Thermodynamics, An Engineering Approach, eighth edition, covers the basic principles of thermodynamics while presenting a wealth of real-world engineering examples so students get a feel for how thermodynamics is applied in engineering practice. This text helps students develop an intuitive understanding by emphasizing the physics and physical arguments. Cengel and Boles explore the various facets of thermodynamics through careful explanations of concepts and use of numerous practical examples and figures, having students develop necessary skills to bridge the gap between knowledge and the confidence to properly apply their knowledge.

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slide 2:

THERMODYNAMICS
AN ENGINEERING APPROACH
EIGHTH EDITION
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THERMODYNAMICS
AN ENGINEERING APPROACH
EIGHTH EDITION
YUNUS A.
ÇENGEL
University of Nevada
Reno
MICHAEL A.
BOLES
North Carolina State
University
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Quotes on Ethics
Without ethics everything happens as if we were all five billion passengers
on a big machinery and nobody is driving the machinery. And it’s going
faster and faster but we don’t know where.
—Jacques Cousteau
Because you’re able to do it and because you have the right to do it doesn’t
mean it’s right to do it.
—Laura Schlessinger
A man without ethics is a wild beast loosed upon this world.
—Manly Hall
The concern for man and his destiny must always be the chief interest of all
technical effort. Never forget it among your diagrams and equations.
—Albert Einstein
Cowardice asks the question ‘Is it safe’ Expediency asks the question ‘Is it
politic’ Vanity asks the question ‘Is it popular’ But conscience asks the
question ‘Is it right’ And there comes a time when one must take a posi-
tion that is neither safe nor politic nor popular but one must take it because
one’s conscience tells one that it is right.
—Martin Luther King Jr
To educate a man in mind and not in morals is to educate a
menace to society.
—Theodore Roosevelt
Politics which revolves around benefit is savagery.
—Said Nursi
The true test of civilization is not the census nor the size of the cities nor
the crops but the kind of man that the country turns out.
—Ralph W. Emerson
The measure of a man’s character is what he would do if he knew he never
would be found out.
—Thomas B. Macaulay
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Yunus A. Çengel is Professor Emeritus of Mechanical Engineering at the
University of Nevada Reno. He received his B.S. in mechanical engineering from
Istanbul Technical University and his M.S. and Ph.D. in mechanical engineering
from North Carolina State University. His areas of interest are renewable energy
energy efficiency energy policies heat transfer enhancement and engineering edu-
cation. He served as the director of the Industrial Assessment Center IAC at the
University of Nevada Reno from 1996 to 2000. He has led teams of engineering
students to numerous manufacturing facilities in Northern Nevada and California to
perform industrial assessments and has prepared energy conservation waste mini-
mization and productivity enhancement reports for them. He has also served as an
advisor for various government organizations and corporations.
Dr. Çengel is also the author or coauthor of the widely adopted textbooks
Heat and Mass Transfer: Fundamentals and Applications 5th ed. 2015 Fluid
Mechanics:Fundamentals and Applications 3rd ed. 2014 Fundamentals of
Thermal-Fluid Sciences 4th ed. 2012 Introduction to Thermodynamics and
Heat Transfer 2nd ed. 2008 and Differential Equations for Engineers and
Scientists 1st ed. 2013 all published by McGraw-Hill. Some of his textbooks
have been translated into Chinese Japanese Korean Thai Spanish Portuguese
Turkish Italian Greek and French.
Dr. Çengel is the recipient of several outstanding teacher awards and he has
received the ASEE Meriam/Wiley Distinguished Author Award for excellence in
authorship in 1992 and again in 2000. Dr. Çengel is a registered Professional Engi-
neer in the State of Nevada and is a member of the American Society of Mechanical
Engineers ASME and the American Society for Engineering Education ASEE.
Michael A. Boles is Associate Professor of Mechanical and Aerospace Engi-
neering at North Carolina State University where he earned his Ph.D. in mechani-
cal engineering and is an Alumni Distinguished Professor. Dr. Boles has received
numerous awards and citations for excellence as an engineering educator. He is a
past recipient of the SAE Ralph R. Teetor Edu cation Award and has been twice
elected to the NCSU Academy of Outstanding Teachers. The NCSU ASME student
section has consistently recognized him as the outstanding teacher of the year and
the faculty member having the most impact on mechanical engineering students.
Dr. Boles specializes in heat transfer and has been involved in the ana-
lytical and numerical solution of phase change and drying of porous media.
He is a member of the American Society of Mechanical Engineers ASME
the American Society for Engineering Education ASEE and Sigma Xi.
Dr. Boles received the ASEE Meriam/Wiley Distinguished Author Award in 1992
for excellence in authorship.
About the Authors
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Brief Contents
chapter one
INTRODUCTION AND BASIC CONCEPTS 1
chapter two
ENERGY ENERGY TRANSFER AND GENERAL ENERGY ANALYSIS 51
chapter three
PROPERTIES OF PURE SUBSTANCES 111
chapter four
ENERGY ANALYSIS OF CLOSED SYSTEMS 163
chapter five
MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES 213
chapter six
THE SECOND LAW OF THERMODYNAMICS 275
chapter seven
ENTROPY 329
chapter eight
EXERGY 421
chapter nine
GAS POWER CYCLES 485
chapter ten
VAPOR AND COMBINED POWER CYCLES 553
chapter eleven
REFRIGERATION CYCLES 607
chapter twelve
THERMODYNAMIC PROPERTY RELATIONS 655
chapter thirteen
GAS MIXTURES 687
chapter fourteen
GAS–VAPOR MIXTURES AND AIR-CONDITIONING 725
chapter fifteen
CHEMICAL REACTIONS 759
chapter sixteen
CHEMICAL AND PHASE EQUILIBRIUM 805
chapter seventeen
COMPRESSIBLE FLOW 839
chapter eighteen web chapter
RENEWABLE ENERGY
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viii
THERMODYNAMICS
appendix 1
PROPERTY TABLES AND CHARTS SI UNITS 897
appendix 2
PROPERTY TABLES AND CHARTS ENGLISH UNITS 947
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Preface xvii
chapter one
INTRODUCTION AND BASIC CONCEPTS 1
1–1 Thermodynamics and Energy 2
Application Areas of Thermodynamics 3
1–2 Importance of Dimensions and Units 3
Some SI and English Units 6
Dimensional Homogeneity 8
Unity Conversion Ratios 9
1–3 Systems and Control V olumes 10
1–4 Properties of a System 12
Continuum 12
1–5 Density and Specific Gravity 13
1–6 State and Equilibrium 14
The State Postulate 15
1–7 Processes and Cycles 15
The Steady-Flow Process 16
1–8 Temperature and the Zeroth Law
of Thermodynamics 17
Temperature Scales 18
The International Temperature Scale of 1990
ITS-90 20
1–9 Pressure 22
Variation of Pressure with Depth 24
1–10 Pressure Measurement Devices 27
The Barometer 27
The Manometer 30
Other Pressure Measurement Devices 33
1–11 Problem-Solving Technique 34
Step 1: Problem Statement 34
Step 2: Schematic 35
Step 3: Assumptions and Approximations 35
Step 4: Physical Laws 35
Step 5: Properties 35
Step 6: Calculations 35
Step 7: Reasoning Verification and Discussion 35
Engineering Software Packages 36
Engineering Equation Solver EES 37
A Remark on Significant Digits 39
Summary 40
References and Suggested Readings 41
Problems 41
chapter two
ENERGY ENERGY TRANSFER AND GENERAL
ENERGY ANALYSIS 51
2–1 Introduction 52
2–2 Forms of Energy 53
Some Physical Insight to Internal Energy 55
More on Nuclear Energy 56
Mechanical Energy 58
2–3 Energy Transfer by Heat 60
Historical Background on Heat 61
2–4 Energy Transfer by Work 62
Electrical Work 65
2–5 Mechanical Forms of Work 66
Shaft Work 66
Spring Work 67
Work Done on Elastic Solid Bars 67
Work Associated with the Stretching of a Liquid Film 68
Work Done to Raise or to Accelerate a Body 68
Nonmechanical Forms of Work 70
2–6 The First Law of Thermodynamics 70
Energy Balance 72
Energy Change of a System DE
system
72
Mechanisms of Energy Transfer E
in
and E
out
73
2–7 Energy Conversion Efficiencies 78
Efficiencies of Mechanical and Electrical Devices 82
2–8 Energy and Environment 85
Ozone and Smog 86
Acid Rain 87
The Greenhouse Effect:
Global Warming and Climate Change 88
Topic of Special Interest: Mechanisms of Heat
Transfer 91
Summary 96
References and Suggested Readings 97
Problems 97
Contents
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x
THERMODYNAMICS
chapter three
PROPERTIES OF PURE SUBSTANCES 111
3–1 Pure Substance 112
3–2 Phases of a Pure Substance 112
3–3 Phase-Change Processes
of Pure Substances 113
Compressed Liquid and Saturated Liquid 114
Saturated Vapor and Superheated Vapor 114
Saturation Temperature and Saturation Pressure 115
Some Consequences of T
sat
and P
sat
Dependence 116
3–4 Property Diagrams for Phase-Change
Processes 118
1 The T-v Diagram 118
2 The P-v Diagram 120
Extending the Diagrams to Include the Solid Phase 120
3 The P-T Diagram 122
The P-v-T Surface 123
3–5 Property Tables 124
Enthalpy—A Combination Property 124
1a Saturated Liquid and Saturated
Vapor States 125
1b Saturated Liquid–Vapor Mixture 127
2 Superheated Vapor 130
3 Compressed Liquid 131
Reference State and Reference Values 132
3–6 The Ideal-Gas Equation of State 134
Is Water Vapor an Ideal Gas 137
3–7 Compressibility Factor—A Measure of
Deviation from Ideal-Gas Behavior 138
3–8 Other Equations of State 141
van der Waals Equation of State 142
Beattie-Bridgeman Equation of State 142
Benedict-Webb-Rubin Equation of State 143
Virial Equation of State 144
Topic of Special Interest: Vapor Pressure and Phase
Equilibrium 146
Summary 150
References and Suggested Readings 151
Problems 151
chapter four
ENERGY ANALYSIS OF CLOSED SYSTEMS 163
4–1 Moving Boundary Work 164
Polytropic Process 168
4–2 Energy Balance for Closed Systems 169
4–3 Specific Heats 174
4–4 Internal Energy Enthalpy and Specific Heats
of Ideal Gases 176
Specific Heat Relations of Ideal Gases 178
4–5 Internal Energy Enthalpy and Specific Heats of
