Thermodynamics is fundamental and applicable to all technical endeavors. Its two brief laws provide a complete basis for establishing the states of pure substances and their mixtures. It shows us the directions in which those states tend to change when systems are prodded by external forces. It provides a secure foundation for scientific investigations into all forms of matter. It reveals constraints on interconversions of heat and work, on separations of components from solutions, and on ultimate extents of chemical reactions. It can guide screening for feasibility of alternative processes, and when a design has been selected, it can contribute to the optimization of that design.

Although thermodynamics describes natural phenomena, those descriptions are in fact products of creative, systematic, human minds. Nature unfolds without any explicit reference to energy, entropy, or fugacity; these are unnatural concepts created by humans. Nevertheless, the complexities observed in Nature can be organized by appealing to thermodynamic methodology. With proper understanding, generalized thermodynamic techniques can be used to deal effectively with many aspects of reality. But to gain that understanding, thermodynamics must be studied in a systematic way that uncovers its structure and economy.

Thermodynamic ideas originated almost 200 years ago, but the subject continues to evolve. Although some claim that “there is nothing new in thermodynamics,” scholars still find challenges in its abstractness, rigor, and universality. They debate the “best” ways to phrase its basic principles and to identify the limits of its application.

When we apply thermodynamics to industrial and research problems, we should draw fundamental ideas from Parts I and II, devise an appropriate solution strategy, as in Chapter 10, and combine those with a computational technique, as in Chapter 11. Such a procedure provides values for measurables that can be used to interpret novel phenomena, to design new processes, and to improve existing processes. The procedure is illustrated in this chapter for several well-developed situations. They include conventional phase-equilibrium calculations for vapor-liquid, liquid-liquid, and solid-solid equilibria (§ 12.1); solubility calculations for gases in liquids, solids in liquids, and solutes in near-critical solvents (§ 12.2); independent variables in steady-flow processes (§ 12.3); heat effects for flash separators, absorbers, and chemical rectors (§ 12.4); and effects of changes of state on selected properties (§ 12.5).

PHASE EQUILIBRIA

When two or more bulk phases are in contact and at equilibrium, the measurables of interest are usually temperature, pressure, and the compositions of the phases. Of these measurables, the most important are often the compositions; for example, in the design and operation of separation processes, we routinely need the composition of a particular phase, or when the temperature and pressure change, we need to know the extent to which the compositions also change. When engineering applications involve fluid-fluid equilibria, we often find that, besides absolute compositions, relative compositions can be informative and important.

In the previous chapter we accomplished our first objective: we showed how the process variables heat and work are related to changes in system properties, the internal energy U and the entropy S. Those relations are provided by the first and second laws. Now our problem is to learn how to compute changes in U and S. Since U and S cannot be obtained directly from experiment, we must first relate ΔU and ΔS to measurable state functions, particularly temperature, pressure, volume, composition, and heat capacities. When we can establish such relations, our strategy in a process analysis can take the path on the left branch of the diagram shown in Figure 3.1.

Unfortunately, ΔU and ΔS are not always simply related to measurables, nor are ΔU and ΔS always directly related to convenient changes of state. So to ease conceptual and computational difficulties, we create additional state functions. Then we must establish how ΔU and ΔS are related to these new state functions and, in turn, how changes in the new functions are related to measurables. In these situations, our strategy follows the right branch of the diagram in Figure 3.1. In this chapter we develop relations that allow us to follow both strategies represented in the figure.

Our long-term goal is to be able to analyze processes, and since processes cause changes in system states, we begin by discussing the conditions that must be satisfied to characterize a state (§ 3.1).

When two or more homogeneous systems are brought into contact to form a single heterogeneous system, any of several actions may occur before equilibrium is reestablished. The possibilities include mass and energy transfers, chemical reactions, and the appearance or disappearance of phases. In this chapter we provide thermodynamic criteria for determining whether and to what extent such phenomena actually occur. Surprisingly, these criteria invoke no new thermodynamics—we need only combine familiar thermodynamic quantities in new ways and, in some cases, apply to those quantities mathematical operations that we have not used heretofore.

The heterogeneities of most concern to us are those that involve the presence of more than one phase. The analysis of multiphase systems can be important to the design and operation of many industrial processes, especially those in which multiple phases influence chemical reactions, heat transfer, or mixing. For example, phase-equilibrium calculations form the bases for many separation processes, including stagewise operations, such as distillation, solvent extraction, crystallization, and supercritical extraction, and rate-limited operations, such as membrane separations.

