Thermodynamics and heat power

It examines energy, heat, and work in relation to thermodynamics, and also explores the properties of temperature and pressures.. What’s New in the Eighth Edition: • An emphasis on a sys

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Thermodynamics

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Thermodynamics

and Heat Power

Irving Granet and Maurice Bluestein

Eighth Edition

“The authors have adopted simple yet engaging ways to present and discuss complex concepts of thermodynamics

Solved illustrative problems are discreetly placed following the explanation of each new concept The concepts

have been introduced from the basic principles and progressively taken to the advanced level.”

—Mohammad Hossain, Ph.D., York Technical College, Rock Hill, South Carolina, USA

Building on the last edition, (dedicated to exploring alternatives to coal- and oil-based energy conversion methods

and published more than ten years ago), Thermodynamics and Heat Power, Eighth Edition updates the status

of existing direct energy conversion methods as described in the previous work Offering a systems approach to

the analysis of energy conversion methods, this text focuses on the fundamentals involved in thermodynamics,

and further explores concepts in the areas of ideal gas flow, engine analysis, air conditioning, and heat transfer

It examines energy, heat, and work in relation to thermodynamics, and also explores the properties of temperature

and pressures The book emphasizes practical mechanical systems and incorporates problems at the end of the

chapters to advance the application of the material

What’s New in the Eighth Edition:

• An emphasis on a systems approach to problems

• More discussion of the types of heat and of entropy

• Added explanations for understanding pound mass and the mole

• Analysis of steady-flow gas processes, replacing the compressible flow section

• The concept of paddle work to illustrate how frictional effects can be analyzed

• A clearer discussion of the psychrometric chart and its usage in analyzing air conditioning systems

• Updates of the status of direct energy conversion systems

• A description of how the cooling tower is utilized in high-rise buildings

• Practical automotive engine analysis

• Expanded Brayton cycle analysis including intercooling, reheat, and regeneration and their effect

on gas turbine efficiency

• A description of fins and how they improve heat transfer rates

• Added illustrative problems and new homework problems

• Availability of a publisher’s website for fluid properties and other reference materials

• Properties of the latest in commercial refrigerants

This text presents an understanding of basic concepts on the subject of thermodynamics and is a definitive

resource for undergraduate students in engineering programs, most specifically, students studying engineering

technology

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and Heat Power

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Taylor & Francis Group, an informa business