Solids and Liquids 183
Internal Energy Changes 184
Enthalpy Changes 184
Topic of Special Interest: Thermodynamic Aspects of
Biological Systems 187
Summary 195
References and Suggested Readings 195
Problems 196
chapter five
MASS AND ENERGY ANALYSIS OF CONTROL
VOLUMES 213
5–1 Conservation of Mass 214
Mass and Volume Flow Rates 214
Conservation of Mass Principle 216
Mass Balance for Steady-Flow
Processes 218
Special Case: Incompressible Flow 219
5–2 Flow Work and the Energy of a Flowing
Fluid 221
Total Energy of a Flowing Fluid 222
Energy Transport by Mass 223
5–3 Energy Analysis of Steady-Flow
Systems 225
5–4 Some Steady-Flow Engineering
Devices 228
1 Nozzles and Diffusers 229
2 Turbines and Compressors 232
3 Throttling Valves 234
4a Mixing Chambers 236
4b Heat Exchangers 238
5 Pipe and Duct Flow 240
5–5 Energy Analysis of Unsteady-Flow
Processes 242
Topic of Special Interest: General Energy
Equation 247
Summary 251
References and Suggested Readings 252
Problems 252
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CONTENTS
xi
chapter six
THE SECOND LAW OF THERMODYNAMICS 275
6–1 Introduction to the Second Law 276
6–2 Thermal Energy Reservoirs 277
6–3 Heat Engines 278
Thermal Efficiency 279
Can We Save Q
out
281
The Second Law of Thermodynamics:
Kelvin–Planck Statement 283
6–4 Refrigerators and Heat Pumps 283
Coefficient of Performance 284
Heat Pumps 285
Performance of Refrigerators Air-Conditioners
and Heat Pumps 286
The Second Law of Thermodynamics:
Clausius Statement 288
Equivalence of the Two Statements 289
6–5 Perpetual-Motion Machines 290
6–6 Reversible and Irreversible Processes 292
Irreversibilities 293
Internally and Externally Reversible Processes 294
6–7 The Carnot Cycle 295
The Reversed Carnot Cycle 297
6–8 The Carnot Principles 297
6–9 The Thermodynamic Temperature Scale 299
6–10 The Carnot Heat Engine 301
The Quality of Energy 302
Quantity versus Quality in Daily Life 303
6–11 The Carnot Refrigerator and Heat Pump 304
Topic of Special Interest: Household Refrigerators 307
Summary 311
References and Suggested Readings 312
Problems 312
chapter seven
ENTROPY 329
7–1 Entropy 330
A Special Case: Internally Reversible
Isothermal Heat Transfer Processes 333
7–2 The Increase of Entropy Principle 334
Some Remarks about Entropy 336
7–3 Entropy Change of Pure Substances 337
7–4 Isentropic Processes 340
7–5 Property Diagrams Involving Entropy 342
7–6 What Is Entropy 343
Entropy and Entropy Generation in Daily Life 346
7–7 The T ds Relations 347
7–8 Entropy Change of Liquids and Solids 349
7–9 The Entropy Change of Ideal Gases 352
Constant Specific Heats Approximate Analysis 353
Variable Specific Heats Exact Analysis 353
Isentropic Processes of Ideal Gases 355
Constant Specific Heats Approximate Analysis 355
Variable Specific Heats Exact Analysis 356
Relative Pressure and Relative Specific Volume 356
7–10 Reversible Steady-Flow Work 359
Proof that Steady-Flow Devices Deliver
the Most and Consume the Least Work
When the Process is Reversible 362
7–11 Minimizing the Compressor Work 363
Multistage Compression with Intercooling 364
7–12 Isentropic Efficiencies of Steady-Flow
Devices 367
Isentropic Efficiency of Turbines 367
Isentropic Efficiencies of Compressors and Pumps 369
Isentropic Efficiency of Nozzles 371
7–13 Entropy Balance 373
Entropy Change of a System DS
system
374
Mechanisms of Entropy Transfer S
in
and S
out
374
1 Heat Transfer 374
2 Mass Flow 375
Entropy Generation S
gen
376
Closed Systems 377
Control Volumes 378
Entropy Generation Associated
with a Heat Transfer Process 385
Topic of Special Interest: Reducing the Cost of
Compressed Air 386
Summary 395
References and Suggested Readings 396
Problems 397
chapter eight
EXERGY 421
8–1 Exergy: Work Potential of Energy 422
Exergy Work Potential Associated
with Kinetic and Potential Energy 423
8–2 Reversible Work and Irreversibility 425
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xii
THERMODYNAMICS
8–3 Second-Law Efficiency 430
8–4 Exergy Change of a System 433
Exergy of a Fixed Mass: Nonflow or Closed System
Exergy 433
Exergy of a Flow Stream: Flow or Stream
Exergy 436
8–5 Exergy Transfer by Heat Work
And Mass 438
Exergy by Heat Transfer Q 439
Exergy Transfer by Work W 440
Exergy Transfer by Mass m 440
8–6 The Decrease of Exergy Principle and Exergy
Destruction 441
Exergy Destruction 442
8–7 Exergy Balance: Closed Systems 443
8–8 Exergy Balance: Control V olumes 454
Exergy Balance for Steady-Flow Systems 455
Reversible Work 456
Second-Law Efficiency of Steady-Flow
Devices 456
Topic of Special Interest: Second-Law
Aspects of Daily Life 463
Summary 467
References and Suggested Readings 468
Problems 468
chapter nine
GAS POWER CYCLES 485
9–1 Basic Considerations in the Analysis of Power
Cycles 486
9–2 The Carnot Cycle and its Value in
Engineering 488
9–3 Air-Standard Assumptions 490
9–4 An Overview of Reciprocating Engines 490
9–5 Otto Cycle: The Ideal Cycle for Spark-Ignition
Engines 492
9–6 Diesel Cycle: The Ideal Cycle for
Compression-Ignition Engines 499
9–7 Stirling and Ericsson Cycles 502
9–8 Brayton Cycle: The Ideal Cycle for
Gas-Turbine Engines 506
Development of Gas Turbines 509
Deviation of Actual Gas-Turbine Cycles
from Idealized Ones 512
9–9 The Brayton Cycle with Regeneration 513
9–10 The Brayton Cycle with Intercooling Reheating
and Regeneration 516
9–11 Ideal Jet-Propulsion Cycles 520
Modifications to Turbojet Engines 524
9–12 Second-Law Analysis of Gas Power
Cycles 526
Topic of Special Interest: Saving Fuel and Money by Driving
Sensibly 530
Summary 536
References and Suggested Readings 538
Problems 538
chapter ten
VAPOR AND COMBINED POWER CYCLES 553
10–1 The Carnot Vapor Cycle 554
10–2 Rankine Cycle: The Ideal Cycle for Vapor Power
Cycles 555
Energy Analysis of the Ideal Rankine Cycle 555
10–3 Deviation of Actual Vapor Power Cycles from
Idealized Ones 558
10–4 How Can We Increase the Efficiency of the
Rankine Cycle 561
Lowering the Condenser Pressure
Lowers T
lowavg
561
Superheating the Steam to High Temperatures
Increases T
highavg
562
Increasing the Boiler Pressure
Increases T
highavg
562
10–5 The Ideal Reheat Rankine Cycle 565
10–6 The Ideal Regenerative Rankine
Cycle 569
Open Feedwater Heaters 569
Closed Feedwater Heaters 571
10–7 Second-Law Analysis of Vapor Power
Cycles 577
10–8 Cogeneration 579
10–9 Combined Gas–Vapor Power
Cycles 584
Topic of Special Interest: Binary Vapor
Cycles 587
Summary 589
References and Suggested Readings 590
Problems 590
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CONTENTS
xiii
chapter eleven
REFRIGERATION CYCLES 607
11–1 Refrigerators and Heat Pumps 608
11–2 The Reversed Carnot Cycle 609
11–3 The Ideal Vapor-Compression Refrigeration
Cycle 610
11–4 Actual Vapor-Compression Refrigeration
Cycle 613
11–5 Second-Law Analysis of Vapor- Compression
Refrigeration Cycle 615
11–6 Selecting the Right Refrigerant 620
11–7 Heat Pump Systems 622
11–8 Innovative Vapor-Compression Refrigeration
Systems 623
Cascade Refrigeration Systems 624
Multistage Compression Refrigeration
Systems 626
Multipurpose Refrigeration Systems
with a Single Compressor 628
Liquefaction of Gases 629
11–9 Gas Refrigeration Cycles 630
11–10 Absorption Refrigeration Systems 633
Topic of Special Interest: Thermoelectric Power Generation
and Refrigeration Systems 636
Summary 638
References and Suggested Readings 639
Problems 639
chapter twelve
THERMODYNAMIC PROPERTY RELATIONS 655
12–1 A Little Math—Partial Derivatives and
Associated Relations 656
Partial Differentials 657
Partial Differential Relations 659
12–2 The Maxwell Relations 661
12–3 The Clapeyron Equation 662
12–4 General Relations For du dh ds c
v
and c
p
665
Internal Energy Changes 666
Enthalpy Changes 666
Entropy Changes 667
Specific Heats c
v
and c
p
668
12–5 The Joule-Thomson Coefficient 672
12–6 The Dh Du and Ds of Real Gases 674
Enthalpy Changes of Real Gases 674
Internal Energy Changes of Real Gases 675
Entropy Changes of Real Gases 676
Summary 679
References and Suggested Readings 680
Problems 680
chapter thirteen
GAS MIXTURES 687
13–1 Composition of a Gas Mixture: Mass and Mole
Fractions 688
13–2 P-v-T Behavior of Gas Mixtures: Ideal and Real
Gases 690
Ideal-Gas Mixtures 691
Real-Gas Mixtures 692
13–3 Properties of Gas Mixtures: Ideal and Real
Gases 695
Ideal-Gas Mixtures 696
Real-Gas Mixtures 700
Topic of Special Interest: Chemical Potential and the
Separation Work of Mixtures 704
Summary 714
References and Suggested Readings 715
Problems 716
chapter fourteen
GAS–VAPOR MIXTURES AND
AIR-CONDITIONING 725
14–1 Dry and Atmospheric Air 726
14–2 Specific and Relative Humidity of Air 727
14–3 Dew-Point Temperature 729
14–4 Adiabatic Saturation and Wet-Bulb
Temperatures 731
14– 5 The Psychrometric Chart 734
14–6 Human Comfort and Air-Conditioning 735
14–7 Air-Conditioning Processes 737
Simple Heating and Cooling v 5 constant 738
Heating with Humidification 739
Cooling with Dehumidification 740
Evaporative Cooling 742
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xiv
THERMODYNAMICS
Adiabatic Mixing of Airstreams 743
Wet Cooling Towers 745
Summary 747
References and Suggested Readings 748
Problems 749
chapter fifteen
CHEMICAL REACTIONS 759
15–1 Fuels and Combustion 760
15–2 Theoretical and Actual Combustion
Processes 764
15–3 Enthalpy of Formation and Enthalpy of
Combustion 771
15–4 First-Law Analysis of Reacting
Systems 774
Steady-Flow Systems 775
Closed Systems 776
15–5 Adiabatic Flame Temperature 780
15–6 Entropy Change of Reacting
Systems 782
15–7 Second-Law Analysis of Reacting Systems 784
Topic of Special Interest: Fuel Cells 790
Summary 792
References and Suggested Readings 793
Problems 793
chapter sixteen
CHEMICAL AND PHASE EQUILIBRIUM 805
16–1 Criterion for Chemical
Equilibrium 806
16–2 The Equilibrium Constant for Ideal-Gas
Mixtures 808
16–3 Some Remarks about the K
p
of Ideal-Gas
Mixtures 812
16–4 Chemical Equilibrium for Simultaneous
Reactions 816
16–5 Variation of K
p
with Temperature 818
16–6 Phase Equilibrium 820
Phase Equilibrium for a Single-Component System 820
The Phase Rule 822
Phase Equilibrium for a Multicomponent System 822
Summary 828
References and Suggested Readings 829
Problems 829
chapter seventeen
COMPRESSIBLE FLOW 839
17–1 Stagnation Properties 840
17–2 Speed of Sound and Mach Number 843
