The phase transitions that we discussed in Section 6.6 are all discontinuous phase transitions. They are step-wise changes in the structure of matter, for instance, the destruction of the crystalline structure during melting or sublimation, or the breakdown of molecular bonds in a liquid during boiling. These are microscopic changes that are accompanied by a macroscopic exchange of heat with the environment, what we call the enthalpy of transition (melting, vaporization, etc.), or also “latent heat”. There is another type of phase transition, which takes place without there being a discontinuity either in the microscopic structure of a substance or in its macroscopic properties, and during which there is no energy exchange with the environment. Such phase transitions are called continuous or critical phase transitions, and play important roles in many planetary processes. For example, they underlie exsolution phenomena such as are observed in feldspars, pyroxenes, oxides and meteoritic metal, hydrogen–helium unmixing in fluid planets and liquid immiscibility phenomena in magmatic systems. They also explain order–disorder transformations in crystalline substances. Critical phase transitions also play an important role in the study of fluids (Chapter 9).

An intuitive approach to critical phase transitions

Consider a binary solution between components A and B with unit site multiplicity.

A comprehensive understanding of planetary bodies requires that we study how changes in physical conditions give rise to chemical phenomena. Physical conditions may be determined, for example, by the intensive variables P and T, where possible P–T combinations are in turn determined by the nature of heat sources and heat transfer mechanisms (Chapters 2 and 3). Chemical phenomena are transformations that entail redistribution of matter among and within phases. Some examples are: mineral transformations and melting in solid planets, changes in the relative amounts of molecular species that make up a gas or a supercritical fluid phase, and changes in the ionic constituents in an electrolyte solution such as seawater. The study of phenomena such as these is based on a mathematical description of chemical equilibrium, even in those cases in which departures from equilibrium cannot be ignored (Chapter 12). In this chapter we lay the foundations for the study of chemical equilibrium, including a comprehensive discussion of the use of composition as a thermodynamic variable. The principles and mathematical formalisms that we develop here are general, but important differences in implementation for different types of systems exist. These are dealt with in subsequent chapters.

Chemical equilibrium

Fundamental concepts

We begin by distinguishing between homogeneous and heterogenous systems. A homogeneous system consists of a single phase.

This book is about the physical chemistry of planetary processes. Although in detail each planetary body in the Solar System looks very different, all of the planets and moons have reached their current states as a result of the same fundamental laws of nature, which are codified into the sciences that we know as physics and chemistry. A real understanding of the nature and evolution of the bodies that make up the Solar System requires that we immerse ourselves in physics and chemistry, and that we come to think of planetary processes as specific applications of these sciences. These applications can be more complex, in the sense of the number of variables involved, than those that physicists and chemists deal with when working under controlled laboratory conditions. Perhaps for this reason students of geological and planetary sciences tend to view these sciences as separate or “stand alone”. This is not so, however. Using an analogy that most of us are likely to be familiar with (and that, admittedly, may be a bit stretched), the sciences that we know as geology and planetary science (and their “sub-fields” such as petrology, mineralogy, or oceanography, to name just a few) are the “user interface”, the set of graphics and icons and mnemonics that we see on our computer screens. This user interface is supported and made possible by a rich and complex operating system (e.g. Linux, Windows, Mac, according to our tastes).

With the exceptions of Chapters 2 and 3, our discussions have largely focused on equilibrium conditions, and chiefly on the equilibrium of systems in which the only kind of mechanical work that takes place is expansion work. Even with these severe restrictions thermodynamics can provide a wealth of information about the nature and evolution of planetary bodies. But these are by no means the limits of thermodynamics. In fact, one could argue that thermodynamics only begins to get interesting when these restrictions are lifted. An in-depth discussion of the possibilities that open up would demand an entire book, at least as long as this one. That is a fight for another day. The goal of this chapter is to lift a corner of the proverbial veil. I will introduce some of the principles of linear non-equilibrium thermodynamics and use them to examine chemical diffusion and chemical reaction mechanisms and rates. These are two classes of processes that are responsible for displacing systems towards equilibrium in a wide range of situations.

Non-equilibrium thermodynamics

By definition, equilibrium thermodynamics concerns itself with static systems and with “quasi-static” transformations between equilibrium states. These are abstractions, but if our discussions so far are any indication, they are very useful ones. Throughout the previous chapters we have also come across non-equilibrium processes, however. Examples include catastrophic planetesimal collisions (Chapter 2), heat transfer (Chapter 3) and non-isentropic melting (Chapter 10).