Irving Granet, PE

Professor of Engineering City University of New York

Maurice Bluestein

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Thermodynamics

and

Heat Power

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Preface xiii

Author xv

Symbols xvii

1 Fundamental Concepts 1

1.1 Introduction 1

1.2 Thermodynamic Systems 2

1.2.1 Application of System Concept 2

1.2.2 Properties of a System 3

1.3 Temperature 4

1.4 Force and Mass 15

1.4.1 English System 15

1.4.2 SI System 17

1.5 Elementary Kinetic Theory of Gases 25

1.6 Pressure 28

1.6.1 Dead-Weight Piston Gauge 35

1.6.2 Manometer 36

1.6.3 Micromanometer 40

1.6.4 Barometers 42

1.6.5 McLeod Gauge 43

1.7 Review 50

Key Terms 50

Equations Developed in This Chapter 51

Questions 52

Problems 52

2 Work, Energy, and Heat 59

2.1 Introduction 59

2.2 Work 60

2.3 Energy 62

2.4 Internal Energy 63

2.5 Potential Energy 64

2.6 Kinetic Energy 68

2.7 Heat 72

2.8 Flow Work 73

2.9 Nonflow Work 75

2.10 Review 81

Key Terms 81

Equations Developed in This Chapter 82

Questions 82

Problems 82

3 First Law of Thermodynamics 89

3.1 Introduction 89

3.2 First Law of Thermodynamics 90

3.3 Nonflow System 90

3.4 Steady-Flow System 97

3.4.1 Conservation of Mass—Continuity Equation 97

3.4.2 Steady-Flow Energy Equation 102

3.4.3 Bernoulli Equation 106

3.4.4 Specific Heat 107

3.5 Applications of First Law of Thermodynamics 109

3.5.1 Turbine 110

3.5.2 Pipe Flow 116

3.5.3 Boiler 118

3.5.4 Nozzle 120

3.5.5 Throttling Process 123

3.5.6 Heat Exchanger 124

3.5.7 Filling a Tank 127

3.6 Review 128

Key Terms 129

Equations Developed in This Chapter 129

Questions 130

Problems 131

4 The Second Law of Thermodynamics 141

4.1 Introduction 142

4.2 Reversibility—Second Law of Thermodynamics 143

4.3 The Carnot Cycle 145

4.4 Entropy 157

4.5 Review 173

Key Terms 173

Equations Developed in This Chapter 174

Questions 174

Problems 175

5 Properties of Liquids and Gases 183

5.1 Introduction 183

5.2 Liquids and Vapors 184

5.3 Thermodynamic Properties of Steam 188

5.4 Computerized Properties 212

5.5 Thermodynamic Diagrams 216

5.6 Processes 224

5.6.1 Throttling 224

5.6.2 Constant-Volume Process (Isometric Process) 226

5.6.3 Adiabatic Processes 229

5.6.4 Constant-Pressure Process (Isobaric Process) 233

5.6.5 Constant-Temperature Process (Isothermal Process) 233

5.7 Review 235

Key Terms 236

Equations Developed in This Chapter 236

Questions 237

Problems 237

6 The Ideal Gas 243

6.1 Introduction 243

6.2 Basic Considerations 244

6.3 Specific Heat 252

6.4 Entropy Changes of Ideal Gas 263

6.5 Nonflow Gas Processes 269

6.5.1 Constant-Volume Process (Isometric Process) 269

6.5.2 Constant-Pressure Process (Isobaric Process) 272

6.5.3 Constant-Temperature Process (Isothermal Process) 274

6.5.4 Constant-Entropy Process (Isentropic Process) 278

6.5.5 Polytropic Process 283

6.6 The Gas Tables 290

6.7 Steady-Flow Gas Processes 295

6.7.1 Constant-Specific Volume Process 296

6.7.2 Constant-Pressure Process 297

6.7.3 Constant-Temperature Process 297

6.7.4 Isentropic Process 297

6.7.5 Polytropic Process 299

6.8 Real Gases 300

6.9 Frictional Effects 302

6.10 Review 303

Key Terms 304

Equations Developed in This Chapter 305

Questions 307

Problems 307

7 Mixtures of Ideal Gases 317

7.1 Introduction 317

7.2 Pressure of a Mixture 318

7.3 Volume of a Mixture 323

7.4 Mixture Composition 327

7.5 Thermodynamic Properties of a Gas Mixture 330

7.6 Air–Water Vapor Mixtures 336

7.7 Thermodynamic Properties of Air–Water Vapor Mixtures 343

7.8 Psychrometric Chart 343

7.9 Air Conditioning 358

7.10 Review 363

Key Terms 364

Equations Developed in This Chapter 365

Questions 366

Problems 367

8 Vapor Power Cycles 373

8.1 Introduction 374

8.2 Carnot Cycle 374

8.3 The Rankine Cycle 375

8.3.1 Process 1–2 377

8.3.2 Process 2–3 377

8.3.3 Process 2–4 377

8.3.4 Process 4–5 378

8.3.5 Process 5–1 379

8.4 Rating of Power-Plant Cycles 384

8.5 The Reheat Cycle 386

8.6 The Regenerative Cycle 389

8.7 The Steam Generator 400

8.8 The Steam Turbine 401

8.9 Cogeneration 403

8.10 Direct Energy Conversion 405

8.10.1 Thermoelectrical Converter 406

8.10.2 Fuel Cell 407

8.10.3 Thermionic Converter 408

8.10.4 Magnetohydrodynamic Generator 409

8.10.5 Solar Energy 410

8.10.6 Wind Power 412

8.10.7 Waste-to-Energy Resource Recovery 415

8.10.8 Geothermal Energy 415

8.10.9 Nuclear Power 416

8.10.10 Motion-Generated Energy 416

8.11 Review 416

Key Terms 417

Equations Developed in This Chapter 418

Questions 418

Problems 419

9 Gas Power Cycles 425

9.1 Introduction 426

9.2 Air-Standard Analysis of the Otto Cycle 431

9.3 Diesel Engine (Compression Ignition Engine) 443

9.4 Air-Standard Analysis of the Diesel Cycle 446

9.5 Automotive Engine Analysis 451

9.6 Brayton Cycle 454

9.7 Air-Standard Brayton Cycle Analysis 456

9.8 The Dual Combustion Cycle (The Dual Cycle) 464

9.9 Stirling Cycle and Ericsson Cycle (Regeneration) 465

9.10 Review 466

Key Terms 467

Equations Developed in This Chapter 468

Questions 469

Problems 469

10 Refrigeration 475

10.1 Introduction 476

10.2 Reversed Carnot Cycle 476

10.3 Defined Ratings 481

10.4 Refrigeration Cycles 483

10.4.1 Vapor-Compression Cycle 483