17–3 One-Dimensional Isentropic Flow 845
Variation of Fluid Velocity with Flow Area 847
Property Relations for Isentropic Flow
of Ideal Gases 849
17–4 Isentropic Flow Through Nozzles 851
Converging Nozzles 852
Converging–Diverging Nozzles 856
17–5 Shock Waves and Expansion Waves 860
Normal Shocks 860
Oblique Shocks 866
Prandtl–Meyer Expansion Waves 870
17–6 Duct Flow with Heat Transfer and Negligible
Friction Rayleigh Flow 875
Property Relations for Rayleigh
Flow 881
Choked Rayleigh Flow 882
17–7 Steam Nozzles 884
Summary 887
References and Suggested Readings 888
Problems 889
chapter eighteen
web chapter
RENEWABLE ENERGY
18–1 Introduction
18-2 Solar Energy
Solar Radiation
Flat-Plate Solar Collector
Concentrating Solar Collector
Linear Concentrating Solar Power Collector
Solar-Power Tower Plant
Solar Pond
Photovoltaic Cell
Passive Solar
Applications
Solar Heat Gain through Windows
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CONTENTS
xv
Figure A–14 P-h diagram for
refrigerant-134a 921
Figure A–15 Nelson–Obert generalized
compressibility chart 922
Table A–16 Properties of the atmosphere at high
altitude 923
Table A–17 Ideal-gas properties
of air 924
Table A–18 Ideal-gas properties of nitrogen
N
2
926
Table A–19 Ideal-gas properties of oxygen
O
2
928
Table A–20 Ideal-gas properties of carbon dioxide
CO
2
930
Table A–21 Ideal-gas properties of carbon
monoxide CO 932
Table A–22 Ideal-gas properties of hydrogen
H
2
934
Table A–23 Ideal-gas properties of water vapor
H
2
O 935
Table A–24 Ideal-gas properties of monatomic
oxygen O 937
Table A–25 Ideal-gas properties of hydroxyl
OH 937
Table A–26 Enthalpy of formation Gibbs function
of formation and absolute entropy at
258C 1 atm 938
Table A–27 Properties of some common fuels and
hydrocarbons 939
Table A–28 Natural logarithms of the equilibrium
constant K
p
940
Figure A–29 Generalized enthalpy departure
chart 941
Figure A–30 Generalized entropy departure
chart 942
Figure A–31 Psychrometric chart at 1 atm total
pressure 943
Table A–32 One-dimensional isentropic
compressible-flow functions for an
ideal gas with k 5 1.4 944
Table A–33 One-dimensional normal-shock
functions for an ideal gas
with k 5 1.4 945
Table A–34 Rayleigh flow functions for an ideal
gas with k 5 1.4 946
18-3 Wind Energy
Wind Turbine Types and Power
Performance Curve
Wind Power Potential
Wind Power Density
Wind Turbine Efficiency
Betz Limit for Wind Turbine Efficiency
18-4 Hydropower
Analysis of Hydroelectric Power Plant
Turbine Types
18–5 Geothermal Energy
Geothermal Power Production
18–6 Biomass Energy
Biomass Resources
Conversion of Biomass to Biofuel
Biomass Products
Electricity and Heat Production by Biomass
Solid Municipality Waste
Summary
References and Suggested Readings
Problems
appendix one
PROPERTY TABLES AND CHARTS
SI UNITS 897
Table A–1 Molar mass gas constant and critical-
point properties 898
Table A–2 Ideal-gas specific heats of various
common gases 899
Table A–3 Properties of common liquids solids
and foods 902
Table A–4 Saturated water—Temperature
table 904
Table A–5 Saturated water—Pressure table 906
Table A–6 Superheated water 908
Table A–7 Compressed liquid water 912
Table A–8 Saturated ice–water vapor 913
Figure A–9 T-s diagram for water 914
Figure A–10 Mollier diagram for water 915
Table A–11 Saturated refrigerant-134a—
Temperature table 916
Table A–12 Saturated refrigerant-134a—
Pressure table 918
Table A–13 Superheated refrigerant-134a 919
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xvi
THERMODYNAMICS
appendix two
PROPERTY TABLES AND CHARTS
ENGLISH UNITS 947
Table A–1E Molar mass gas constant and critical-
point properties 948
Table A–2E Ideal-gas specific heats of various
common gases 949
Table A–3E Properties of common liquids solids
and foods 952
Table A–4E Saturated water—Temperature
table 954
Table A–5E Saturated water—Pressure table 956
Table A–6E Superheated water 958
Table A–7E Compressed liquid water 962
Table A–8E Saturated ice–water vapor 963
Figure A–9E T-s diagram for water 964
Figure A–10E Mollier diagram for water 965
Table A–11E Saturated refrigerant-134a—
Temperature table 966
Table A–12E Saturated refrigerant-134a—Pressure
table 967
Table A–13E Superheated refrigerant-134a 968
Figure A–14E P-h diagram for refrigerant-134a 970
Table A–16E Properties of the atmosphere at high
altitude 971
Table A–17E Ideal-gas properties of air 972
Table A–18E Ideal-gas properties of nitrogen
N
2
974
Table A–19E Ideal-gas properties of oxygen O
2
976
Table A–20E Ideal-gas properties of carbon dioxide
CO
2
978
Table A–21E Ideal-gas properties of carbon
monoxide CO 980
Table A–22E Ideal-gas properties of hydrogen
H
2
982
Table A–23E Ideal-gas properties of water vapor
H
2
O 983
Table A–26E Enthalpy of formation Gibbs function
of formation and absolute entropy at
778C 1 atm 985
Table A–27E Properties of some common fuels and
hydrocarbons 986
Figure A–31E Psychrometric chart at 1 atm total
pressure 987
INDEX 989
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slide 18:

BACKGROUND
Thermodynamics is an exciting and fascinating subject that deals with energy
and thermodynamics has long been an essential part of engineering curricula
all over the world. It has a broad application area ranging from microscopic
organisms to common household appliances transportation vehicles power
generation systems and even philosophy. This introductory book contains
sufficient material for two sequential courses in thermodynamics. Students
are assumed to have an adequate background in calculus and physics.
OBJECTIVES
This book is intended for use as a textbook by undergraduate engineering stu-
dents in their sophomore or junior year and as a reference book for practicing
engineers. The objectives of this text are
• To cover the basic principles of thermodynamics.
• To present a wealth of real-world engineering examples to give students
a feel for how thermodynamics is applied in engineering practice.
• To develop an intuitive understanding of thermodynamics by emphasiz-
ing the physics and physical arguments that underpin the theory.
It is our hope that this book through its careful explanations of concepts and
its use of numerous practical examples and figures helps students develop the
necessary skills to bridge the gap between knowledge and the confidence to
properly apply knowledge.
PHILOSOPHY AND GOAL
The philosophy that contributed to the overwhelming popularity of the prior
editions of this book has remained unchanged in this edition. Namely our
goal has been to offer an engineering textbook that
• Communicates directly to the minds of tomorrow’s engineers in a
simple yet precise manner.
• Leads students toward a clear understanding and firm grasp of the basic
principles of thermodynamics.
• Encourages creative thinking and development of a deeper understand-
ing and intuitive feel for thermodynamics.
• Is read by students with interest and enthusiasm rather than being used
as an aid to solve problems.
Special effort has been made to appeal to students’ natural curiosity and to
help them explore the various facets of the exciting subject area of thermo-
dynamics. The enthusiastic responses we have received from users of prior
editions—from small colleges to large universities all over the world—and
the continued translations into new languages indicate that our objectives
Preface
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slide 19:

xviii
THERMODYNAMICS
have largely been achieved. It is our philosophy that the best way to learn is
by practice. Therefore special effort is made throughout the book to reinforce
material that was presented earlier.
Yesterday’s engineer spent a major portion of his or her time substituting
values into the formulas and obtaining numerical results. However formula
manipulations and number crunching are now being left mainly to computers.
Tomorrow’s engineer will need a clear understanding and a firm grasp of the
basic principles so that he or she can understand even the most complex prob-
lems formulate them and interpret the results. A conscious effort is made to
emphasize these basic principles while also providing students with a per-
spective of how computational tools are used in engineering practice.
The traditional classical or macroscopic approach is used throughout the
text with microscopic arguments serving in a supporting role as appropriate.
This approach is more in line with students’ intuition and makes learning the
subject matter much easier.
NEW IN THIS EDITION
The primary change in this eighth edition of the text is the effective use of
full color to enhance the learning experience of students and to make it more
enjoyable. Another significant change is the addition of a new web chapter
on Renewable Energy available via the Online Learning Center. The third
important change is the update of the R-134a tables to make property values
consistent with those from the latest version of EES. All the solved examples
and end-of-chapter problems dealing with R-134a are modified to reflect
this change. This edition includes numerous new problems with a variety of
applications. Problems whose solutions require parametric investigations and
thus the use of a computer are identified by a computer-EES icon as before.
Some existing problems from previous editions have been removed and other
updates and changes for clarity and readability have been made throughout
the text.
The eighth edition also includes McGraw-Hill’s Connect® Engineering.
This online homework management tool allows assignment of algorithmic
problems for homework quizzes and tests. It connects students with the
tools and resources they’ll need to achieve success. To learn more visit
www.mcgrawhillconnect.com.
McGraw-Hill LearnSmart™ is also available as an integrated feature
of McGraw-Hill Connect® Engineering. It is an adaptive learning system
designed to help students learn faster study more efficiently and retain more
knowledge for greater success. LearnSmart assesses a student’s knowledge of
course content through a series of adaptive questions. It pinpoints concepts
the student does not understand and maps out a personalized study plan for
success. Visit the following site for a demonstration: www.mhlearnsmart.com.
