Thermodynamics for the Practicing Engineer

Preface

Sir Walter Scott [1771–1832]

Good wine needs neither bush nor preface to make it welcome.

—Peveril of the Peak

This project was a rather unique undertaking. Rather than prepare a textbook on thermodynamics in the usual and traditional format, the authors considered writing a book that highlighted applications rather then theory. The book would hopefully serve as a training tool for those individuals in academia and industry involved directly, or indirectly, with this topic. Despite the significant reduction in theoretical matter, it addresses both technical and pragmatic problems in this field. While this book can be viewed as a text in thermodynamics, it also stands alone as a self-teaching aid.

The book is divided into four parts:

I. Introduction

II. Enthalpy Effects

III. Equilibrium Thermodynamics

IV. Other Topics

The first part of the book serves as an introduction to the subject of thermodynamics and reviews such topics as units and dimensions, the conservation laws, gas laws, and the second law of thermodynamics. The second part of the book is concerned with enthalpy effects and reviews such topics as sensible, latent, mixing, and chemical enthalpy effects. The third part of the book examines equilibrium thermodynamics. Topics here include both phase and chemical reaction equilibrium. The fourth section of the book addresses the general all purpose title of other topics. Subjects reviewed here include economics, open-ended problems, environmental concerns, health and safety management, numerical methods, ethics, and exergy analysis.

The authors cannot claim sole authorship to all the problems and material in this book. The present text has evolved from a host of sources, including: notes, homework problems and exam problems prepared by L. Theodore for a required one-semester, three-credit Chemical Engineering Thermodynamics undergraduate course offered at Manhattan College; Introduction to Hazardous Waste Incineration, 2nd Edition, J. Santoleri, J. Reynolds, and L. Theodore, John Wiley & Sons; Chemical Reaction Kinetics, L. Theodore, a Theodore Tutorial; and, Introduction to Chemical Engineering Thermodynamics, 3rd Edition, J.M. Smith and H.C. Van Ness, McGraw-Hill. Although the bulk of the problems are original and/or taken from the sources that the authors have been directly involved with, every effort has been made to acknowledge material drawn from other sources.

The policy of most technical societies and publications is to use SI (metric) units or to list both the common British engineering unit and its SI equivalent. However, British units are primarily used in this book for the convenience of the majority of the reading audience. Readers who are more familiar and at ease with SI units are advised to refer to the Appendix of this book.

It is hoped that this writing will place in the hands of academic and industrial individuals a book covering the principles and applications of thermodynamics in a thorough and clear manner. Upon completion of the text, the reader should have acquired not only a working knowledge of the principles of thermodynamics but also experience in their application; and, the reader should find himself/herself approaching advanced texts, engineering literature, and industrial applications (even unique ones) with more confidence.

Sincere thanks are extended to Shannon O’Brien at Manhattan College for her invaluable help in solving some of the problems in the text, preparing part of the initial draft of the solutions manual, and proofing the manuscript. Special thanks are due Eric Huang and Pat Abulencia for their technical assistance in preparing parts of the manuscript.

L. THEODORE

F. RICCI

T. VAN VLIET

February 2009

Part I

Introduction

Nicolò Machiavelli [1469–1527]

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

—The Prince. Chap. 6

Part I serves as the introductory section to this book. It reviews engineering and science fundamentals that are an integral part of the field of thermodynamics. It consists of six chapters, as noted below:

1 Basic Calculations

2 Process Variables

3 Gas Laws

4 Conservation Laws

5 Stoichiometry

6 The Second Law of Thermodynamics

Those individuals with a strong background in the above area(s) may choose to bypass this Part.

Chapter 1

Basic Calculations

Johann Wolfgang Von Goethe [1749–1832]

The sum which two married people owe to one another defies calculation. It is an infinite debt, which can only be discharged through all eternity.

—Elective Affinities [1808]. Book I, Chap. 9

INTRODUCTION

This first chapter provides a review of basic calculations and the fundamentals of measurement. Four topics receive treatment:

1 Units and Dimensions

2 Conversion of Units

3 The Gravitational Constant, gc

4 Significant Figures and Scientific Notation

The reader is directed to the literature in the reference section of this chapter if additional information on these four topics is deemed necessary.(1–3)

UNITS AND DIMENSIONS

The units used in this text are consistent with those adopted by the engineering profession in the United States. For engineering work, SI (Système International) and English units are most often employed; in the United States, the English engineering units are generally used, although efforts are still underway to obtain universal adoption of SI units for all engineering and science applications. The SI units have the advantage of being based on the decimal system, which allows for more convenient conversion of units within the system.

There are other systems of units. Some of the more common of these are shown in Table 1.1; however, English engineering units are primarily used in this text. Tables 1.2 and 1.3 present units for both the English and SI systems, respectively.