10.4.2 Gas-Cycle Refrigeration 495

10.4.3 Absorption Refrigeration Cycle 501

10.4.4 Vacuum Refrigeration Cycle 501

10.4.5 Thermoelectric Refrigerator 504

10.5 Compressors 505

10.5.1 Volumetric Efficiency 508

10.6 The Heat Pump 510

10.7 Review 514

Key Terms 515

Equations Developed in This Chapter 515

Questions 517

Problems 517

11 Heat Transfer 523

11.1 Introduction 524

11.2 Conduction 524

11.3 Convection 543

11.3.1 Natural Convection 545

11.3.2 Forced Convection 551

11.4 Radiation 556

11.5 Heat Exchangers 566

11.6 Combined Modes of Heat Transfer 579

11.7 Cooling Electronic Equipment 580

11.8 Analysis of Fins 581

11.9 Heat Pipes 583

11.10 Review 584

Key Terms 585

Equations Developed in This Chapter 586

Questions 587

Problems 588

Appendix 1: Answers to Even-Numbered Problems 599

Appendix 2: Supplemental Tables 617

References 811

It has been over ten years since this textbook was last revised There have been many advancements in technology during this time, especially in the area of direct energy con-version There has also been a need to expand on concepts in the areas of ideal gas flow, engine analysis, air conditioning, and heat transfer This new edition marks a joining with the Taylor & Francis Group, including CRC Press, to continue what has been a 40-year pro-cess of providing students with an understanding of basic concepts in thermodynamics Specifically, the following material has been added in this eighth edition:

• An emphasis on a system approach to problems

• More discussion of the types of heat and of entropy

• Added explanations for understanding pound mass and the mole

• Analysis of steady-flow gas processes, replacing the compressible flow section

• The concept of paddle work to illustrate how frictional effects can be analyzed

• A clearer discussion of the psychrometric chart and its usage in analyzing air conditioning systems

• Updates of the status of direct energy conversion systems

• A description of how the cooling tower is utilized in high-rise buildings

• Practical automotive engine analysis

• Expanded Brayton cycle analysis including intercooling, reheat, and regeneration and their effect on gas turbine efficiency

• A description of fins and how they improve heat transfer rates

• Added illustrative problems and new homework problems

• Availability of a publisher’s website for fluid properties and other reference materials

• Properties of the latest in commercial refrigerants

To make room for these additions, out-of-date photographs have been removed as they were felt to lend little to the understanding of the basic concepts Many of these changes have resulted from the input of reviewers A special thanks to Professor Herbert Crosby

of the University of Maine and Professor M David Burghardt of Hofstra University for supplying new, challenging problems I thank Professor Mohammad Hossain of York Technical College for his suggestions

My thanks to the staff at Taylor & Francis for their help with this new edition: Jonathan Plant, Arlene Kopeloff, Cynthia Klivecka, Florence Kizza, and especially Amber Donley

I thank my family, somewhat expanded since the last edition, for their support and agement: Maris, Karen, Richard, Jennifer, Michaelbarry, Chris, Jaxanna, and Bennett

encour-Maurice Bluestein

Pompano Beach, Florida

Maurice Bluestein is a professor emeritus of Mechanical Engineering Technology at Indiana University–Purdue University Indianapolis He taught for 19 years at the under-graduate and graduate levels, following a 25-year career in the biomedical engineering industry His industrial experience included developing artificial limbs for the Veterans Affairs Department, designing waste management systems for the Apollo space mission, managing the clinical usage of the intra-aortic balloon pump as a cardiac assist device, and using ultrasound imaging to detect carotid artery blockages and to aid in the diagnosis

of breast cancer He received a PhD degree in biomedical engineering from Northwestern University and MS and BS degrees in mechanical engineering from New York University and the City College of New York, respectively He has authored numerous scientific papers and is the codeveloper of the Wind Chill Temperature Chart used by the weather services

of the United States and Canada

MW Molecular weight lb m /lb m ·mol kg/kg·mol





v c Critical specific volume ft 3 /lb m m 3 /kg

1

Fundamental Concepts

LE A R N I NG GOALS

After reading and studying the material in this chapter, you should be able to

1 Define thermodynamics as the study of energy and the conversion of energy from one form to another

2 Use the observable external characteristics that are known as properties to describe

a system

3 Establish and convert from one system of temperature measurement to another and understand the four methods of measuring temperature

4 Use both the English and SI systems of units

5 Use the elementary kinetic theory of gases to establish the concepts of pressure, temperature, density, specific weight, specific volume, and Avogadro’s law

6 Use the concept of pressure in both English and SI units (Gauge and absolute sure definitions are important ideas that are necessary in engineering applications.)

