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Summary

The text considers the ideal gas and van der Waals equations of state in some detail. In addition to these, we summarize here several more-accurate equations of state. This appendix presents but a small fraction of such equations. A more comprehensive discussion of the quality of such equations is given in [118].

Note that all fluid equations of state reduce to the general ideal gas at low densities. For small deviations from ideal behavior, the virial expansion is the most reliable. However, it is not appropriate for predicting vapor–liquid equilibria. The cubic equations of state are straightforward to use and computationally simple. However, some sacrifice must be made for accuracy. Of these, the Peng–Robinson, Soave–Redlich–Kwong, and Schmidt–Wenzel equations are usually superior. However, all cubic equations are suspect near the critical region. For an excellent review of many such equations, see [5]. If computational ease should be sacrificed for accuracy, the Benedict–Webb–Rubin and the Anderko–Pitzer equations are usually more accurate.

The parameters in the cubic PVT equations of state are usually determined from the critical properties of a fluid, and these equations are given. Critical values for a few substances are given in Table D.3 in Appendix D. More values can be found from the NIST web page. If the critical values of a substance are not known, they may be estimated from group methods on the basis of the chemical structure of the substance. These methods are reviewed in [102].

Summary

It began, to use the formula familiar in today's newspapers, with an “act of state-sponsored terrorism.” The archduke Francis Ferdinand was the heir apparent to the Habsburg throne of Austria–Hungary; when, on June 28, 1914, a Serbian student shot him and his wife to death in Sarajevo, the capital of the Austrian province of Bosnia, the act provoked astonishment and outrage throughout Europe. Public excitement quickly receded, however, despite lingering rumors in the newspapers – subsequently substantiated – that officials of the Serbian government had been complicit in the assassination. In Germany and elsewhere the summer season had begun. The onset of warm weather signaled travel for those who could afford it; and, for those who could not, it brought less idle adjustments in the annual rhythms of life in town and countryside.

In Berlin, as elsewhere, the events in Sarajevo provoked a series of fateful deliberations during the first weeks of July. The German leadership concluded that the assassination carried far-reaching implications for German security. Austria–Hungary was Germany's principal ally. The Serbian affront promised to encourage discontent not only among the South Slav inhabitants of Austria–Hungary but also among the other ethnic groups that made up the Habsburg monarchy. In the eyes of the German leaders, the logic of this process boded the dissolution of the monarchy and, ultimately, Germany's full diplomatic and military isolation in Europe.

This alarming prospect loomed over the consultations in the German capital. The decisions that emerged out of these deliberations have themselves given rise to a bitter dispute among professional historians. At the center of the dispute stands the German chancellor, Theobald von Bethmann Hollweg (see Plate 1), the civilian head of the German federal government. Some historians, with Fritz Fischer in the lead, have argued that Bethmann seized upon the assassination as the pretext to launch a long-planned war of aggression, whose goal was German hegemony on the European continent. The preponderance of evidence now suggests instead, however, that the chancellor pursued a somewhat more cautious policy, which grew out of his anxiety over the future of the Austrian monarchy, whose survival, he believed, did justify the risk of a European war. Bethmann was strengthened in this belief by the country's leading soldier, the chief of the army's General Staff, Helmuth von Moltke. Moltke's calculations were technical.

Summary

Thermodynamics is the combination of a structure plus an underlying governing equation. Before designing plays in basketball or volleyball, we first need to lay down the rules to the game – or the structure. Once the structure is in place, we can design an infinite variety of plays and ways that the game can run. Some of these plays will be more successful than others, but all of them should fit the rules. Of course, in sports you can sometimes get away with breaking the rules, but Mother Nature is not so lax. You might be able to convince your boss to fund construction of a perpetual-motion machine, but the machine will never work.

In this chapter we lay the foundation for the entire structure of thermodynamics. Remarkably, the structure is simple, yet powerfully predictive. The cost for such elegance and power, however, is that we must begin somewhat abstractly. We need to begin with two concepts: energy and entropy. While most of us feel comfortable and are familiar with energy, entropy might be new. However, entropy is no more abstract than energy – perhaps less so – and the approach we take allows us to become as skilled at manipulating the concept of entropy as we are at thinking about energy. Therefore, in order to gain these skills, we consider many examples where an underlying governing equation is specified. For example, we consider the fundamental relations that lead to the ideal-gas law, the van der Waals equation of state, and more sophisticated equations of state that interrelate pressure, volume, and temperature.