LEARNING TOOLS
EARLY INTRODUCTION OF THE FIRST LAW OF THERMODYNAMICS
The first law of thermodynamics is introduced early in Chapter 2 “Energy
Energy Transfer and General Energy Analysis.” This introductory chapter
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xix
PREFACE
sets the framework of establishing a general understanding of various forms
of energy mechanisms of energy transfer the concept of energy balance
thermo-economics energy conversion and conversion efficiency using
fa mil iar settings that involve mostly electrical and mechanical forms of
energy. It also exposes students to some exciting real-world applications
of thermodynamics early in the course and helps them establish a sense of
the monetary value of energy. There is special emphasis on the utilization of
renewable energy such as wind power and hydraulic energy and the efficient
use of existing resources.
EMPHASIS ON PHYSICS
A distinctive feature of this book is its emphasis on the physical aspects of the
subject matter in addition to mathematical representations and manipulations.
The authors believe that the emphasis in undergraduate education should
remain on developing a sense of underlying physical mechanisms and a mas-
tery of solving practical problems that an engineer is likely to face in the real
world. Developing an intuitive understanding should also make the course a
more motivating and worthwhile experience for students.
EFFECTIVE USE OF ASSOCIATION
An observant mind should have no difficulty understanding engineering
sciences. After all the principles of engineering sciences are based on our
everyday experiences and experimental observations. Therefore a physi-
cal intuitive approach is used throughout this text. Frequently parallels are
drawn between the subject matter and students’ everyday experiences so that
they can relate the subject matter to what they already know. The process of
cooking for example serves as an excellent vehicle to demonstrate the basic
principles of thermodynamics.
SELF-INSTRUCTING
The material in the text is introduced at a level that an average student can
follow comfortably. It speaks to students not over students. In fact it is self-
instructive. The order of coverage is from simple to general. That is it starts
with the simplest case and adds complexities gradually. In this way the basic
principles are repeatedly applied to different systems and students master
how to apply the principles instead of how to simplify a general formula. Not-
ing that the principles of sciences are based on experimental observations all
the derivations in this text are based on physical arguments and thus they are
easy to follow and understand.
EXTENSIVE USE OF ARTWORK
Figures are important learning tools that help students “get the picture” and
the text makes very effective use of graphics. This edition of Thermodynamics:
An Engineering Approach Eighth Edition features an enhanced art program
done in four colors to provide more realism and pedagogical understand-
ing. Further a large number of figures have been upgraded to become three-
dimensional and thus more real-life. Figures attract attention and stimulate
curiosity and interest. Most of the figures in this text are intended to serve as a
means of emphasizing some key concepts that would otherwise go unnoticed
some serve as page summaries.
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xx
THERMODYNAMICS
LEARNING OBJECTIVES AND SUMMARIES
Each chapter begins with an overview of the material to be covered and
chapter-specific learning objectives. A summary is included at the end of
each chapter providing a quick review of basic concepts and important rela-
tions and pointing out the relevance of the material.
NUMEROUS WORKED-OUT EXAMPLES
WITH A SYSTEMATIC SOLUTIONS PROCEDURE
Each chapter contains several worked-out examples that clarify the material and
illustrate the use of the basic principles. An intuitive and systematic approach is
used in the solution of the example problems while maintaining an informal
conversational style. The problem is first stated and the objectives are identified.
The assumptions are then stated together with their justifications. The proper-
ties needed to solve the problem are listed separately if appropriate. Numerical
values are used together with their units to emphasize that numbers without units
are meaningless and that unit manipulations are as important as manipulating
the numerical values with a calculator. The significance of the findings is dis-
cussed following the solutions. This approach is also used consistently in the
solutions presented in the instructor’s solutions manual.
A WEALTH OF REAL-WORLD END-OF-CHAPTER PROBLEMS
The end-of-chapter problems are grouped under specific topics to make prob-
lem selection easier for both instructors and students. Within each group of
problems are Concept Questions indicated by “C” to check the students’
level of understanding of basic concepts. The problems under Review Prob-
lems are more comprehensive in nature and are not directly tied to any specific
section of a chapter—in some cases they require review of material learned
in previous chapters. Problems designated as Design and Essay are intended
to encourage students to make engineering judgments to conduct indepen-
dent exploration of topics of interest and to communicate their findings in
a professional manner. Problems designated by an “E” are in English units
and SI users can ignore them. Problems with the are solved using EES
and complete solutions together with parametric studies are included on the
textbook’s website. Problems with the are comprehensive in nature and
are intended to be solved with a computer possibly using the EES software.
Several economics- and safety-related problems are incorporated throughout
to promote cost and safety awareness among engineering students. Answers
to selected problems are listed immediately following the problem for conve-
nience to students. In addition to prepare students for the Fundamentals of
Engineering Exam that is becoming more important for the outcome-based
ABET 2000 criteria and to facilitate multiple-choice tests over 200 multiple-
choice problems are included in the end-of-chapter problem sets. They are
placed under the title Fundamentals of Engineering FE Exam Problems for
easy recognition. These problems are intended to check the understanding of
fundamentals and to help readers avoid common pitfalls.
RELAXED SIGN CONVENTION
The use of a formal sign convention for heat and work is abandoned as it
often becomes counterproductive. A physically meaningful and engag-
ing approach is adopted for interactions instead of a mechanical approach.
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xxi
PREFACE
Subscripts “in” and “out” rather than the plus and minus signs are used to
indicate the directions of interactions.
PHYSICALLY MEANINGFUL FORMULAS
The physically meaningful forms of the balance equations rather than formu-
las are used to foster deeper understanding and to avoid a cookbook approach.
The mass energy entropy and exergy balances for any system undergoing
any process are expressed as
Mass balance: m
in
2 m
out
5 Dm
system
Energy balance: E
in
2 E
out
5 DE
system
Net energy transfer Change in internal kinetic
by heat work and mass potential etc. energies
Entropy balance: S
in
2 S
out
1 S
gen
5 DS
system
Net entropy transfer Entropy Change
by heat and mass generation in entropy
Exergy balance: X
in
2 X
out
2 X
destroyed
5 DX
system
Net exergy transfer Exergy Change
by heat work and mass destruction in exergy
These relations reinforce the fundamental principles that during an actual
process mass and energy are conserved entropy is generated and exergy is
destroyed. Students are encouraged to use these forms of balances in early
chapters after they specify the system and to simplify them for the particular
problem. A more relaxed approach is used in later chapters as students gain
mastery.
A CHOICE OF SI ALONE OR SI/ENGLISH UNITS
In recognition of the fact that English units are still widely used in some
industries both SI and English units are used in this text with an emphasis on
SI. The material in this text can be covered using combined SI/English units
or SI units alone depending on the preference of the instructor. The property
tables and charts in the appendices are presented in both units except the ones
that involve dimensionless quantities. Problems tables and charts in English
units are designated by “E” after the number for easy recognition and they
can be ignored by SI users.
TOPICS OF SPECIAL INTEREST
Most chapters contain a section called “Topic of Special Interest” where
interesting aspects of thermodynamics are discussed. Examples include Ther-
modynamic Aspects of Biological Systems in Chapter 4 Household Refrigera-
tors in Chapter 6 Second-Law Aspects of Daily Life in Chapter 8 and Saving
Fuel and Money by Driving Sensibly in Chapter 9. The topics selected for
these sections provide intriguing extensions to thermodynamics but they can
be ignored if desired without a loss in continuity.
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xxii
THERMODYNAMICS
GLOSSARY OF THERMODYNAMIC TERMS
Throughout the chapters when an important key term or concept is intro-
duced and defined it appears in boldface type. Fundamental thermo dynamic
terms and concepts also appear in a glossary located on our accompanying
website www.mhhe.com/cengel. This unique glossary helps to reinforce
key terminology and is an excellent learning and review tool for students as
they move forward in their study of thermodynamics. In addition students
can test their knowledge of these fundamental terms by using the flash cards
and other interactive resources.
CONVERSION FACTORS
Frequently used conversion factors and physical constants are listed on the
inner cover pages of the text for easy reference.
SUPPLEMENTS
The following supplements are available to users of the book.
ENGINEERING EQUATION SOLVER EES
Developed by Sanford Klein and William Beckman from the University of
Wisconsin—Madison this software combines equation-solving capability
and engineering property data. EES can do optimization parametric analysis
and linear and nonlinear regression and provides publication-quality plot-
ting capabilities. Thermodynamics and transport properties for air water and
many other fluids are built in and EES allows the user to enter property data
or functional relationships.
EES is a powerful equation solver with built-in functions and property
tables for thermodynamic and transport properties as well as automatic unit
checking capability. It requires less time than a calculator for data entry and
allows more time for thinking critically about modeling and solving engineer-
ing problems. Look for the EES icons in the homework problems sections of
the text.
The Limited Academic Version of EES is available for departmental license
upon adoption of the Eighth Edition of Thermodynamics: An Engineering
Approach meaning that the text is required for students in the course. You
may load this software onto your institution’s computer system for use by
students and faculty related to the course as long as the arrangement between
McGraw-Hill Education and F-Chart is in effect. There are minimum order
requirements stipulated by F-Chart to qualify.
PROPERTIES TABLE BOOKLET
ISBN 0-07-762477-7
This booklet provides students with an easy reference to the most important
property tables and charts many of which are found at the back of the text-
book in both the SI and English units.
COSMOS
McGraw-Hill’s COSMOS Complete Online Solutions Manual Organization
System allows instructors to streamline the creation of assignments quizzes
and tests by using problems and solutions from the textbook as well as their own
custom material. COSMOS is now available online at http://cosmos.mhhe.com/
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xxiii
PREFACE
ACKNOWLEDGMENTS
The authors would like to acknowledge with appreciation the numerous and
valuable comments suggestions constructive criticisms and praise from the
following evaluators and reviewers:
Edward Anderson
Texas Tech University
John Biddle
Cal Poly Pomona University
Gianfranco DiGiuseppe
Kettering University
Shoeleh Di Julio
California State University-Northridge
Afshin Ghajar
Oklahoma State University
Harry Hardee
New Mexico State University
Kevin Lyons
North Carolina State University
Kevin Macfarlan
John Brown University
Saeed Manafzadeh
University of Illinois-Chicago
Alex Moutsoglou
South Dakota State University
Rishi Raj
The City College of New York
Maria Sanchez
California State University-Fresno
Kalyan Srinivasan
Mississippi State University
Robert Stiger
Gonzaga University
Their suggestions have greatly helped to improve the quality of this text. In
particular we would like to express our gratitude to Mehmet Kanoglu of the
University of Gaziantep Turkey for his valuable contributions his critical
review of the manuscript and for his special attention to accuracy and detail.