The focus of this chapter is on liquid solutions in which one component is present in much greater abundance, say at least one order of magnitude greater, than all others. Examples that underscore the importance of this type of solutions include seawater, and natural terrestrial waters in general, but one can imagine more exotic possibilities, such as hydrocarbon-based solutions on Titan's surface and ammonia-based solutions in its interior. What all of these examples share is the fact that it is convenient to make a distinction between dilute solutes that may not be liquid in their standard states, and a liquid solvent that is generally close to being in its standard state. Depending on the nature of the solvent and of the solutes the latter may exist as electrically neutral chemical species, as ions, or as a combination of both. Solutions in which solutes dissociate into ions are known as electrolyte solutions. Among these, those in which water is the solvent are by far the most important ones, at least in terrestrial environments. The chapter emphasizes aqueous electrolyte solutions, but virtually all of the thermodynamic framework is applicable to any type of dilute solution. We begin with a discussion of dilute solutions in general, and shift the focus to electrolyte solutions in Section 11.3.

In this final chapter we examine life, and in particular how life may have originated, from a strictly thermodynamic point of view. I will not get anywhere close to biochemistry, biophysics or genetics, nor will I offer a definition of life. Rather, I begin from a concept that everybody must agree upon. This is the fact that a necessary (but not sufficient!) component of the definition of life is that it is a process that never reaches thermodynamic equilibrium, for if thermodynamic equilibrium is reached then the process stops, and life is no more. Life must therefore be powered by a gradient in free energy, which for the only type of life that we know takes the form of a chemical potential gradient, i.e. a non-zero affinity. Catabolic metabolism (henceforth simply metabolism, as I will not discuss anabolic metabolism in detail) is a chemical reaction (or rather a set of coupled chemical reactions) that transfers chemical energy from reactants in an organism's inorganic environment, known as the substrate, to complex organic molecules inside the organism, such as ATP (adenosine triphosphate), that are capable of delivering this energy to structures where the chemical energy is transformed to mechanical energy (e.g. motion), electrical energy (e.g. conscience), electromagnetic energy (e.g. fireflies), etc.

Atmospheric composition, and in particular the oxidation state of the atmosphere, is one of the factors in understanding the origin of life.

My first words when meeting a new class at the beginning of every semester, whether an introductory physical geology course or a graduate seminar, are always more or less the same: “Geology does not exist!”. Some students start frantically going over their schedules, wondering whether they are in the right room, but most of them just stare at me, wondering whether I am a lunatic. While they do this I explain that what I meant was that the Earth and other planets are complex systems in which every process can, and must, be dismantled until we can understand it in terms of the simplest possible physics and chemistry. This does little to put them at ease, but over the course of the first few weeks of class many of them come to understand what I mean, and even to agree with it.

This brings me to the several reasons why I decided to write this book. First, although a few good textbooks on thermodynamics applied to Earth systems are available, I find that none of them goes into the fundamentals of thermodynamics with the depth that I am convinced is necessary. Rather, they tend to discuss the foundational principles of thermodynamics on a “need to know” basis. My approach is exactly the opposite: build a solid understanding of the foundations of thermodynamics first, and explain everything else in terms of this understanding.

We have developed a comprehensive physical description of the processes and pathways by which planetary bodies acquire internal energy. Our next task is to examine how this internal energy drives planetary processes. The hallmark of an active planetary body is that it has surface features, other than impact craters, that have ages that are negligible compared to the age of the Solar System. This is true for any epoch of the Solar System. For instance, the youngest features on the Moon, the immense basaltic plains that we call lunar maria, are about 3 billion years old. This means that the Moon is dead today, but it was active when the age of the Solar System was of the order of 1.5 billion years

Active planetary processes are associated to heat flow, but the causal connection is not always the same. Consider the ascent of magmas. This is a process that transfers mass and heat from the planet's interior towards its surface, and that is made possible by melting, which entails conversion of thermal energy to chemical energy. Ascent of magma and construction of volcanoes, however, are not driven by thermal energy but by gravitational energy. Magmas rise to the surface of a planet if they are buoyant, and magmas are buoyant if melting causes a decrease in density.