7 Use the concept that fluids exert pressures that can be expressed in terms of the height and specific weight of the column of fluid

8 Describe the various methods of measuring pressure and the methods used to calibrate pressure-measuring devices

1.1 Introduction

and the processes involved Thermodynamics is also the study of the conversion of one form of energy to another Because energy can be derived from electrical, chemical, nuclear,

or other means, thermodynamics plays an important role in all branches of engineering, physics, chemistry, and the biological sciences

In defining the word thermodynamics, we have used the terms energy, heat, and work It is

necessary to examine these terms in detail, and this will be done in subsequent chapters

In this chapter, certain fundamental concepts are defined, and basic ideas are developed for future use

Even in our modern age, which has seen changes in our understanding of how the world works, the basics of thermodynamics remain valid Even as Newton’s laws have been shown not to apply in all cases, the fundamental laws of thermodynamics are always applicable They apply to biological, chemical, electromagnetic, and mechanical systems They apply to microscopic as well as macroscopic systems In this textbook, the emphasis

is on practical mechanical systems, including engines and heat transfer devices

1.2 Thermodynamic Systems

In physics, when studying the motion of a rigid body (i.e., a body that is not deformed or

only slightly deformed by the forces acting on it), extensive use is made of free-body

show-ing all the external forces actshow-ing on it A free-body diagram is one example of the concept

of a system As a general concept applicable to all situations, we can define a system as

a grouping of matter taken in any convenient or arbitrary manner We can consider a fixed amount of mass and follow it as it changes shape, volume, or position The mass will have a boundary that prevents any portion of mass from entering or leaving; this is

called a closed system It still permits energy (i.e., heat and/or work) to cross the

bound-ary On the other hand, we can choose as our system a region in space with a geographic boundary Such a system permits mass to enter or leave the system across the boundary

It too allows for the movement of energy across the boundary This is called an open

from it or to it and can also have energy stored in it From this definition, it will be noted that we are at liberty to choose the grouping, but once having made a choice, we must

take into account all energies involved An example of a closed system is the refrigerant

fluid inside an air conditioner An example of an open system is an automobile engine cylinder

1.2.1 Application of System Concept

Thermodynamic equipment is best analyzed by rigorously applying the concept of a system It can be applied to a volume in space, to a single body or a body of components, and even to a series of processes To see how effective such a system analysis can be, consider as an example a well-insulated closed room with only a refrigerator in it There

is an electrical outlet in the wall to power the refrigerator The room is so well insulated that no work or heat can pass through the walls except for electrical energy through the outlet The refrigerator is plugged in and its door left open What will happen to the temperature of the air inside the room? Will it rise, fall, or remain constant? The room air represents a closed system There is an inflow of energy to the system through the outlet and the refrigerator No other energy or mass change occurs; thus, the air temperature must rise

This concept of the system should be remembered when considering alternative energy sources for transportation In an attempt to find substitutes for our dependence on foreign oil, electric vehicles have been developed and ethanol has been added to gasoline All too often, such measures ignore the system cost for developing those energy sources In the case of electric vehicles, one must consider the source of the electricity: batteries and

coal-fired electric plants As for ethanol, there is a significant energy cost in producing it,

as for example planting and processing our most common source, corn

Another proposed energy source has been the fuel cell, using, for example, hydrogen and oxygen inputs with water and electricity as outputs While the benefits to the atmo-sphere and the efficiency of such devices are often stressed, the means of production of the

two gases and their inherent costs are often ignored Treating all components of

produc-tion is system analysis at its best

1.2.2 Properties of a System

Let us consider a given system and then ask ourselves how we can distinguish changes that occur in the system It is necessary to have external characteristics that permit us to measure and evaluate system changes If these external characteristics do not change, we should be able to state that the system has not changed Some of these measurements that can be made on a system are temperature, pressure, volume, and position These observ-

able external characteristics are called properties When all properties of a system are

the same at two different times, we can say that we cannot distinguish any difference in the system at these times The properties of a system enable us to uncover differences in the system after it has undergone a change Therefore, the complete description of a system is given by its properties The condition of the system, that is, its position, energy content, and

so on, is called the state of the system Thus, its properties determine its state Those erties that depend on the size and total mass of a system are termed extensive properties; that is, they depend on the extent of the system An intensive property is independent of the

prop-size of the system Pressure and temperature are examples of intensive properties In

addi-tion, there are properties that are known as specific properties because they are given per

unit mass or per defined mass in the system Specific properties are intensive properties