We also would like to thank our students who provided plenty of feedback
from students’ perspectives. Finally we would like to express our apprecia-
tion to our wives Zehra Çengel and Sylvia Boles and to our children for their
continued patience understanding and support throughout the preparation of
this text.
Yunus A. Çengel
Michael A. Boles
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slide 26:

MCGRAW-HILL CONNECT
®
ENGINEERING
McGraw-Hill Connect Engineering is a web-based assignment and assessment
platform that gives students the means to better connect with their course-
work with their instructors and with the important concepts that they will
need to know for success now and in the future. With Connect Engineering
instructors can deliver assignments quizzes and tests easily online. Students
can practice important skills at their own pace and on their own schedule.
Connect Engineering for Thermodynamics: An Engineering Approach
Eighth Edition is available via the text website at www.mhhe.com/cengel
COSMOS
McGraw-Hill’s COSMOS Complete Online Solutions Manual Organization
System allows instructors to streamline the creation of assignments quiz-
zes and tests by using problems and solutions from the textbook as well as
their own custom material. COSMOS is now available online at http://cosmos.
mhhe.com/
WWW.MHHE.COM/CENGEL
This site offers resources for students and instructors.
The following resources are available for students:
• Glossary of Key Terms in Thermodynamics—Bolded terms in the text are
defined in this accessible glossary. Organized at the chapter level or
available as one large file.
• Student Study Guide—This resource outlines the fundamental concepts of
the text and is a helpful guide that allows students to focus on the most
important concepts. The guide can also serve as a lecture outline for
instructors.
• Learning Objectives—The chapter learning objectives are outlined here.
Organized by chapter and tied to ABET objectives.
• Self-Quizzing—Students can test their knowledge using multiple-choice
quizzing. These self-tests provide immediate feedback and are an excellent
learning tool.
• Flashcards—Interactive flashcards test student understanding of the text
terms and their definitions. The program also allows students to flag terms
that require further understanding.
• Crossword Puzzles—An interactive timed puzzle that provides hints as well
as a notes section.
• Errata—If errors should be found in the text they will be reported here.
Online Resources for Students and Instructors
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xxvi
THERMODYNAMICS
The following resources are available for instructors under password
protection:
• Instructor Testbank—Additional problems prepared for instructors to assign
to students. Solutions are given and use of EES is recommended to verify
accuracy.
• Correlation Guide—New users of this text will appreciate this resource. The
guide provides a smooth transition for instructors not currently using the
Çengel/Boles text.
• Image Library—The electronic version of the figures are supplied for easy
integration into course presentations exams and assignments.
• Instructor’s Guide—Provides instructors with helpful tools such as sample
syllabi and exams an ABET conversion guide a thermodynamics glossary
and chapter objectives.
• Errata—If errors should be found in the solutions manual they will be
reported here.
• Solutions Manual—The detailed solutions to all text homework problems are
provided in PDF form.
• EES Solutions Manual—The entire solutions manual is also available in
EES. Any problem in the text can be modified and the solution of the
modified problem can readily be obtained by copying and pasting the given
EES solution on a blank EES screen and hitting the solve button.
• PP slides—Powerpoint presentation slides for all chapters in the text are
available for use in lectures
• Appendices—These are provided in PDF form for ease of use.
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1
INTRODUCTION AND
BASIC CONCEPTS
E
very science has a unique vocabulary associated with it and thermo-
dynamics is no exception. Precise definition of basic concepts forms
a sound foundation for the development of a science and prevents
possible misunderstandings. We start this chapter with an overview of ther-
modynamics and the unit systems and continue with a discussion of some
basic concepts such as system state state postulate equilibrium and pro-
cess. We discuss intensive and extensive properties of a system and define
density specific gravity and specific weight. We also discuss temperature
and temperature scales with particular emphasis on the International Tem-
perature Scale of 1990. We then present pressure which is the normal force
exerted by a fluid per unit area and discuss absolute and gage pressures the
variation of pressure with depth and pressure measurement devices such
as manometers and barometers. Careful study of these concepts is essential
for a good understanding of the topics in the following chapters. Finally we
present an intuitive systematic problem-solving technique that can be used
as a model in solving engineering problems.
1
1
OBJECTIVES
The objectives of Chapter 1 are to:
■ Identify the unique vocabulary
associated with thermodynamics
through the precise definition of
basic concepts to form a sound
foundation for the development
of the principles of thermody-
namics.
■ Review the metric SI and the
English unit systems that will be
used throughout the text.
■ Explain the basic concepts
of thermodynamics such as
system state state postulate
equilibrium process and cycle.
■ Discuss properties of a system
and define density specific
gravity and specific weight.
■ Review concepts of temperature
temperature scales pressure
and absolute and gage pressure.
■ Introduce an intuitive systematic
problem-solving technique.
CHAPTER
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slide 29:

2
INTRODUCTION AND BASIC CONCEPTS
1–1
■
THERMODYNAMICS AND ENERGY
Thermodynamics can be defined as the science of energy. Although every-
body has a feeling of what energy is it is difficult to give a precise defini-
tion for it. Energy can be viewed as the ability to cause changes.
The name thermodynamics stems from the Greek words therme heat and
dynamis power which is most descriptive of the early efforts to convert
heat into power. Today the same name is broadly interpreted to include all
aspects of energy and energy transformations including power generation
refrigeration and relationships among the properties of matter.
One of the most fundamental laws of nature is the conservation of energy
principle. It simply states that during an interaction energy can change from
one form to another but the total amount of energy remains constant. That is
energy cannot be created or destroyed. A rock falling off a cliff for example
picks up speed as a result of its potential energy being converted to kinetic
energy Fig. 1–1. The conservation of energy principle also forms the back-
bone of the diet industry: A person who has a greater energy input food
than energy output exercise will gain weight store energy in the form
of fat and a person who has a smaller energy input than output will lose
weight Fig. 1–2. The change in the energy content of a body or any other
system is equal to the difference between the energy input and the energy
output and the energy balance is expressed as E
in
2 E
out
5 DE.
The first law of thermodynamics is simply an expression of the con-
servation of energy principle and it asserts that energy is a thermodynamic
property. The second law of thermodynamics asserts that energy has
quality as well as quantity and actual processes occur in the direction of
decreasing quality of energy. For example a cup of hot coffee left on a table
eventually cools but a cup of cool coffee in the same room never gets hot
by itself Fig. 1–3. The high-temperature energy of the coffee is degraded
transformed into a less useful form at a lower temperature once it is trans-
ferred to the surrounding air.
Although the principles of thermodynamics have been in existence since
the creation of the universe thermodynamics did not emerge as a science
until the construction of the first successful atmospheric steam engines in
England by Thomas Savery in 1697 and Thomas Newcomen in 1712. These
engines were very slow and inefficient but they opened the way for the
development of a new science.
The first and second laws of thermodynamics emerged simultaneously in
the 1850s primarily out of the works of William Rankine Rudolph Clausius
and Lord Kelvin formerly William Thomson. The term thermodynamics
was first used in a publication by Lord Kelvin in 1849. The first thermody-
namics textbook was written in 1859 by William Rankine a professor at the
University of Glasgow.
It is well-known that a substance consists of a large number of particles
called molecules. The properties of the substance naturally depend on the
behavior of these particles. For example the pressure of a gas in a container
is the result of momentum transfer between the molecules and the walls of
the container. However one does not need to know the behavior of the gas
particles to determine the pressure in the container. It would be sufficient to
attach a pressure gage to the container. This macroscopic approach to the
FIGURE 1–1
Energy cannot be created or
destroyed it can only change
forms the first law.
Potential
energy
Kinetic
energy
PE 7 units
KE 3 units
PE 10 units
KE 0
FIGURE 1–2
Conservation of energy principle for
the human body.
Energy out
4 units
Energy in
5 units
Energy storage
1 unit
FIGURE 1–3
Heat flows in the direction of
decreasing temperature.
Heat
Cool
environment
20°C
Hot
coffee
70°C
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3
CHAPTER 1
study of thermodynamics that does not require a knowledge of the behavior
of individual particles is called classical thermodynamics. It provides a
direct and easy way to the solution of engineering problems. A more elabo-
rate approach based on the average behavior of large groups of individual
particles is called statistical thermodynamics. This microscopic approach
is rather involved and is used in this text only in the supporting role.
Application Areas of Thermodynamics
All activities in nature involve some interaction between energy and matter
thus it is hard to imagine an area that does not relate to thermodynam-
ics in some manner. Therefore developing a good understanding of basic
principles of thermodynamics has long been an essential part of engineering
education.
Thermodynamics is commonly encountered in many engineering systems
and other aspects of life and one does not need to go very far to see some
application areas of it. In fact one does not need to go anywhere. The heart
is constantly pumping blood to all parts of the human body various energy
conversions occur in trillions of body cells and the body heat generated is
constantly rejected to the environment. The human comfort is closely tied to
the rate of this metabolic heat rejection. We try to control this heat transfer
rate by adjusting our clothing to the environmental conditions.
Other applications of thermodynamics are right where one lives. An ordi-
nary house is in some respects an exhibition hall filled with wonders of
thermodynamics Fig. 1–4. Many ordinary household utensils and appli-
ances are designed in whole or in part by using the principles of thermo-
dynamics. Some examples include the electric or gas range the heating
and air-conditioning systems the refrigerator the humidifier the pressure
cooker the water heater the shower the iron and even the computer and
the TV. On a larger scale thermodynamics plays a major part in the design
and analysis of automotive engines rockets jet engines and conventional or
nuclear power plants solar collectors and the design of vehicles from ordi-
nary cars to airplanes Fig. 1–5. The energy-efficient home that you may
be living in for example is designed on the basis of minimizing heat loss
in winter and heat gain in summer. The size location and the power input
of the fan of your computer is also selected after an analysis that involves
thermodynamics.
1–2
■
IMPORTANCE OF DIMENSIONS AND UNITS
Any physical quantity can be characterized by dimensions. The magnitudes
assigned to the dimensions are called units. Some basic dimensions such
as mass m length L time t and temperature T are selected as primary or
fundamental dimensions while others such as velocity V energy E and
volume V are expressed in terms of the primary dimensions and are called
secondary dimensions or derived dimensions.
A number of unit systems have been developed over the years. Despite
strong efforts in the scientific and engineering community to unify the
world with a single unit system two sets of units are still in common
use today: the English system which is also known as the United States
FIGURE 1–4
The design of many engineering
systems such as this solar hot water
system involves thermodynamics.
Solar
collectors
Hot
water
Heat
exchanger
Pump
Shower
Cold
water
Hot water tank
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5
CHAPTER 1
find universal acceptance until 1875 when The Metric Convention Treaty
was prepared and signed by 17 nations including the United States. In this
international treaty meter and gram were established as the metric units
for length and mass respectively and a General Conference of Weights
and Measures CGPM was established that was to meet every six years.