Summary

Now that we have a reasonably complete structure of thermodynamics, we can tackle more complicated problems. In the following section we introduce the concepts of local and global stability, and show how local stability puts restrictions on second-order derivatives. In Section 4.2 we see that application of local stability criteria to the proposed fundamental relations leads to predictions of spinodal curves, which indicate when substances will spontaneously change state. In Section 4.2.2 the application of global stability to a van der Waals fluid leads to predictions of vapor saturation curves and liquid saturation curves. These curves are sometimes called binodal curves (or coexistence curves), and can be predicted from PVT equations of state alone. We then show how thermodynamic diagrams useful for refrigeration, or power-cycle design, can be constructed from PVT relations in Section 4.4. Section 4.4.2 shows generically how one can make predictions of differences in thermodynamic quantities from any of the equations of state shown in Appendix B or from experimental data.

STABILITY CRITERIA

What happens if you take gaseous nitrogen and compress it, keeping the internal energy constant by removing heat? Eventually, the nitrogen begins to condense in the container, and you have a mixture of liquid and gaseous nitrogen. If you isolate this system and wait for a long time, then you see that the system is indeed at a stable equilibrium. From Section 2.8 we know that these two phases have the same temperature and pressure. How can that be? Why is some of the nitrogen happy to stay gaseous, while the rest saw fit to condense into a liquid? The two phases have the same temperature and pressure, yet they have different densities.

Summary

This book originated in another project, which is at once broader in scope and much narrower in focus. In deference to the principle that total war requires total history, I have been studying the comprehensive impact of the First World War in a single mid-sized German city. In conjunction with this project, I decided several years ago to explore the history of the war and German society with a class of undergraduate students at the University of Oregon. I discovered that there was no suitable text for such a course. The present volume grew directly out of discussions with students in that class. It is conceived in the first instance for readers like them, but it is also intended for others who are interested in the modern history of Germany and Europe, as well as the history of war and society. The scholarly apparatus is designed for those whom the text entices into further reading.

It is now a pleasure to repay my many intellectual debts with public gratitude. My thanks go first to my students in Oregon, my former home, for contributions that pervade the volume. In addition, I owe great thanks to a number of scholars who have offered comments on the manuscript as it progressed. They include Gerald Feldman, Wilhelm Deist, Belinda Davis, Stig Förster, and Richard Stites, who is now my colleague at Georgetown. My friend Bruce Wonder, who counts himself in the category of “informed general reader,” has also offered invaluable suggestions for the manuscript's improvement. My research assistant, David Freudenwald, provided much-needed help in my dealings with a number of libraries. Several institutions have also supported the manuscript in various stages of its gestation. My gratitude goes to the Gerda Henkel Foundation, which supported a year's research in Europe in 1991–2, the Graduate School at Georgetown University, which made possible several subsequent trips to Europe, and the Woodrow Wilson International Center for Scholars in Washington, DC, which providedme with the opportunity to complete the work in a stimulating atmosphere of intellectual exchange.

Preface to the Third Edition

When I began to work on the First World War in the late 1980s, I had no idea that I would still be writing about it on the occasion of its centenary. A lot has happened in the meantime. This volume has now gone through two English-language editions, as well as a German translation.

Summary

The pressure inside a soap bubble is slightly larger than that outside the bubble. If those two pressures were equal, the bubble would simply collapse. The liquid film that constitutes the bubble is under tension, and is therefore able to sustain the force imbalance that arises from that pressure difference. Throughout most of this text, we have focused our attention on the properties of bulk phases. The boundaries or interfacial regions between bulk phases at equilibrium exhibit a number of interesting properties that are often different from those of the bulk. These properties are particularly important in a wide variety of technologies, including nano-fabrication, ink-jet printing, coatings, and biotechnology. This chapter discusses a few extensions of ideas presented earlier in the text to determine the behavior of interfaces.