Table 1.1 Common Systems of Units

Table 1.2 English Engineering Units

Table 1.3 SI Units

Some of the more common prefixes for SI units are given in Table 1.4, and decimal equivalents are provided in Table 1.5. Conversion factors between SI and English units and additional details on the SI system are provided in the Appendix III.

Table 1.4 Prefixes for SI Units

Table 1.5 Decimal Equivalents

Two units that appear in dated literature are the poundal and slug. By definition, one poundal force will give a one pound mass an acceleration of one ft/s². Alternatively, one slug can be defined as the mass that will accelerate one ft/s² when acted upon by a one pound force; thus, a slug is equal to 32.2 pounds mass.

CONVERSION OF UNITS

Converting a measurement from one unit to another can be conveniently accomplished by using unit conversion factors; these factors are obtained from simple equations that relate the two units numerically. For example, from

(1.1) equation

the following conversion factor can be obtained:

(1.2) equation

Since this factor is equal to unity, multiplying some quantity (e.g., 18 ft) by this factor cannot alter its value. Hence

(1.3) equation

Note that in Equation (1.3), the old units of feet on the left-hand side cancel out leaving only the desired units of inches.

Physical equations must be dimensionally consistent. For the equality to hold, each term in the equation must have the same dimensions. This condition can be and should be checked when solving engineering problems. Throughout the text, great care is exercised in maintaining the dimensional formulas of all terms and the dimensional homogeneity of each equation. Equations will generally be developed in terms of specific units rather than general dimensions (e.g., feet rather than length). This approach should help the reader to more easily attach physical significance to the equations presented in these chapters.

ILLUSTRATIVE EXAMPLE 1.1

Convert units of acceleration in cm/s² to miles/yr².

SOLUTION: The procedure outlined above is applied to the units of cm/s²:

Thus, 1.0 cm/s² is equal to 6.18 × 10⁹ miles/yr².

THE GRAVITATIONAL CONSTANT, gc

The momentum of a system is defined as the product of the mass and velocity of the system:

(1.4) equation

One set of units for momentum are therefore lb · ft/s. The units of the time rate of change of momentum (hereafter referred to as rate of momentum) are simply the units of momentum divided by time, i.e.,

The above units can be converted to lbf if multiplied by an appropriate constant. As noted earlier, a conversion constant is a term that is used to obtain units in a more convenient form; all conversion constants have magnitude and units in the term, but can also be shown to be equal to 1.0 (unity) with no units.

A defining equation is

(1.5) equation

If this equation is divided by lbf, one obtains

(1.6) equation

This serves to define the conversion constant gc. If the rate of momentum is divided by gc as 32.2 lb · ft/lbf · s²—this operation being equivalent to dividing by 1.0—the following units result:

(1.7) equation

It can be concluded from the above dimensional analysis that a force is equivalent to a rate of momentum.

SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION(3)

Significant figures provide an indication of the precision with which a quantity is measured or known. The last digit represents, in a qualitative sense, some degree of doubt. For example, a measurement of 8.32 inches implies that the actual quantity is somewhere between 8.315 and 8.325 inches. This applies to calculated and measured quantities; quantities that are known exactly (e.g., pure integers) have an infinite number of significant figures.

The significant digits of a number are the digits from the first nonzero digit on the left to either (a) the last digit (whether it is nonzero or zero) on the right if there is a decimal point, or (b) the last nonzero digit of the number if there is no decimal point. For example:

Whenever quantities are combined by multiplication and/or division, the number of significant figures in the result should equal the lowest number of significant figures of any of the quantities. In long calculations, the final result should be rounded off to the correct number of significant figures. When quantities are combined by addition and/or subtraction, the final result cannot be more precise than any of the quantities added or subtracted. Therefore, the position (relative to the decimal point) of the last significant digit in the number that has the lowest degree of precision is the position of the last permissible significant digit in the result. For example, the sum of 3702., 370, 0.037, 4, and 37. should be reported as 4110 (without a decimal). The least precise of the five numbers is 370, which has its last significant digit in the tens position. The answer should also have its last significant digit in the tens position.

Unfortunately, engineers and scientists rarely concern themselves with significant figures in their calculations. However, it is recommended that—at least for this chapter—the reader attempt to follow the calculational procedure set forth in this subsection.

In the process of performing engineering calculations, very large and very small numbers are often encountered. A convenient way to represent these numbers is to use scientific notation. Generally, a number represented in scientific notation is the product of a number (< 10 but > or = 1) and 10 raised to an integer power. For example,

A positive feature of using scientific notation is that only the significant figures need appear in the number.

REFERENCES

1. R. Perry and D. Green (editors), "Perry’s Chemical Engineers’ Handbook," 8th edition, McGraw-Hill, New York, 2008.

2. J. REYNOLDS, J. JERIS, and L. THEODORE, "Handbook of Chemical and Environmental Engineering Calculations," John Wiley & Sons, Hoboken, NJ, 2004.