A phase diagram is a graph that shows the distribution of stable phase assemblages as a function of the values of the intensive variables used to describe the thermodynamic system. If pressure and temperature are the variables of interest then the stable assemblage is the one with the lowest Gibbs free energy, although other thermodynamic potentials may be used if the variables of interest are different, for example, Helmholtz free energy if one is interested in temperature and volume (more on this in Chapter 9). Phase diagrams are powerful analytical tools in many branches of planetary sciences, as they provide a way to quickly visualize how phase assemblages change in response to changes in pressure, temperature, chemical potentials, or any other combination of intensive variables. There are many different types of phase diagrams and it is not the purpose of this book to offer a comprehensive review of all of them. Rather, in this chapter I will focus on the fundamental rules that phase diagrams must abide by in order to be thermodynamically valid. We therefore begin with a discussion of the thermodynamic underpinnings of phase diagrams.

The foundations of phase equilibrium

The Gibbs–Duhem equation

Any extensive thermodynamic property can be written as a sum of products of partial molar properties times mol numbers (equation (5.27)).

Planetary bodies can be thought of as combinations of heat reservoirs and heat engines. The heat reservoirs store internal energy, E, and the heat engines convert some of this thermal energy into various types of mechanical, electrical and chemical energies. This simple physical picture is true of all active planetary bodies, regardless of their composition (rocks, gases or ices) or size. The details, however, vary widely throughout the Solar System. In this chapter we discuss the storage of thermal energy in planetary bodies.

We begin by distinguishing internal from external heat reservoirs, and we define the latter as those that derive their energy from solar electromagnetic radiation. External heat reservoirs occur in surface and near-surface environments. Examples include the Earth's oceans and atmosphere. Internal heat reservoirs store energy at various depths, from near-surface environments to the planet's core. They are fed by dissipation of various types of non-thermal energy but there is one unifying characteristic, which is that dissipation takes place deep enough that the rate of heating exceeds the rate of heat transfer to the planet's surface (Chapter 3). The relative magnitudes of the energy fluxes from external and internal reservoirs at a planet's surface vary widely among the bodies of the Solar System. In solid planetary bodies (rocky and icy) surface energy flux is typically dominated by solar radiation, despite the fact that internal energy reservoirs in some of them are large enough to make noticeable, perhaps dominant, contributions to the planet's surface features.

From a physical point of view a fluid is a material that lacks shear strength, i.e. that deforms, or “flows”, when subject to shear stress. The strain rate for a given shear stress is of course highly variable, and defines the viscosity of the fluid. From a chemical thermodynamic point of view it is convenient to distinguish between different types of fluids. There are fluids with relatively low densities and low viscosities, which tend to be highly mobile in planetary environments. These are often referred to as “volatiles”, and are typically composed of species in the system C–O–H–N–S–F–Cl, with inert gases (particularly He) also important in gas giants. There are also fluids with generally higher densities than volatiles, which also have much higher viscosities, typically by several orders of magnitude. If such fluids exist at equilibrium with solids of broadly similar bulk composition we call them melts (Chapter 10). Melts in terrestrial planets are chiefly silicates, although natural carbonate melts also exist, as do metallic melts in planetary cores. Melts in icy satellites, in contrast, are likely to be composed chiefly of species in the system C–O–H–N. A third type of fluids are liquids at conditions that are far removed from equilibrium with solids of similar bulk composition, but that may contain species in solution that crystallize their own solids.

The First Law of Thermodynamics, like all conservation laws, is expressed mathematically by an identity relationship. As such, it is incapable of predicting the direction in which a natural process will occur. For example, on the basis of energy conservation alone it is not possible to decide whether heat flows from a hot body to a colder one, or the other way around. We know that heat flows down a temperature gradient, but this does not follow from the First Law. Similarly, energy conservation cannot predict that ice will melt at 20°C, or that water will freeze at -20°C, and it cannot predict that a gas will expand to fill all of the volume available to it.

Another law of nature is required to predict the direction of spontaneous changes. By “spontaneous” we mean a process that occurs in nature in the direction towards equilibrium and without outside intervention. For example, heat flow down a temperature gradient is a spontaneous process. It is possible to transfer heat from a cold body to a hotter one, but this requires “outside intervention” in the form of a heat pump, which uses mechanical energy to accomplish a process that is not “naturally spontaneous”. As soon as the expenditure of mechanical energy ceases the spontaneous process takes over and the cold body heats up at the expense of the hotter one.