The study of the thermodynamics of surfaces usually adopts one of two conventions. In the approach of Gibbs [17], a sharp dividing surface is introduced between two distinct phases (e.g. a liquid and a vapor). In the approach of Guggenheim [51], the interfacial region has a finite volume Vσ, over which the thermodynamic properties of the system change gradually. The latter approach is followed closely in this chapter because it is more physically intuitive. We note, however, that in our discussion of mixtures and surface quantities we adopt the view that the volume of the interfacial region is so small as to be negligible. In that limit, we implicitly return to the Gibbs treatment of an interface.

Summary

In Chapter 4 we saw how simple stability criteria derived from the postulates have important consequences for the calculation of vapor–liquid equilibria. More specifically, we discussed how the spinodal curve of a pure fluid defines the boundary between locally stable and unstable states, and we also saw how global stability leads to guidelines for the calculation of binodal, or coexistence, curves.

As the number of components of a mixture increases, the stability criteria become increasingly complex and more difficult to apply, although the principles are the same. Calculations of phase equilibria for multicomponent mixtures therefore become more elaborate. These calculations are commonplace in applications, and it is therefore important to have an efficient machinery to address this problem. This chapter presents that machinery.

Previous chapters dealt mostly with pure-component systems. For these we first introduced the idea of fundamental relations for U or for S (Chapter 2), and then, through Legendre transforms, we introduced fundamental relations in the generalized potentials (Chapter 3). In Chapter 4 we showed how these fundamental relations for a one-component system can be derived from two equations of state, typically a mechanical equation of state, and a thermal equation of state. We also showed in Chapter 6 how to derive fundamental relations from simple molecular models.

However, in Chapter 4 we also showed how many things could be accomplished through the mechanical equation of state alone, such as calculations of vapor–liquid equilibrium and residual properties. For multicomponent vapor–liquid equilibrium, we will find in this chapter that mechanical equations of state are sufficient when we use a quantity called fugacity in place of the chemical potential.

Summary

WEBSITES WITH DATA AND PROGRAMS

There are many sources available for finding physical properties, such as critical properties, heat capacities, molecular weights, etc. Besides texts, many computer packages may be accessed for the data. Below is a list of URLs that may be used to find data for many species and computer programs on the web. Most of these are free, but they may contain links to services requiring fees. Since we have no control over their content, we cannot be responsible for the accuracy or usefulness of the information supplied. URLs are not particularly stable, but they should be obtainable from a search engine, such as Google.

Summary

Despite increasing misery on the home front, growing unrest, the radicalization of the labor movement, and the polarization of opinion to the brink of constitutional crisis, the prospects for a German victory appeared brighter at the beginning of 1918 than they had at any time since the summer of 1914. To be sure, the American entry into the war in April 1917 promised eventual relief to the Entente powers, but staggering losses among the armies of these powers in the spring and summer of 1917 threatened to end the conflict before an American army could arrive in Europe. Renewed French and British offensives in 1917 failed again to break the strategic stalemate on the western front; they also brought the French army to the verge of collapse. Events elsewhere, meanwhile, turned catastrophic for the Entente. To the south, the Italian army suffered a crippling defeat. In the east, the war ended amid the dissolution of the Russian armies. The domestic beneficiaries of the Russian military collapse were the Bolsheviks, who seized power in November 1917 and immediately called for an end to the war. The other beneficiaries were the Germans, who began to sense a happy end to the war.

The Germans won the war in the east in 1917. The prospect of victory in the south and west in 1918 elevated spirits on the home front and dampened the domestic discord. Events appeared to ratify Ludendorff's leadership. They also ratified his vision of the war's conclusion and eliminated the final, frail possibility of a negotiated peace.

“Peace feelers”

Although their armies were locked in combat, the belligerent sides remained in almost constant diplomatic contact throughout the war. Willing intermediaries were to be found in the neutral lands, above all in Switzerland. They included businessmen who had dealings in both camps, representatives of Europe's minor royalty who had relatives in both camps, and members of the papal diplomatic corps. Many of these contacts were the stuff of novels: stories of intrigue, shadowy go-betweens, and secret meetings among agents armed with vague promises.

The year 1917 brought a flurry of such activity. Its overture came in December 1916, when, in the glow of victory over Romania, the Central Powers offered publicly to negotiate. In its ambiguity and haughty tone, the offer married Bethmann Hollweg's hopes and Ludendorff's designs. It produced only skepticism in the Allied camp.