In 1960 the CGPM produced the SI which was based on six fundamental
quantities and their units were adopted in 1954 at the Tenth General Con-
ference of Weights and Measures: meter m for length kilogram kg for
mass second s for time ampere A for electric current degree Kelvin
°K for temperature and candela cd for luminous intensity amount of
light. In 1971 the CGPM added a seventh fundamental quantity and unit:
mole mol for the amount of matter.
Based on the notational scheme introduced in 1967 the degree symbol
was officially dropped from the absolute temperature unit and all unit
names were to be written without capitalization even if they were derived
from proper names Table 1–1. However the abbreviation of a unit was
to be capitalized if the unit was derived from a proper name. For example
the SI unit of force which is named after Sir Isaac Newton 1647–1723
is newton not Newton and it is abbreviated as N. Also the full name of a
unit may be pluralized but its abbreviation cannot. For example the length
of an object can be 5 m or 5 meters not 5 ms or 5 meter. Finally no period
is to be used in unit abbreviations unless they appear at the end of a sen-
tence. For example the proper abbreviation of meter is m not m..
The recent move toward the metric system in the United States seems to
have started in 1968 when Congress in response to what was happening
in the rest of the world passed a Metric Study Act. Congress continued
to promote a voluntary switch to the metric system by passing the Metric
Conversion Act in 1975. A trade bill passed by Congress in 1988 set a
September 1992 deadline for all federal agencies to convert to the metric
system. However the deadlines were relaxed later with no clear plans for
the future.
The industries that are heavily involved in international trade such as the
automotive soft drink and liquor industries have been quick in convert-
ing to the metric system for economic reasons having a single worldwide
design fewer sizes smaller inventories etc.. Today nearly all the cars
manufactured in the United States are metric. Most car owners probably do
not realize this until they try an English socket wrench on a metric bolt.
Most industries however resisted the change thus slowing down the con-
version process.
Presently the United States is a dual-system society and it will stay that
way until the transition to the metric system is completed. This puts an extra
burden on today’s engineering students since they are expected to retain
their understanding of the English system while learning thinking and
working in terms of the SI. Given the position of the engineers in the transi-
tion period both unit systems are used in this text with particular emphasis
on SI units.
As pointed out the SI is based on a decimal relationship between units.
The prefixes used to express the multiples of the various units are listed in
Table 1–2. They are standard for all units and the student is encouraged to
memorize them because of their widespread use Fig. 1–6.
TABLE 1–1
The seven fundamental or primary
dimensions and their units in SI
Dimension Unit
Length meter m
Mass kilogram kg
Time second s
Temperature kelvin K
Electric current ampere A
Amount of light candela cd
Amount of matter mole mol
TABLE 1–2
Standard prefixes in SI units
Multiple Prefix
10
24
yotta Y
10
21
zetta Z
10
18
exa E
10
15
peta P
10
12
tera T
10
9
giga G
10
6
mega M
10
3
kilo k
10
2
hecto h
10
1
deka da
10
21
deci d
10
22
centi c
10
23
milli m
10
26
micro m
10
29
nano n
10
212
pico p
10
215
femto f
10
218
atto a
10
221
zepto z
10
224
yocto y
FIGURE 1–6
The SI unit prefixes are used in all
branches of engineering.
1 kg 200 mL
0.2 L 10
3
g
1 M 10
6
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6
INTRODUCTION AND BASIC CONCEPTS
Some SI and English Units
In SI the units of mass length and time are the kilogram kg meter m
and second s respectively. The respective units in the English system are
the pound-mass lbm foot ft and second s. The pound symbol lb is
actually the abbreviation of libra which was the ancient Roman unit of
weight. The English retained this symbol even after the end of the Roman
occupation of Britain in 410. The mass and length units in the two systems
are related to each other by
1 lbm 5 0.45359 kg
1 ft 5 0.3048 m
In the English system force is usually considered to be one of the
primary dimensions and is assigned a nonderived unit. This is a source
of confusion and error that necessitates the use of a dimensional
constant g
c
in many formulas. To avoid this nuisance we consider
force to be a secondary dimension whose unit is derived from Newton’s
second law that is
Force 5 MassAcceleration
or
F 5 ma 1–1
In SI the force unit is the newton N and it is defined as the force required
to accelerate a mass of 1 kg at a rate of 1 m/s
2
. In the English system the
force unit is the pound-force lbf and is defined as the force required to
accelerate a mass of 32.174 lbm 1 slug at a rate of 1 ft/s
2
Fig. 1–7. That is
1 N 5 1 kg·m/s
2
1 lbf 5 32.174 lbm·ft/s
2
A force of 1 N is roughly equivalent to the weight of a small apple
m 5 102 g whereas a force of 1 lbf is roughly equivalent to the weight of
four medium apples m
total
5 454 g as shown in Fig. 1–8. Another force
unit in common use in many European countries is the kilogram-force kgf
which is the weight of 1 kg mass at sea level 1 kgf 5 9.807 N.
The term weight is often incorrectly used to express mass particularly
by the “weight watchers.” Unlike mass weight W is a force. It is the gravi-
tational force applied to a body and its magnitude is determined from
Newton’s second law
W 5 mg N 1–2
where m is the mass of the body and g is the local gravitational acceleration
g is 9.807 m/s
2
or 32.174 ft/s
2
at sea level and 45° latitude. An ordinary
bathroom scale measures the gravitational force acting on a body.
The mass of a body remains the same regardless of its location in the
universe. Its weight however changes with a change in gravitational
acceleration. A body weighs less on top of a mountain since g decreases
FIGURE 1–7
The definition of the force units.
m 1 kg
m 32.174 lbm
a 1 m/s
2
a 1 ft/s
2
F 1 lbf
F 1 N
FIGURE 1–8
The relative magnitudes of the force
units newton N kilogram-force kgf
and pound-force lbf.
1 kgf
10 apples
m 1 kg
4 apples
m 1 lbm
1 lbf
1 apple
m 102 g
1 N
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7
CHAPTER 1
with altitude. On the surface of the moon an astronaut weighs about one-
sixth of what she or he normally weighs on earth Fig. 1–9.
At sea level a mass of 1 kg weighs 9.807 N as illustrated in Fig. 1–10. A
mass of 1 lbm however weighs 1 lbf which misleads people to believe that
pound-mass and pound-force can be used interchangeably as pound lb
which is a major source of error in the English system.
It should be noted that the gravity force acting on a mass is due to the
attraction between the masses and thus it is proportional to the mag-
nitudes of the masses and inversely proportional to the square of the dis-
tance between them. Therefore the gravitational acceleration g at a location
depends on the local density of the earth’s crust the distance to the center
of the earth and to a lesser extent the positions of the moon and the sun.
The value of g varies with location from 9.832 m/s
2
at the poles 9.789 at
the equator to 7.322 m/s
2
at 1000 km above sea level. However at altitudes
up to 30 km the variation of g from the sea-level value of 9.807 m/s
2
is
less than 1 percent. Therefore for most practical purposes the gravitational
acceleration can be assumed to be constant at 9.807 m/s
2
often rounded to
9.81 m/s
2
. It is interesting to note that at locations below sea level the value
of g increases with distance from the sea level reaches a maximum at about
4500 m and then starts decreasing. What do you think the value of g is at
the center of the earth
The primary cause of confusion between mass and weight is that mass is
usually measured indirectly by measuring the gravity force it exerts. This
approach also assumes that the forces exerted by other effects such as air
buoyancy and fluid motion are negligible. This is like measuring the dis-
tance to a star by measuring its red shift or measuring the altitude of an
airplane by measuring barometric pressure. Both of these are also indirect
measurements. The correct direct way of measuring mass is to compare it
to a known mass. This is cumbersome however and it is mostly used for
calibration and measuring precious metals.
Work which is a form of energy can simply be defined as force times
distance therefore it has the unit “newton-meter N·m” which is called a
joule J. That is
1 J 5 1 N·m 1–3
A more common unit for energy in SI is the kilojoule 1 kJ 5 10
3
J. In the
English system the energy unit is the Btu British thermal unit which is
defined as the energy required to raise the temperature of 1 lbm of water at
68°F by 1°F. In the metric system the amount of energy needed to raise the
temperature of 1 g of water at 14.5°C by 1°C is defined as 1 calorie cal
and 1 cal 5 4.1868 J. The magnitudes of the kilojoule and Btu are almost
identical 1 Btu 5 1.0551 kJ. Here is a good way to get a feel for these
units: If you light a typical match and let it burn itself out it yields approxi-
mately one Btu or one kJ of energy Fig. 1–11.
The unit for time rate of energy is joule per second J/s which is called
a watt W. In the case of work the time rate of energy is called power.
A commonly used unit of power is horsepower hp which is equivalent
to 746 W. Electrical energy typically is expressed in the unit kilowatt-hour
kWh which is equivalent to 3600 kJ. An electric appliance with a rated
power of 1 kW consumes 1 kWh of electricity when running continuously
FIGURE 1–9
A body weighing 150 lbf on earth will
weigh only 25 lbf on the moon.
FIGURE 1–10
The weight of a unit mass at sea level.
g 9.807 m/s
2
W 9.807 kg·m/s
2
9.807 N
1 kgf
W 32.174 lbm·ft/s
2
1 lbf
g 32.174 ft/s
2
kg
lbm
FIGURE 1–11
A typical match yields about one Btu or
one kJ of energy if completely burned.
Photo by John M. Cimbala
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9
CHAPTER 1
EXAMPLE 1–2 Obtaining Formulas from Unit Considerations
A tank is filled with oil whose density is r 5 850 kg/m
3
. If the volume of the
tank is V 5 2 m
3
determine the amount of mass m in the tank.
SOLUTION The volume of an oil tank is given. The mass of oil is to be
determined.
Assumptions Oil is a nearly incompressible substance and thus its density
is constant.
Analysis A sketch of the system just described is given in Fig. 1–13.
Suppose we forgot the formula that relates mass to density and volume.
However we know that mass has the unit of kilograms. That is whatever
calculations we do we should end up with the unit of kilograms. Putting the
given information into perspective we have
r 5 850 kg/m
3
and V 5 2 m
3
It is obvious that we can eliminate m
3
and end up with kg by multiplying
these two quantities. Therefore the formula we are looking for should be
m 5 rV
Thus
m 5 850 kg/m
3
2 m
3
5 1700 kg
Discussion Note that this approach may not work for more complicated for-
mulas. Nondimensional constants also may be present in the formulas and
these cannot be derived from unit considerations alone.
You should keep in mind that a formula that is not dimensionally homo-
geneous is definitely wrong Fig. 1–14 but a dimensionally homogeneous
formula is not necessarily right.