Analysis of multiphase systems is a principal theme of chemistry and chemical engineering; another is analysis of chemical reactions—processes in which chemical bonds are rearranged among species. Rearranging chemical bonds is the most efficient way to store and release energy, it drives many natural processes, and it is used industrially to make substitutes for, and concentrated forms of, natural products.

You are a member of a group assigned to experimentally determine the behavior of certain mixtures that are to be used in a new process. Your first task is to make a 1000-ml mixture that is roughly equimolar in isopropanol and water; then you will determine the exact composition to within ±0.002 mole fraction. Your equipment consists of a 1000-ml volumetric flask, assorted pipettes and graduated cylinders, a thermometer, a barometer, a library, and a brain. You measure 300 ml of water and stir it into 700 ml of alcohol—Oops!—the meniscus falls below the 1000-ml line. Must have been careless. You repeat the procedure: same result. Something doesn't seem right.

At the daily meeting it quickly becomes clear that other members of the group are also perplexed. For example, Leia reports that she's getting peculiar results with the isopropanol-methyl(ethyl)ketone mixtures: her volumes are greater than the sum of the pure component volumes. Meanwhile, Luke has been measuring the freezing points of water in ethylene glycol and he claims that the freezing point of the 50% mixture is well below the freezing points of both pure water and pure glycol. Then Han interrupts to say that 50:50 mixtures of benzene and hexafluorobenzene freeze at temperatures higher than either pure component.

During the design and operation of chemical processes, we routinely propose a state for a system by specifying a temperature, pressure, composition, and phase. Then the question is, Can the system be brought to that state? This is a question of observability. In many situations, particularly those involving multicomponent mixtures, the answer is not at all obvious. For example, at certain values for T and P, mixtures of phenol and water can undergo drastic phase changes in response to slight changes in composition: a mixture of phenol in water might be a one-phase vapor, or a one-phase water-rich liquid, or a phenol-rich liquid in equilibrium with a water-rich liquid, or it might be in three-phase vapor-liquid-liquid equilibrium.

In the previous chapter we derived criteria for identifying equilibrium states; for example, in a closed system at fixed T and P, the equilibrium state is the one that minimizes the Gibbs energy. That minimization is equivalent to satisfying the equality of component fugacities. More generally, we derived criteria for thermal, mechanical, and diffusional equilibrium in open systems. But although those criteria can be used to identify equilibrium states, they are not always sufficient to answer the question of observability. Observability requires stability. Thermodynamic states can be stable, metastable, or unstable; a stable equilibrium state is always observable, a metastable state may sometimes be observed, and an unstable state is never observed.

Introduction

Throughout history there has been a never-ending effort to develop materials with higher yield strength. However, a higher yield strength is generally accompanied by a lower ductility and a lower toughness. Toughness is the energy absorbed in fracturing. A high-strength material has low toughness because it can be subjected to higher stresses. The stress necessary to cause fracture may be reached before there has been much plastic deformation to absorb energy. Ductility and toughness are lowered by factors that inhibit plastic flow. As schematically indicated in Figure 13.1, these factors include decreased temperatures, increased strain rates, and the presence of notches. Developments that increase yield strength usually result in lower toughness.

In many ways the fracture behavior of steel is like that of taffy candy. It is difficult to break a warm bar of taffy candy to share with a friend. Even children know that warm taffy tends to bend rather than break. However, there are three ways to promote its fracture. A knife may be used to notch the candy bar, producing a stress concentration. The candy may be refrigerated to raise its resistance to deformation. Finally, rapping it against a hard surface raises the loading rate, increasing the likelihood of fracture. Notches, low temperatures, and high rates of loading also embrittle steel.

There are two important reasons for engineers to be interested in ductility and fracture. The first is that a reasonable amount of ductility is required to form metals into useful parts by forging, rolling, extrusion, or other plastic working processes.