3. J. SANTOLERI, J. REYNOLDS, and L. THEODORE, "Introduction to Hazardous Waste Incineration," 2nd edition, John Wiley & Sons, Hoboken, NJ, 2000.

NOTE: Additional problems for each chapter are available for all readers at www. These problems may be used for additional review or homework purposes.

Chapter 2

Process Variables

Seneca [8 B.C.-A.D. 65]

The best ideas are common property.

—Epistles. 12, 11

INTRODUCTION

The authors originally considered the title State, Physical, and Chemical Properties for this chapter. However, since these three properties have been used interchangeably and have come to mean different things to different people, it was decided to simply employ the title Process Variables. The three aforementioned properties were therefore integrated into this all-purpose title and eliminated the need for differentiating between the three.

This second chapter provides a review of some basic concepts from physics, chemistry, and engineering in preparation for material that is covered in later chapters. All of these topics are vital to thermodynamics and thermodynamic applications. Because many of these topics are unrelated to each other, this chapter admittedly lacks the cohesiveness that chapters covering a single topic might have. This is usually the case when basic material from such widely differing areas of knowledge as physics, chemistry, and engineering is surveyed. Though these topics are widely divergent and covered with varying degrees of thoroughness, all of them will find later use in this text. If additional information on these review topics is needed, the reader is directed to the literature in the reference section of this chapter.

ILLUSTRATIVE EXAMPLE 2.1

Discuss the traditional difference (in definition) between chemical and physical properties.

SOLUTION: Every compound has a unique set of properties that allows one to recognize and distinguish it from other compounds. These properties can be grouped into two main categories: physical and chemical. Physical properties are defined as those that can be measured without changing the identity and composition of the substance. Key properties include viscosity, density, surface tension, melting point, boiling point, etc. Chemical properties are defined as those that may be altered via reaction to form other compounds or substances. Key chemical properties include upper and lower flammability limits, enthalpy of reaction, autoignition temperature, etc.

These properties may be further divided into two categories—intensive and extensive. Intensive properties are not a function of the quantity of the substance, while extensive properties depend on the quantity of the substance.

TEMPERATURE

Whether in the gaseous, liquid, or solid state, all molecules possess some degree of kinetic energy, i.e., they are in constant motion—vibrating, rotating, or translating. The kinetic energies of individual molecules cannot be measured, but the combined effect of these energies in a very large number of molecules can. This measurable quantity is known as temperature; it is a macroscopic concept only and as such does not exist on the molecular level.

Temperature can be measured in many ways; the most common method makes use of the expansion of mercury (usually encased inside a glass capillary tube) with increasing temperature. (In thermal applications, however, thermocouples or thermistors are more commonly employed.) The two most commonly used temperature scales are the Celsius (or Centigrade) and Fahrenheit scales. The Celsius is based on the boiling and freezing points of water at 1-atm pressure; to the former, a value of 100°C is assigned, and to the latter, a value of 0°C. On the older Fahrenheit scale, these temperatures correspond to 212°F and 32°F, respectively. Equations (2.1) and (2.2) show the conversion from one scale to the other:

(2.1) equation

(2.2) equation

where °F = a temperature on the Fahrenheit scale

°C = a temperature on the Celsius scale

Experiments with gases at low-to-moderate pressures (up to a few atmospheres) have shown that, if the pressure is kept constant, the volume of a gas and its temperature are linearly related via Charles’ law (see next chapter) and that a decrease of 0.3663% or (1/273) of the initial volume is experienced for every temperature drop of 1 °C. These experiments were not extended to very low temperatures, but if the linear relationship were extrapolated, the volume of the gas would theoretically be zero at a temperature of approximately — 273°C or — 460°F. This temperature has become known as absolute zero and is the basis for the definition of two absolute temperature scales. (An absolute scale is one which does not allow negative quantities.) These absolute temperature scales are the Kelvin (K) and Rankine (°R) scales; the former is defined by shifting the Celsius scale by 273°C so that 0 K is equal to -273°C; Eq. (4.3.3) shows this relationship:

(2.3) equation

The Rankine scale is defined by shifting the Fahrenheit scale 460°, so that

(2.4) equation

The relationships among the various temperature scales are shown in Fig. 2.1.

Figure 2.1 Temperature scales.