It has already been noted that a given state of a system is reproduced when all its erties are the same Because a given set of properties determines the state of a system, the state is reproduced regardless of the history or path the system may undergo to achieve the state For example, consider a weight that is lifted vertically from one position to another This weight can be brought to the same position by first lifting it vertically part of the way, then moving it horizontally to the right, then lifting it another part of the way, then mov-ing it horizontally to the left, and, finally, lifting it vertically to the desired point In this example, the state of the system at the end of the two processes is the same, and the path the system took did not affect its state after the change had occurred

prop-As we shall see in Chapter 2, a consequence of the foregoing is that the change in energy

of a system between two given states is the same, regardless of the method of attaining the state In mathematical terminology, energy is a state function, not a path function

The properties temperature and pressure are used throughout this book, and it is essary to have a good understanding of them The following sections deal in detail with these properties

nec-CALCULUS ENRICHMENT

As we have stated, a property has a unique and singular value when the system in question is in a given state This value does not depend on the intermediate states that the system has experienced Thus, a property is not a function of the system’s path

1.3 Temperature

The temperature of a system is a measure of the random motion of the molecules in the

sys-tem Temperature is therefore also a measure of the thermal energy in a syssys-tem It is

differ-ent from heat, which is the transfer of thermal energy from one body or system to another

If there are different temperatures within the body (or bodies composing the system), the question arises as to how the temperature at a given location is measured and how this measurement is interpreted Let us examine this question in detail, because similar ques-tions will also have to be considered when other properties of a system are studied In air

centimeter If we divide the cube whose dimensions are 1 cm on a side into smaller cubes,

molecules in each of the smaller cubes, still an extraordinarily large number Although we speak of temperature at a point, we really mean the average temperature of the molecules

in the neighborhood of the point

Let us now consider two volumes of inert gases separated from each other by a third volume of inert gas By inert, we mean that the gases will not react chemically with each other If the first volume is brought into contact with the second volume and left there until

no observable change occurs in any physical property, the two volumes are said to be in

and no noticeable change in physical properties is observed, the second and third volumes can also be said to be in thermal equilibrium For the assumed conditions of this experi-ment, it can be concluded that the three volumes are in thermal equilibrium Based on this discussion, the three volumes can also be stated to be at the same temperature This sim-ple experiment can be repeated under the same conditions for solids, liquids, and gases, with the same result every time The results of all these experiments are summarized

and embodied in the zeroth law of thermodynamics, which states that two systems having

equal temperatures with a third system also have equal temperatures with each other As

an alternative definition of the zeroth law, we can say that if two bodies are each in mal equilibrium with a third body, they are in thermal equilibrium with each other The importance of this apparently obvious statement was recognized after the first law was

ther-The change of a property is a function only of the initial and final states of the system Mathematically, this can be written as

it becomes necessary to specify the path in order to evaluate them These quantities

are known as path functions.

given its name, and consequently, it was called the zeroth law to denote that it precedes the first law It should be noted that a thermometer measures only its own temperature, and for it to be an accurate indication of the temperature of a second system, the thermometer and the second system must be in thermal equilibrium As a consequence of the zeroth law, we can measure the temperatures of two bodies by a third body (a thermometer) with-out bringing the bodies in contact with each other.

The common scales of temperature are called the Fahrenheit and Celsius (centigrade) temperatures and are defined by using the ice point and boiling point of water at atmo-spheric pressure The Fahrenheit scale was developed by Gabriel Fahrenheit in 1724, who wanted a scale that had a normal body temperature of 100; he came close, as the normal body temperature is 98.6 The Fahrenheit scale is used in the United States and a few much smaller countries It is used with English system units The Celsius scale was devel-oped by Anders Celsius in 1742 He wanted a scale that was much numerically simpler

It is used in the metric system In the Celsius temperature scale, the interval between the ice point and the boiling point is divided into 100 equal parts In addition, as shown in Table 1.1, the Celsius ice point is zero and the Fahrenheit ice point is 32 The conversion from one scale to the other is directly derived from Table 1.1 and results in the following relations:

The ability to extrapolate to temperatures below the ice point and above the boiling

point of water and to interpolate in these regions is provided by the International Scale

differ-ent elemdiffer-ents and establishes suitable interpolation formulas in the various temperature ranges between these elements The data for these elements are given in Table 1.2

By using the results of Illustrative Problem 1.1, it is possible to derive an alternative set

of equations to convert from the Fahrenheit to the Celsius temperature scale When this is done, we obtain

5

49

160940

It is also possible to define an absolute temperature scale that is independent of the ties of any substance, and we will consider this point later in this book.

proper-The absolute temperature scale begins at absolute zero temperature, is always positive, and more accurately represents the concept that temperature is a measure of the molecu-lar motion of matter Thus, molecular motion ceases at absolute zero temperature In the English system of units, absolute temperature is given in degrees Rankine In the SI sys-tem, the absolute temperature is given in degrees Kelvin Thus, we define

1 Methods utilizing the expansion of gases, liquids, or solids

2 Methods utilizing the change in electrical resistance of an element

3 Methods utilizing the change in electrical potential of an element

4 Methods utilizing the optical changes of a sensor

The most common device used to measure temperature is the familiar liquid-in-glass

capillary The operation of this type of thermometer is based on the coefficient of sion of the liquid (usually mercury) being greater than the coefficient of expansion of the glass For accurate measurements, these thermometers are calibrated by partial, total, or complete immersion in a suitable bath, as shown in Figure 1.2 If the thermometer is cali-brated by one method but is used in a different way, it is necessary to make corrections to the readings for the difference in usage Advantages of the liquid-in-glass thermometers are low cost, simplicity, good reliability, and long life

expan-Temperature

Cylinder of constant cross-sectional area Piston (free to move)

Gas Heat in or out

FIGURE 1.1

Gas thermometer.

Another device that is used to measure temperature or temperature differences depends

on the expansion of materials and is called the bimetallic element This element usually

con-sists of two thin, flat strips placed side by side and welded together The composite strip can

be used flat or coiled into a helix or spiral Changes in temperature cause the strip to change its curvature, and the motion produced can be used to move a pointer The flat bimetallic strip is commonly used in room thermostats, where the motion of one end is used to close

or open an electrical contact The action of a bimetallic strip is shown in Figure 1.3

Resistance thermometers (Figure 1.4) are commonly used in industry to measure process temperatures The basic principle of this type of instrument is that the change in electrical resistance of a sensor due to a change in its temperature is easily measurable The electrical resistivity of some metals increases very nearly in direct proportion to an increase of temper-ature Thus, the measured change in resistance of a sensor can be converted to a temperature change Metals used for the sensors include nickel, copper, and platinum Because of their calibration stability, high temperature coefficient, and moderate cost, nickel resistance units are normally recommended for temperature ranges between –100 and +500°F The resistance

of the sensing element is usually measured by a Wheatstone bridge (shown schematically in

Partial immersion line Liquid level

FIGURE 1.3

Bimetallic strip.

r r

r r

e b

2 (1.7)

where the various resistances are as shown in Figure 1.5 Errors in using the Wheatstone bridge make the circuit shown in Figure 1.5 unsatisfactory for highly accurate work These errors are due to the contact resistance of the variable resistor, resistance changes in lead wires due to temperature gradients along them, and self-heating of the sensor due to the supply current Modifications of the basic Wheatstone bridge have been made to compensate for and correct these faults These circuits will be found in the references by interested students

Thermistors are also included as resistance elements The name thermistor is derived from thermally sensitive resistors, because their resistance varies rapidly with temperature Thermistors are included in the class of solids known as semiconductors, which have electrical

conductivities between those of conductors and insulators The advantages of the thermistor over the resistance thermometer and the thermocouple (to be discussed later) are as follows:

1 A temperature coefficient of resistance approximately 10 times that of metals, with

a correspondingly greater sensitivity to temperature change

2 A much higher resistivity than the metals so that small units may have high tance, virtually eliminating the lead and contact resistance problem

3 No need for cold-end or lead material compensation, because the thermistor tance is a function of its absolute temperature

For a limited temperature range, the thermistor combines all the best features of tance thermometers and thermocouples and has greater sensitivity than either

When two wires of different materials are joined at their ends and their junctions are at different temperatures, a net thermal electromotive force (EMF) is generated that induces

a net electric current This is shown schematically in Figure 1.6a The thermocouple is used

as a thermometer by placing one junction in contact with the body whose temperature is

to be measured and measuring the voltage produced at the other junction with a meter, as shown schematically in Figure 1.6b The practical reduction of the thermocouple

millivolt-to use as a temperature-measuring device in industry depends on three so-called laws:

