For example, we cover lens-shaped phase diagrams, the simplest type of behavior in binary mixtures. We show how these diagrams are related to the process of distillation. In more complex systems, these lens-shaped diagrams can pinch in and produce azeotropes. Similar behavior in liquid–solid systems result in eutectic points. Finally, we explore binary liquid mixtures and the case of closed-loop phase diagrams, with their re-entrant – or upside-down – phase transitions. To study these systems, we introduce a generalized Ising-like model referred to as the WV model. This model shows the crucial role played by hydrogen bonds in these systems.

Chapter 1 explores the most common phases of matter: solid, liquid, and gas. We cover the pressure–temperature phase diagrams that show the boundaries separating these phases. This includes special points such as the critical point and the triple point. Next, we consider the Gibbs free energy and its connection to phase transitions. This leads naturally to the Clausius–Clapeyron equation, which relates the slope of phase boundaries to the entropy and volumes of the coexisting phases. We then turn to pressure–volume phase diagrams, showing explicitly the coexistence that occurs in first-order, discontinuous phase transitions.

Chapter 2 delves into the interconnections between heat, entropy, and temperature, and their relation to phases of matter. We cover heat capacities, specific heats, and the relation they have to the change in entropy. Similarly, we cover latent heat and its direct connection to entropy and enthalpy. We then return to the Clausius–Clapeyron equation and express it in terms of quantities that are readily measured experimentally, such as heat, temperature, and density. It is then applied to both the solid–liquid and liquid–vapor phase boundaries. Finally, we turn to the topic of heat engines and refrigerators, emphasizing the Carnot cycle and its connection to maximum efficiency and absolute temperature.

Chapter 4 is devoted to the van der Waals equation and its relation to real substances whose behavior differs from that of ideal gases. We start by exploring two basic alterations to the ideal gas isotherm and their implications for real gases. We examine the van der Waals isotherm in detail, showing regions where the substance is metastable or unstable. We then present the Maxwell construction that connects the liquid and gas phases, circumventing the instabilities. This is the well-known equal-area construction. The amount of material in the coexisting phases is determined with the lever rule. Finally, we look at the critical point in detail and show how the use of corresponding states connects the behavior of a wide range of physical systems.

Chapter 7 examines phases that have been discovered and investigated in modern times. These include plasmas, liquid crystals, superfluids, superconductors, and Bose–Einstein condensates. We cover the behavior of these systems and the basic results known about them. In liquid crystals we show the different types of phases, such as isotropic, nematic, and smectic. In quantum phases, we discuss the discovery of superconductivity, and then examine in detail the ideas behind Cooper pairs and BCS theory.

Chapter 3 is devoted to the special case of water, its phases, and phase transitions. We start with the structure of the water molecule itself, and point out that it is strongly dipolar in its distribution of electric charge. We explore its basic phases, including vapor (steam), liquid (water), and solid (ice). We show the structure of ice and point out that its open structure leads to a density that is lower than that of the liquid phase. The phase diagram of water is presented, and special attention is paid to the boundary between the liquid and solid phases, which has a negative slope in a pressure-versus-temperature phase diagram, in contrast to most other substances. We point out how this negative slope is related to floating icebergs and freshwater lakes that freeze from the top down. Next, we apply the Clausius–Clapeyron relation to the liquid–gas phase boundary, and point out the location of the critical point. We explore the topics of relative humidity and dew points, and the relation these quantities have to our physical experience of mugginess. Finally, we consider hurricanes and show how they are effectively large heat engines operating in the atmosphere.