ILLUSTRATIVE EXAMPLE 2.2

Perform the following temperature conversions:

1 Convert 55°F to (a) Rankine, (b) Celsius, and (c) Kelvin.

2 Convert 55°C to (a) Fahrenheit, (b) Rankine, and (c) Kelvin.

SOLUTION

1 (a) °R = °F + 460 = 55 + 460 = 515

(b) °C = 5/9(°F - 32) = 5/9(55 - 32) = 12.8

(c) K = 5/9(°F + 460) = 5/9(55 + 460) = 286

2 (a) °F = 1.8(°C) + 32 = 1.8(55) + 32 = 131

(b) °R = 1.8(°C) + 492 = 1.8(55) + 492 = 591

(c) K = °C + 273 = 55 + 273 = 328

PRESSURE

Molecules in the gaseous state possess a high degree of translational kinetic energy, which means they are able to move quite freely throughout the body of the gas. If the gas is in a container of some type, the molecules are constantly bombarding the walls of the container. The macroscopic effect of this bombardment by a tremendous number of molecules—enough to make the effect measurable—is called pressure. The natural units of pressure are force per unit area. In the example of the gas in a container, the unit area is a portion of the inside solid surface of the container wall and the force, measured perpendicularly to the unit area, is the result of the molecules hitting the unit area and giving up momentum during the sudden change of direction.

There are a number of different methods used to express a pressure measurement. Some of them are natural units, i.e., based on a force per unit area, e.g., pound (force) per square inch (abbreviated lbf/in² or psi) or dyne per square centimeter (dyn/cm²). Others are based on a fluid height, such as inches of water (in H2O) or millimeters of mercury (mm Hg); units such as these are convenient when the pressure is indicated by a difference between two levels of a liquid as in a manometer or barometer. Barometric pressure and atmospheric pressure are synonymous and measure the ambient air pressure. Standard barometric pressure is the average atmospheric pressure at sea level, 45° north latitude at 32°F. It is used to define another unit of pressure called the atmosphere (atm). Standard barometric pressure is 1 atm and is equivalent to 14.696 psi and 29.921 in Hg. As one might expect, barometric pressure varies with weather and altitude.

Measurements of pressure by most gauges indicate the difference in pressure either above or below that of the atmosphere surrounding the gauge. Gauge pressure is the pressure indicated by such a device. If the pressure in the system measured by the gauge is greater than the pressure prevailing in the atmosphere, the gauge pressure is expressed positively. If lower than atmospheric pressure, the gauge pressure is a negative quantity; the term vacuum designates a negative gauge pressure. Gauge pressures are often identified by the letter g after the pressure unit; for example, psig (pounds per square inch gauge) is a gauge pressure in psi units.

Since gauge pressure is the pressure relative to the prevailing atmospheric pressure, the sum of the two gives the absolute pressure, indicated by the letter a after the unit [e.g., psia (pounds per square inch absolute)]:

(2.5) equation

where P = absolute pressure (psia)

Pa = atmospheric pressure (psia)

Pg = gauge pressure (psig)

The absolute pressure scale is absolute in the same sense that the absolute temperature scale is absolute, i.e., a pressure of zero psia is the lowest possible pressure theoretically achievable—a perfect vacuum.

ILLUSTRATIVE EXAMPLE 2.3

Consider the following pressure calculations.

1 A liquid weighing 100 lb held in a cylindrical column with a base area of 3 in² exerts how much pressure at the base in lbf/ft²?

2 If the pressure is 35 psig (pounds per square inch gauge), what is the absolute pressure?

SOLUTION

1 See Chapter 1.

Note: As discussed in Chapter 1, gc is a conversion factor equal to 32.2 lb · ft/lbf · s²; g is the gravitational acceleration, which is equal, or close to, 32.2 ft/s² on Earth’s surface. Therefore,

2 P = Pg + Pa = 35 + 14.7

= 49.7 psia

MOLES AND MOLECULAR WEIGHTS

An atom consists of protons and neutrons in a nucleus surrounded by electrons. An electron has such a small mass relative to that of the proton and neutron that the weight of the atom (called the atomic weight) is approximately equal to the sum of the weights of the particles in its nucleus. Atomic weight may be expressed in atomic mass units (amu) per atom or in grams per gram · atom. One gram · atom contains 6.02 × 10²³ atoms (Avogadro’s number). The atomic weights of the elements are listed in Table 2.1.

The molecular weight (MW) of a compound is the sum of the atomic weights of the atoms that make up the molecule. Atomic mass units per molecule (amu/molecule) or grams per gram-mole (g/gmol) are used for molecular weight. One gram · mole (gmol) contains an Avogadro number of molecules. For the English system, a pound mole (lbmol) contains 454 × 6.023 × 10²³ molecules.

Table 2.1 Atomic Weights of the Elementsa,b

Molal units are used extensively in thermodynamic calculations as they greatly simplify material balances where chemical (including combustion) reactions are occurring. For mixtures of substances (gases, liquids, or solids), it is also convenient to express compositions in mole fractions or mole percentages instead of mass fractions. The mole fraction is the ratio of the number of moles of one component to the total number