1 If each section of wire in the circuit is homogeneous, that is, if there is no change in composition or physical properties along its length, the EMF in the circuit depends only on the nature of the metals and the temperatures of the junctions

2 If both of the junctions involving a particular homogeneous metal are at the same temperature, this metal makes no net contribution to the EMF Thus, if the complete circuit consists of iron, constantan (60% copper, 40% nickel alloy), and copper, but both of the junctions involving copper are at the same temperature, we can consider the circuit as if it consisted entirely of iron and constantan, with only two junctions

3 If all junctions of the circuit except one are held at constant temperature, the EMF

in the circuit will be a function of the temperature of the remaining junction and can be used to measure that temperature It is customary to prepare tables giving this EMF as a function of temperature for the case where the reference junction (or junctions) is held at 0°C (32°F)

Figure 1.6b shows a thermocouple with two continuous dissimilar wires from the

mea-suring function to the reference junction From the reference junction, copper wires and the potentiometer (or millivoltmeter) complete the circuit For the case of more than one thermocouple to be monitored, a circuit of the type shown in Figure 1.7 can be used It

is important to note that each thermocouple consists of two continuous wires between the measuring junction and the reference junction Rather than use a circuit with mul-tiple junctions, it is possible to use the circuit shown in Figure 1.8, which has a single

(a)

(b)

Material A Material B

Material B

Measuring junction

junction

Copper Copper

emf Junction 1

Elementary thermocouple circuit (a) Basic thermocouple circuit (b) Thermocouple measurement system

(b:  Benedict, R.P.: Fundamentals of Temperature, Pressure, and Flow Measurements 1969 Copyright Wiley-VCH

Verlag GmbH & Co KGaA Reproduced with permission.)

connecting junctions

junctions

A

A B

B

B

Cu Cu

emf Potentiometer Cu

Cu Cu Cu

wires 1

2

N

B B B

B A

A

A

Cu Cu Cu

Cu

Potentiometer

Selector switch (copper) 2-pole

N-throw

Cu Cu Cu Measuring

wires temperature

Ice bath junction) (reference

reference junction A typical industrial circuit using a potentiometer that is constructed to compensate automatically for the reference junction temperature is shown in Figure 1.9.All bodies radiate energy at a rate proportional to the fourth power of their absolute temperature This is the well-known Stefan–Boltzmann law (discussed in some detail in Chapter 11) For the moment, we concern ourselves with the optical pyrometer, which pro-vides us with a method of converting this radiation to a temperature measurement The optical pyrometer, shown schematically in Figure 1.10, consists of a telescope within which there is mounted a red glass filter and a small light bulb In practice, the telescope is aimed

at the body whose temperature is to be measured The filament of the bulb appears black against the bright background being measured The current through the bulb is varied by adjusting the rheostat until the brightness of the filament matches the brightness of the body being measured By prior calibration, the reading of the ammeter is directly convert-ible to temperature The advantage of this device is that no part of it is in contact with the body, and the optical pyrometer can be used to measure temperature above the melting points of either resistance thermometers or thermocouples

A summary of commercially available measuring devices is given in Table 1.3, showing their temperature ranges and characteristics

M1

M2

A A

A B B

switch

Switch

extension junctions

M n

FIGURE 1.9

Typical industrial thermocouple circuit.

Rheostat

Ammeter Battery

Red

Eye body

FIGURE 1.10

Schematic of the optical pyrometer.

Chromel/ Alumel

Platinum/ Platinum– Rhodium

Low temp limit–38°F (–39°C)–32°F (–196°C) (pentane)–100°F (–73°C)–127°F (–20 K)–125°F (–87°C)

–452°F (4 K)About –320°F (–196°C)

About –300°F (–184°C)

–424°F (20 K)Commonly 32°F (0°C)

High temp limit1100°F (593°C)

1000°F (538°C)600°F (316°C)1200°F (649°C)

Can be compensated accurately for ambient temperatur

12 at 1200°C (alloy 10% Rh) 14 at 1200°C (alloy 13% Rh)

The couple most widely used in industry

1.4 Force and Mass

1.4.1 English System

Force is very often defined in elementary physics texts as the push or pull exerted on a body Although this definition serves to satisfy our daily experience, it is not satisfactory when dealing with the motion of bodies that are subjected to resultant forces that are not zero The following paragraphs deal with the concept of force in a consistent manner, and

we attempt to clarify the confusion concerning the units of force and mass

The basis of much of the physical sciences rests on the work of Newton For the present, two physical laws that are attributed to him will be used:

