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2372 results in Chemical engineering

Page 48 of 119

  • 5 - Application to process design: flow systems

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 149-180

  • Summary

    Traditional application of thermodynamics to engineering problems involves processes that are flowing. For example, an engineer might design a refrigerator in which a refrigerant is pumped in a continuous cycle through a coil of tubing, or a generator where steam is pumped in a power cycle through several pieces of equipment. Hence, engineering has placed a lot of emphasis on balances in flowing systems. Such flow systems involve time as an independent variable. However, thermodynamics applies only to equilibrium states, and the introduction of time is strictly forbidden. The study of time-dependent processes actually falls within the domains of transport phenomena and non-equilibrium thermodynamics.

    Whereas the field of transport phenomena is relatively well advanced and well understood, non-equilibrium thermodynamics is a developing field of research, and the fundamental postulates are by no means agreed upon [11, 94].

    We will restrict ourselves here to the simplest of such time-dependent systems. Namely, we will assume that our system is in a local state of equilibrium. Such an assumption allows us to use the quantities derived for equilibrium systems as local variables that depend upon position and time. This simplification is usually applicable whenever the local response time of a system is much smaller than the time scale of the whole process. In this way, we can simplify many engineering flow problems to equivalent equilibrium thermodynamics problems.

  • 1 - Introduction

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 1-6

  • Summary

    For good or evil, all physical processes observed in the Universe are subject to the laws and limitations of thermodynamics. Since the fundamental laws of thermodynamics are well understood, it is unnecessary to limit your own understanding of these thermodynamic restrictions.

    In this text we lay out the straightforward foundation of thermodynamics, and apply it to systems of interest to engineers and scientists. Aside from considering gases, liquids and their mixtures – traditional problems in engineering thermodynamics – we consider also the thermodynamics of DNA, proteins, polymers, and surfaces. In contrast to the approach adopted by most traditional thermodynamics texts, we begin our exposition with the fundamental postulates of thermodynamics, and rigorously derive all steps. When approximations are necessary, these are made clear. Therefore, the student will not only learn to solve some standard problems, but will also know how to approach a new problem on safe ground before making approximations.

    Thermodynamics gives interrelationships between the properties of matter. Often these relationships are non-intuitive. For example, by measuring the volume and heat capacity as functions of temperature and pressure, we can find all other thermodynamic properties of a pure system. Then, we can use relations between different thermodynamic properties to estimate the temperature rise of a fluid when it is expanded in an insulated container, or, we can use such data to predict the boiling point of a liquid. In Chapter 2, we introduce the necessary variables to describe a system in thermodynamic equilibrium.

  • Appendix B - Fluid equations of state

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 437-450

  • 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].

  • 2 - The postulates of thermodynamics

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 7-51

  • 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.

  • 4 - First applications of thermodynamics

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 112-148

  • 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.

  • 12 - Thermodynamics of surfaces

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 393-425

  • 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.

  • 8 - Fugacity and vapor–liquid equilibrium

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 246-281

  • 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.

  • Appendix D - Physical properties and references

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 461-469

  • 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.

  • • The National Institute for Standards and Technology (NIST) keeps a tremendous amount of data online, and contains links to other sites. They also sell catalogs and computer software (webbook.nist.gov/chemistry).

  • • Data on many thermodynamic, transport, and physical properties are stored by the American Institute of Chemical Engineers at the Design Institute for Physical Property Data. A large database has free access for students (www.aiche.org/dippr).

  • • Free software, and data, such as molecular weights, critical pressures and critical temperatures, may be found for gases at Flexware (http://www.flexwareinc.com/).

  • • Professor G. R. Mansoori of the University of Illinois-Chicago maintains a website with links to many other web pages that contain data, or computer programs for thermodynamic calculation: (http://www.uic.edu/mansoori/Thermodynamic.Data.and.Property_html).

  • • The University of Texas has a Javascript program called “ThermoDex” that searches their bookshelves for thermodynamic data. The program returns only the reference for the book, however: (www.lib.utexas.edu/thermodex).

  • 3 - Generalized thermodynamic potentials

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 52-111

  • 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.

  • Preface

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp xv-xvii

  • 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.

  • 7 - Molecular interactions

  • Juan J. de Pablo, University of Chicago, Jay D. Schieber, Illinois Institute of Technology
  • Book:
    Molecular Engineering Thermodynamics
    Published online:
    28 May 2018
    Print publication:
    10 July 2014, pp 211-245

  • 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.

Molecular Engineering Thermodynamics
  • Juan J. de Pablo, Jay D. Schieber
  • Published online:
    28 May 2018
    Print publication:
    10 July 2014
  • Building up gradually from first principles, this unique introduction to modern thermodynamics integrates classical, statistical and molecular approaches and is especially designed to support students studying chemical and biochemical engineering. In addition to covering traditional problems in engineering thermodynamics in the context of biology and materials chemistry, students are also introduced to the thermodynamics of DNA, proteins, polymers and surfaces. It includes over 80 detailed worked examples, covering a broad range of scenarios such as fuel cell efficiency, DNA/protein binding, semiconductor manufacturing and polymer foaming, emphasizing the practical real-world applications of thermodynamic principles; more than 300 carefully tailored homework problems, designed to stretch and extend students' understanding of key topics, accompanied by an online solution manual for instructors; and all the necessary mathematical background, plus resources summarizing commonly used symbols, useful equations of state, microscopic balances for open systems, and links to useful online tools and datasets.

Page 48 of 119