Unity Conversion Ratios
Just as all nonprimary dimensions can be formed by suitable combina-
tions of primary dimensions all nonprimary units secondary units can be
formed by combinations of primary units. Force units for example can be
expressed as
1 N 5 1 kg
m
s
2
and 1 lbf 5 32.174 lbm
ft
s
2
They can also be expressed more conveniently as unity conversion ratios as
1 N
1 kg·m / s
2
5 1 and
1 lbf
32.174 lbm·ft / s
2
5 1
Unity conversion ratios are identically equal to 1 and are unitless and
thus such ratios or their inverses can be inserted conveniently into any
calculation to properly convert units Fig. 1–15. You are encouraged to
always use unity conversion ratios such as those given here when converting
units. Some textbooks insert the archaic gravitational constant g
c
defined as
g
c
5 32.174 lbm·ft/lbf·s
2
5 1 kg·m/N·s
2
5 1 into equations in order to force
FIGURE 1–13
Schematic for Example 1–2.
Oil
2 m
3
m
ρ 850 kg/m
3
FIGURE 1–14
Always check the units in your
calculations.
FIGURE 1–15
Every unity conversion ratio as well
as its inverse is exactly equal to one.
Shown here are a few commonly used
unity conversion ratios.
0.3048 m
1 ft
1 min
60 s
1 lbm
0.45359 kg
32.174 lbmft/s
2
1 lbf
1 kgm/s
2
1 N
1 kPa
1000 N/m
2
1 kJ
1000 Nm
1 W
1 J/s
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10
INTRODUCTION AND BASIC CONCEPTS
units to match. This practice leads to unnecessary confusion and is strongly
discouraged by the present authors. We recommend that you instead use
unity conversion ratios.
EXAMPLE 1–3 The Weight of One Pound-Mass
Using unity conversion ratios show that 1.00 lbm weighs 1.00 lbf on earth
Fig. 1–16.
SOLUTION A mass of 1.00 lbm is subjected to standard earth gravity. Its
weight in lbf is to be determined.
Assumptions Standard sea-level conditions are assumed.
Properties The gravitational constant is g 5 32.174 ft/s
2
.
Analysis We apply Newton’s second law to calculate the weight force that
corresponds to the known mass and acceleration. The weight of any object
is equal to its mass times the local value of gravitational acceleration. Thus
W 5 mg 5 1.00 lbm32.174 ft /s
2
a
1 lbf
32.174 lbm·ft /s
2
b 5 1.00 lbf
Discussion The quantity in large parentheses in this equation is a unity con-
version ratio. Mass is the same regardless of its location. However on some
other planet with a different value of gravitational acceleration the weight of
1 lbm would differ from that calculated here.
When you buy a box of breakfast cereal the printing may say “Net
weight: One pound 454 grams.” See Fig. 1–17. Technically this means
that the cereal inside the box weighs 1.00 lbf on earth and has a mass of
453.6 g 0.4536 kg. Using Newton’s second law the actual weight of the
cereal on earth is
W 5 mg 5 453.6 g9.81 m/s
2
a
1 N
1 kg·m/s
2
ba
1 kg
1000 g
b 5 4.49 N
1–3
■
SYSTEMS AND CONTROL VOLUMES
A system is defined as a quantity of matter or a region in space chosen for
study. The mass or region outside the system is called the surroundings.
The real or imaginary surface that separates the system from its surround-
ings is called the boundary Fig. 1–18. The boundary of a system can be
fixed or movable. Note that the boundary is the contact surface shared by
both the system and the surroundings. Mathematically speaking the bound-
ary has zero thickness and thus it can neither contain any mass nor occupy
any volume in space.
Systems may be considered to be closed or open depending on whether a
fixed mass or a fixed volume in space is chosen for study. A closed system
also known as a control mass or just system when the context makes it
clear consists of a fixed amount of mass and no mass can cross its boun-
dary. That is no mass can enter or leave a closed system as shown in
FIGURE 1–16
A mass of 1 lbm weighs 1 lbf on earth.
lbm
FIGURE 1–17
A quirk in the metric system of units.
Net weight:
One pound
454 grams
FIGURE 1–18
System surroundings and boundary.
Surroundings
Boundary
System
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11
CHAPTER 1
Fig. 1–19. But energy in the form of heat or work can cross the boundary
and the volume of a closed system does not have to be fixed. If as a special
case even energy is not allowed to cross the boundary that system is called
an isolated system.
Consider the piston-cylinder device shown in Fig. 1–20. Let us say that
we would like to find out what happens to the enclosed gas when it is
heated. Since we are focusing our attention on the gas it is our system. The
inner surfaces of the piston and the cylinder form the boundary and since
no mass is crossing this boundary it is a closed system. Notice that energy
may cross the boundary and part of the boundary the inner surface of the
piston in this case may move. Everything outside the gas including the
piston and the cylinder is the surroundings.
An open system or a control volume as it is often called is a prop-
erly selected region in space. It usually encloses a device that involves
mass flow such as a compressor turbine or nozzle. Flow through these
devices is best studied by selecting the region within the device as the
control volume. Both mass and energy can cross the boundary of a con-
trol volume.
A large number of engineering problems involve mass flow in and out of
a system and therefore are modeled as control volumes. A water heater a
car radiator a turbine and a compressor all involve mass flow and should
be analyzed as control volumes open systems instead of as control
masses closed systems. In general any arbitrary region in space can be
selected as a control volume. There are no concrete rules for the selec-
tion of control volumes but the proper choice certainly makes the analysis
much easier. If we were to analyze the flow of air through a nozzle for
example a good choice for the control volume would be the region within
the nozzle.
The boundaries of a control volume are called a control surface and
they can be real or imaginary. In the case of a nozzle the inner surface of
the nozzle forms the real part of the boundary and the entrance and exit
areas form the imaginary part since there are no physical surfaces there
Fig. 1–21a.
FIGURE 1–19
Mass cannot cross the boundaries of a
closed system but energy can.
Closed
system
Yes
m constant
Energy
No Mass
FIGURE 1–20
A closed system with a moving
boundary.
Gas
2 kg
1.5 m
3
Gas
2 kg
1 m
3
Moving
boundary
Fixed
boundary
FIGURE 1–21
A control volume can involve
fixed moving real and imaginary
boundaries.
Real boundary
a A control volume CV with real and
imaginary boundaries
Imaginary
boundary
CV
a nozzle
CV
Moving
boundary
Fixed
boundary
b A control volume CV with fxed and
moving boundaries as well as real and
imaginary boundaries
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13
CHAPTER 1
The continuum idealization allows us to treat properties as point functions
and to assume the properties vary continually in space with no jump discon-
tinuities. This idealization is valid as long as the size of the system we deal
with is large relative to the space between the molecules. This is the case
in practically all problems except some specialized ones. The continuum
idealization is implicit in many statements we make such as “the density of
water in a glass is the same at any point.”
To have a sense of the distance involved at the molecular level con-
sider a container filled with oxygen at atmospheric conditions. The
diameter of the oxygen molecule is about 3 3 10
210
m and its mass is
5.3 3 10
226
kg. Also the mean free path of oxygen at 1 atm pressure and
20°C is 6.3 3 10
28
m. That is an oxygen molecule travels on average a
distance of 6.3 3 10
28
m about 200 times of its diameter before it col-
lides with another molecule.
Also there are about 3 3 10
16
molecules of oxygen in the tiny volume
of 1 mm
3
at 1 atm pressure and 20°C Fig. 1–24. The continuum model
is applicable as long as the characteristic length of the system such as its
diameter is much larger than the mean free path of the molecules. At very
high vacuums or very high elevations the mean free path may become
large for example it is about 0.1 m for atmospheric air at an elevation
of 100 km. For such cases the rarefied gas flow theory should be used
and the impact of individual molecules should be considered. In this text
we will limit our consideration to substances that can be modeled as a
continuum.
1–5
■
DENSITY AND SPECIFIC GRAVITY
Density is defined as mass per unit volume Fig. 1–25.
Density: r 5
m
V
kg/m
3
1–4
The reciprocal of density is the specific volume v which is defined as vol-
ume per unit mass. That is
v 5
V
m
5
1
r
1–5
For a differential volume element of mass dm and volume dV density can
be expressed as r 5 dm/dV.
The density of a substance in general depends on temperature and pres-
sure. The density of most gases is proportional to pressure and inversely
proportional to temperature. Liquids and solids on the other hand are
essentially incompressible substances and the variation of their density with
pressure is usually negligible. At 20°C for example the density of water
changes from 998 kg/m
3
at 1 atm to 1003 kg/m
3
at 100 atm a change of
just 0.5 percent. The density of liquids and solids depends more strongly on
temperature than it does on pressure. At 1 atm for example the density of
water changes from 998 kg/m
3
at 20°C to 975 kg/m
3
at 75°C a change of
2.3 percent which can still be neglected in many engineering analyses.
FIGURE 1–24
Despite the relatively large gaps
between molecules a gas can usually
be treated as a continuum because of
the very large number of molecules
even in an extremely small volume.
VOID
1 atm 20°C
O
2
3 ´ 10
16
molecules/mm
3
FIGURE 1–25
Density is mass per unit volume
specific volume is volume
per unit mass.
3
12 m 12 m
m 3 kg 3 kg
3
3
/kg /kg
0.25 kg/m 0.25 kg/m
4 m 4 m
1
v
V
r
r
–
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14
INTRODUCTION AND BASIC CONCEPTS
Sometimes the density of a substance is given relative to the density of a
well-known substance. Then it is called specific gravity or relative den-
sity and is defined as the ratio of the density of a substance to the den-
sity of some standard substance at a specified temperature usually water at
4°C for which r
H
2
O
5 1000 kg/m
3
. That is
Specific gravity: SG 5
r
r
H
2
O
1–6
Note that the specific gravity of a substance is a dimensionless quantity.
However in SI units the numerical value of the specific gravity of a sub-
stance is exactly equal to its density in g/cm
3
or kg/L or 0.001 times the
density in kg/m
3
since the density of water at 4°C is 1 g/cm
3
5 1 kg/L 5
1000 kg/m
3
. The specific gravity of mercury at 0°C for example is 13.6.
Therefore its density at 0°C is 13.6 g/cm
3
5 13.6 kg/L 5 13600 kg/m
3
.
The specific gravities of some substances at 0°C are given in Table 1–3.
Note that substances with specific gravities less than 1 are lighter than
water and thus they would float on water.
The weight of a unit volume of a substance is called specific weight and
is expressed as
Specific weight: g
s
5 rg N/m
3
1–7
where g is the gravitational acceleration.
The densities of liquids are essentially constant and thus they can often
be approximated as being incompressible substances during most processes
without sacrificing much in accuracy.
1–6
■
STATE AND EQUILIBRIUM
Consider a system not undergoing any change. At this point all the prop-
erties can be measured or calculated throughout the entire system which
gives us a set of properties that completely describes the condition or
the state of the system. At a given state all the properties of a system
have fixed values. If the value of even one property changes the state will
change to a different one. In Fig. 1–26 a system is shown at two different
states.