1 Law of universal gravitation

2 Second law of motion

The first of these, the law of universal gravitation, states simply that the force of attraction

experienced by two bodies is proportional to the product of their masses and inversely

proportional to the square of the distance (d) separating them At this point, we define the mass of a body as the quantity of matter contained in the body Thus, if the Earth is

assumed to be spherical and its mass center is taken to be at its geometrical center, a body

on the surface will experience a constant force due to the Earth’s attraction This force is

given the name weight Because the Earth is an oblate spheroid, a body at different

loca-tions at the surface will have different weights Also, the surface of the Earth is not smooth,

so weight is a function of elevation While a body’s weight can change with altitude, its mass is constant

So far, it would appear that the foregoing concepts are both clear and relatively simple

In its simplest form, it can be stated that the weight of a body, in a given location, is

pro-portional to its mass By choosing the constant of propro-portionality to be unity, the mass of an

object in pounds at the Earth’s surface may, for most practical purposes, be assumed to be

rela-tion can be stated as follows:

where a is the acceleration of a body due to gravity, m its mass, and F is its weight.

In the English system, the basic unit of mass is the slug; of distance, the foot; and of time,

Equation 1.8, will weigh 32.174 pounds The slug is an inconvenient term; it would be easier

to express mass in pounds so that mass and weight could be expressed the same cally using a familiar word This is accomplished by the introduction of a proportionality

It is in this constant of proportionality, g c, that the confusion occurs, as well as in the

ambiguous use of the word pound To differentiate between the pound force and the pound

provides a benefit in that at sea level, the number of pound mass is the same as the number

of pound force Thus, thermodynamic parameters can be stated as per pound regardless of whether it is a pound mass or a pound force Table 1.4 lists some of the most common com-binations of units that can be used To avoid the obvious confusion that this multitude of units can cause, the definition of pound mass and pound weight, as given in this section,

a consequence of these considerations, weight and mass, at a location in which the local

gravitational attraction is expressed as g, can be interrelated in the following manner:

The force exerted on the mass by the moon will determine its “weight” on the moon

In general, the law of universal gravitation can be written as

Common Combinations of Units

1.4.2 SI System

For the engineer, the greater confusion has been the units for mass and weight As we have noted, the literature abounds with units such as slugs, pounds, mass, pound force, poundal, kilogram force, kilogram mass, dyne, and so on In the SI system, the base unit

for mass (not weight or force) is the kilogram (kg), which is equal to the mass of the

inter-national standard kilogram located at the Interinter-national Bureau of Weights and Measures

It is used to specify the quantity of matter in a body The mass of a body never varies, and

it is independent of gravitational force

The SI derived unit for force is the newton (N) The unit of force is defined from Newton’s law of motion: force is equal to mass times acceleration (F = ma) By this definition, 1 N

new-ton is used in all combinations of units that include force, for example, pressure or stress

related to gravity, as was the older kilogram force

Table 1.5 gives the seven base units of the SI system Several observations concerning

this table should be noted The unit of length is the meter and the kilogram is a unit of mass, not

and lowercase symbols must be used as shown without exception.

Table 1.6 gives the derived units with and without symbols often used in engineering These derived units are formed by the algebraic combination of base and supplementary units Note that where the name is derived from a person, the first letter of the symbol appears as a capital; for example, newton is N Otherwise, the convention is to make the symbol lowercase

where K is a proportionality constant Using the subscripts e for Earth and m for

r F F

m m

r r

m e m

e m

m e

22= 6 06

Thus, a body on Earth feels a force (weight) approximately six times the force it would feel on the moon The solution to the problem is that a mass of 1 lb will weigh approximately 1/6 lb on the moon

Weight has been defined as a measure of gravitational force acting on a material object

at a specified location Thus, weight is a force that has both a mass component and an acceleration component (gravity) Gravitational forces vary by approximately 0.5% over the Earth’s surface For nonprecision measurements, these variations normally can be ignored Thus, a constant mass has an approximate constant weight on the surface of the Earth

illustrates the difference between mass (kilogram) and force (newton)

The term mass or unit mass should be used to indicate only the quantity of matter in an

object, and the old practice of using weight in such cases should be avoided in ing and scientific practice However, because the determination of an object’s mass will

engineer-be accomplished by the use of a weighing process, the common usage of the term weight instead of mass is expected to continue but should be avoided.

Based on the foregoing, Equation 1.10 can be written in SI units as