Introduction

It has been estimated that 90% of all service failures of metal parts are caused by fatigue. A fatigue failure is one that occurs under cyclic or alternating stress of an amplitude that would not cause failure if applied only once. Aircraft are particularly sensitive to fatigue. Automobile parts such as axles, transmission parts, and suspension systems may fail by fatigue. Turbine blades, bridges, and ships are other examples. Fatigue requires cyclic loading, tensile stresses, and plastic strain on each cycle. If any of these are missing, there will be no failure. The fact that a material fails after a number of cycles indicates that some permanent change must occur on every cycle. Each cycle must produce some plastic deformation, even though it may be very small. Metals and polymers fail by fatigue. Fatigue failures of ceramics are rare because there seldom is plastic deformation.

There are three stages of fatigue. The first is nucleation of a crack by small amounts of inhomogeneous plastic deformation at a microscopic level. The second is the slow growth of these cracks by cyclic stressing. Finally sudden fracture occurs when the cracks reach a critical size.

Surface observations

Often visual examination of a fatigue fracture surface will reveal clamshell or beach markings as shown in Figure 17.1. These marks indicate the position of the crack front at some stage during the fatigue life. The initiation site of the crack can easily be located by examining these marks.

Introduction

Tensile test data have many uses. Tensile properties are used in selecting materials for various applications. Material specifications often include minimum tensile properties to ensure quality. Tests must be made to ensure that materials meet these specifications. Tensile properties are also used in research and development to compare new materials or processes. With plasticity theory, tensile stress–strain curves can be used to predict a material's behavior under forms of loading other than uniaxial tension.

Often the primary concern is strength. The level of stress that causes appreciable plastic deformation of a material is called its yield stress. The maximum tensile stress that a material carries is called its tensile strength (or ultimate strength or ultimate tensile strength). Both of these measures are used, with appropriate caution, in engineering design. A material's ductility is also of interest. Ductility is a measure of how much the material can deform before it fractures. Rarely, if ever, is the ductility incorporated directly into design. Rather it is included in specifications to ensure quality and toughness. Elastic properties may be of interest, but these are measured ultrasonically much more accurately that by tension testing.

Tensile specimens

Figure 3.1 shows a typical tensile specimen. It has enlarged ends or shoulders for gripping. The important part of the specimen is the gauge section. The cross-sectional area of the gauge section is less than that of the shoulders and grip region, so the deformation will occur here.

Introduction

Necking limits uniform elongation in tension, making it difficult to study plastic stress–strain relationships at high strains. Much higher strains can be reached in compression, torsion, and bulge tests. The results from these tests can be used, together with the theory of plasticity (Chapter 6), to predict stress–strain behavior under other forms of loading. Bend tests are used to avoid the problem of gripping brittle material without breaking it. Hardness tests eliminate the considerable time and effort required to machine tensile specimens. Also, hardness tests are simple to perform and are not destructive.

Compression test

Much higher strains are achievable in compression tests than in tensile tests. However, two problems limit the usefulness of compression tests: friction and buckling. Friction on the ends of the specimen tends to suppress the lateral spreading of material near the ends (Figure 4.1). A cone-shaped region of dead metal (nondeforming material) can form at each end, with the result that the specimen becomes barrel shaped. Friction can be reduced by lubrication and the effect of friction can be lessened by increasing the height-to-diameter ratio, h/d, of the specimen.

Introduction

Plastic deformation of crystalline materials usually occurs by slip, which is the sliding of planes of atoms over one another (Figure 8.1). The planes on which slip occurs are called slip planes and the directions of the shear are the slip directions. These are crystallographic planes and directions that are characteristic of the crystal structure. The magnitude of the shear displacement is an integral number of interatomic distances, so that the lattice is left unaltered. If slip occurs on only part of a plane, there remains a boundary between the slipped and unslipped portions of the plane, which is called a dislocation. Slip occurs by movement of dislocations through the lattice. It is the accumulation of the dislocations left by slip that is responsible for work hardening. Dislocations and their movement are treated in Chapters 9 and 10. This chapter is concerned only with the geometry of slip.

Visual examination of the surface of a deformed crystal will reveal slip lines. The fact that we can see these indicates that slip is inhomogeneous on an atomic scale. Displacements of thousands of atomic diameters must occur on discrete or closely spaced planes to create steps on the surface that are large enough to be visible. Furthermore, the planes of active slip are widely separated on an atomic scale. Yet the scale of the slip displacements and distances between slip lines is small compared to most grain sizes, so slip usually can be considered as homogeneous on a macroscopic scale.