Summary

From the postulates in Chapter 2, we have already seen that from U(S, V, N1, …, Nm) or S(U, V, N1, …, Nm) we can derive all of the thermodynamic information about a system. For example, we can find mechanical or thermal equations of state. However, we also know that it is sometimes convenient to use other independent variables besides entropy and volume. For example, when we perform an experiment at room temperature open to the atmosphere, we are manipulating temperature and pressure, not entropy and volume. In this case, the more natural independent variables are T and P. Then, the following question arises: Is there a function of (T, P, N1, …, Nm) that contains complete thermodynamic information? In other words, is there some function, say G(T, P, N1, …, Nm), from which we could derive all the equations of state? It turns out that such functions do exist, and that they are very useful for solving practical problems.

In the first section we show how to derive such a function for any complete set of independent variables using something called Legendre transforms. In this book we introduce three widely used potentials: the enthalpy H (S, P, N1, …, Nm), the Helmholtz potential F (T, V, N1, …, Nm), and the Gibbs free energy G (T, P, N1, …, Nm). These functions which contain complete thermodynamic information using independent variables besides S, V, and N1, …, Nm are called generalized thermodynamic potentials.

Summary

Students of engineering and the physical sciences are often introduced to thermodynamics in a way that has evolved little over the last several decades.

This book is an outgrowth of the sense that thermodynamics courses should reflect changes in the problems that engineers and scientists encounter in practice. Important industrial sectors, including the oil, chemical, semiconductor, and pharmaceutical, continue to recruit large numbers of scientists and engineers, but new demands require them to be more versatile, and able to apply fundamental thermodynamic concepts in a wider range of situations. At the same time, start-ups in emerging fields must be nimble and rely on a work force that is equally comfortable applying thermodynamic principles to rationalize observations in biology or advanced materials design. Traditional boundaries between science and engineering are becoming blurred, and versatility in engineering is necessarily built on a broader understanding of far-reaching scientific principles. Engineering students must place greater emphasis on broadly applicable scientific concepts and learn how to use these in different contexts, and students in the sciences must gain a better appreciation for how such concepts are applied in engineering practice.

One clear and common trend in most engineering and scientific disciplines is that of control over smaller length scales. Experimental methods are able to probe and manipulate the behavior of individual molecules, and large-scale processes can be used to mass produce ultra-small electronic devices. We have entered the age of “molecular engineering,” and it is important to emphasize molecular-level concepts in thermodynamics texts.

Summary

Previous chapters established many relations between various thermodynamic properties of a fluid. We have seen, for example, that the heat capacity of a fluid is always positive. We have also shown that the thermal, mechanical, and chemical equations of state must be mutually consistent (i.e. they must satisfy the Gibbs–Duhem equation). In the previous chapter, we showed how statistical mechanics can be used to derive fundamental thermodynamic relations from simple models of molecular interactions. In this chapter we discuss in greater detail important molecular interactions and their relative magnitudes. Specific mathematical expressions taken from physical chemistry are used to estimate when interactions are important and how they might influence thermodynamic quantities. Molecular interactions ultimately determine the behavior of materials and fluids. Hence they have received considerable attention and entire texts have been devoted to their study. Interested readers are referred to [68, 80, 99] for a more complete and thorough discussion.

The equations of state and the transport properties of gases, liquids, and solids are intimately related to the forces between the molecules. The methods of statistical mechanics provide a connection between these forces and measurable thermodynamic properties. An introduction to statistical mechanics was presented in the previous chapter. Here we merely discuss the nature and the origin of intermolecular forces. In the following chapter we will illustrate how everything comes together to generate thermodynamic property predictions from intermolecular interactions. Finally, we note that calculation of intermolecular forces requires knowledge of several fundamental properties of molecules.

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Appendix B - Fluid equations of state

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List of abbreviations

1 - The war begins

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2 - The postulates of thermodynamics

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Index

4 - First applications of thermodynamics

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Preface to the First Edition

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12 - Thermodynamics of surfaces

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8 - Fugacity and vapor–liquid equilibrium

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Frontmatter

Appendix D - Physical properties and references

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Contents

Dedication

Suggestions for further reading

Frontmatter

6 - The war ends

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3 - Generalized thermodynamic potentials

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Prologue: Imperial Germany

Preface

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7 - Molecular interactions

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