Thermodynamics deals with equilibrium states. The word equilibrium
implies a state of balance. In an equilibrium state there are no unbalanced
potentials or driving forces within the system. A system in equilibrium
experiences no changes when it is isolated from its surroundings.
There are many types of equilibrium and a system is not in thermody-
namic equilibrium unless the conditions of all the relevant types of equi-
librium are satisfied. For example a system is in thermal equilibrium
if the temperature is the same throughout the entire system as shown in
Fig. 1–27. That is the system involves no temperature differential which is
the driving force for heat flow. Mechanical equilibrium is related to pres-
sure and a system is in mechanical equilibrium if there is no change in
pressure at any point of the system with time. However the pressure may
vary within the system with elevation as a result of gravitational effects.
TABLE 1–3
Specific gravities of some
substances at 0°C
Substance SG
Water 1.0
Blood 1.05
Seawater 1.025
Gasoline 0.7
Ethyl alcohol 0.79
Mercury 13.6
Wood 0.3–0.9
Gold 19.2
Bones 1.7–2.0
Ice 0.92
Air at 1 atm 0.0013
FIGURE 1–26
A system at two different states.
m 2 kg
T
2
20°C
V
2
2.5 m
3
a State 1
m 2 kg
T
1
20°C
V
1
1.5 m
3
b State 2
FIGURE 1–27
A closed system reaching thermal
equilibrium.
20°C
a Before b After
23°C
35°C 40°C
30°C
42°C
32°C 32°C
32°C 32°C
32°C
32°C
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15
CHAPTER 1
For example the higher pressure at a bottom layer is balanced by the extra
weight it must carry and therefore there is no imbalance of forces. The
variation of pressure as a result of gravity in most thermodynamic systems
is relatively small and usually disregarded. If a system involves two phases
it is in phase equilibrium when the mass of each phase reaches an equi-
librium level and stays there. Finally a system is in chemical equilibrium
if its chemical composition does not change with time that is no chemical
reactions occur. A system will not be in equilibrium unless all the relevant
equilibrium criteria are satisfied.
The State Postulate
As noted earlier the state of a system is described by its properties. But
we know from experience that we do not need to specify all the properties
in order to fix a state. Once a sufficient number of properties are speci-
fied the rest of the properties assume certain values automatically. That is
specifying a certain number of properties is sufficient to fix a state. The
number of properties required to fix the state of a system is given by the
state postulate:
The state of a simple compressible system is completely specified by two
independent intensive properties.
A system is called a simple compressible system in the absence of elec-
trical magnetic gravitational motion and surface tension effects. These
effects are due to external force fields and are negligible for most engineer-
ing problems. Otherwise an additional property needs to be specified for
each effect that is significant. If the gravitational effects are to be consid-
ered for example the elevation z needs to be specified in addition to the
two properties necessary to fix the state.
The state postulate requires that the two properties specified be indepen-
dent to fix the state. Two properties are independent if one property can be
varied while the other one is held constant. Temperature and specific vol-
ume for example are always independent properties and together they can
fix the state of a simple compressible system Fig. 1–28. Temperature and
pressure however are independent properties for single-phase systems but
are dependent properties for multiphase systems. At sea level P 5 1 atm
water boils at 100°C but on a mountaintop where the pressure is lower
water boils at a lower temperature. That is T 5 fP during a phase-change
process thus temperature and pressure are not sufficient to fix the state
of a two-phase system. Phase-change processes are discussed in detail in
Chap. 3.
1–7
■
PROCESSES AND CYCLES
Any change that a system undergoes from one equilibrium state to another
is called a process and the series of states through which a system passes
during a process is called the path of the process Fig. 1–29. To describe
a process completely one should specify the initial and final states of
the process as well as the path it follows and the interactions with the
surroundings.
FIGURE 1–28
The state of nitrogen is fixed by two
independent intensive properties.
Nitrogen
T 25°C
v 0.9 m
3
/kg
FIGURE 1–29
A process between states 1 and 2 and
the process path.
State 1
State 2
Process path
Property B
Property A
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16
INTRODUCTION AND BASIC CONCEPTS
When a process proceeds in such a manner that the system remains infini-
tesimally close to an equilibrium state at all times it is called a quasi-static
or quasi-equilibrium process. A quasi-equilibrium process can be viewed
as a sufficiently slow process that allows the system to adjust itself internally
so that properties in one part of the system do not change any faster than
those at other parts.
This is illustrated in Fig. 1–30. When a gas in a piston-cylinder device
is compressed suddenly the molecules near the face of the piston will not
have enough time to escape and they will have to pile up in a small region
in front of the piston thus creating a high-pressure region there. Because of
this pressure difference the system can no longer be said to be in equilib-
rium and this makes the entire process nonquasi-equilibrium. However if
the piston is moved slowly the molecules will have sufficient time to redis-
tribute and there will not be a molecule pileup in front of the piston. As a
result the pressure inside the cylinder will always be nearly uniform and
will rise at the same rate at all locations. Since equilibrium is maintained at
all times this is a quasi-equilibrium process.
It should be pointed out that a quasi-equilibrium process is an ideal-
ized process and is not a true representation of an actual process. But
many actual processes closely approximate it and they can be modeled as
quasi-equilibrium with negligible error. Engineers are interested in quasi-
equilibrium processes for two reasons. First they are easy to analyze sec-
ond work-producing devices deliver the most work when they operate on
quasi-equilibrium processes. Therefore quasi-equilibrium processes serve
as standards to which actual processes can be compared.
Process diagrams plotted by employing thermodynamic properties as
coordinates are very useful in visualizing the processes. Some common
properties that are used as coordinates are temperature T pressure P and
volume V or specific volume v. Figure 1–31 shows the P-V diagram of a
compression process of a gas.
Note that the process path indicates a series of equilibrium states through
which the system passes during a process and has significance for quasi-
equilibrium processes only. For nonquasi-equilibrium processes we are not
able to characterize the entire system by a single state and thus we cannot
speak of a process path for a system as a whole. A nonquasi-equilibrium
process is denoted by a dashed line between the initial and final states
instead of a solid line.
The prefix iso- is often used to designate a process for which a particular
property remains constant. An isothermal process for example is a process
during which the temperature T remains constant an isobaric process is a
process during which the pressure P remains constant and an isochoric or
isometric process is a process during which the specific volume v remains
constant.
A system is said to have undergone a cycle if it returns to its initial state
at the end of the process. That is for a cycle the initial and final states are
identical.
The Steady-Flow Process
The terms steady and uniform are used frequently in engineering and thus
it is important to have a clear understanding of their meanings. The term
FIGURE 1–30
Quasi-equilibrium and nonquasi-
equilibrium compression processes.
a Slow compression
quasi-equilibrium
b Very fast compression
nonquasi-equilibrium
FIGURE 1–31
The P-V diagram of a compression
process.
Initial
state
Final state
Process path
2
1
P
V
2
V
1 V
2
System
1
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17
CHAPTER 1
steady implies no change with time. The opposite of steady is unsteady or
transient. The term uniform however implies no change with location over
a specified region. These meanings are consistent with their everyday use
steady girlfriend uniform properties etc..
A large number of engineering devices operate for long periods of time
under the same conditions and they are classified as steady-flow devices.
Processes involving such devices can be represented reasonably well by a
somewhat idealized process called the steady-flow process which can be
defined as a process during which a fluid flows through a control volume
steadily Fig. 1–32. That is the fluid properties can change from point to
point within the control volume but at any fixed point they remain the same
during the entire process. Therefore the volume V the mass m and the total
energy content E of the control volume remain constant during a steady-
flow process Fig. 1–33.
Steady-flow conditions can be closely approximated by devices that are
intended for continuous operation such as turbines pumps boilers con-
densers and heat exchangers or power plants or refrigeration systems. Some
cyclic devices such as reciprocating engines or compressors do not sat-
isfy any of the conditions stated above since the flow at the inlets and the
exits will be pulsating and not steady. However the fluid properties vary
with time in a periodic manner and the flow through these devices can still
be analyzed as a steady-flow process by using time-averaged values for the
properties.
1–8
■
TEMPERATURE AND THE ZEROTH LAW OF
THERMODYNAMICS
Although we are familiar with temperature as a measure of “hotness” or
“coldness” it is not easy to give an exact definition for it. Based on our
physiological sensations we express the level of temperature qualitatively
with words like freezing cold cold warm hot and red-hot. However we
cannot assign numerical values to temperatures based on our sensations
alone. Furthermore our senses may be misleading. A metal chair for exam-
ple will feel much colder than a wooden one even when both are at the
same temperature.
Fortunately several properties of materials change with temperature in
a repeatable and predictable way and this forms the basis for accurate
temperature measurement. The commonly used mercury-in-glass thermo-
meter for example is based on the expansion of mercury with temperature.
Temperature is also measured by using several other temperature-dependent
properties.
It is a common experience that a cup of hot coffee left on the table even-
tually cools off and a cold drink eventually warms up. That is when a body
is brought into contact with another body that is at a different tempera-
ture heat is transferred from the body at higher temperature to the one at
lower temperature until both bodies attain the same temperature Fig. 1–34.
At that point the heat transfer stops and the two bodies are said to have
reached thermal equilibrium. The equality of temperature is the only
requirement for thermal equilibrium.
FIGURE 1–32
During a steady-flow process fluid
properties within the control volume
may change with position but not with
time.
300°C 250°C
200°C 150°C
Control volume
225°C
Mass
in
Time: 1 PM
Mass
out
300°C 250°C
200°C 150°C
Control volume
225°C
Mass
in
Time: 3 PM
Mass
out
FIGURE 1–33
Under steady-flow conditions the
mass and energy contents of a control
volume remain constant.
Control
volume
m
CV
const.
E
CV
const.
Mass
in
Mass
out
FIGURE 1–34
Two bodies reaching thermal
equilibrium after being brought into
contact in an isolated enclosure.
150°C
Iron
20°C
Copper
60°C
Iron
60°C
Copper
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18
INTRODUCTION AND BASIC CONCEPTS
The zeroth law of thermodynamics states that if two bodies are in ther-
mal equilibrium with a third body they are also in thermal equilibrium with
each other. It may seem silly that such an obvious fact is called one of the
basic laws of thermodynamics. However it cannot be concluded from the
other laws of thermodynamics and it serves as a basis for the validity of
temperature measurement. By replacing the third body with a thermometer
the zeroth law can be restated as two bodies are in thermal equilibrium if
both have the same temperature reading even if they are not in contact.
The zeroth law was first formulated and labeled by R. H. Fowler in 1931.
As the name suggests its value as a fundamental physical principle was
recognized more than half a century after the formulation of the first and
the second laws of thermodynamics. It was named the zeroth law since it
should have preceded the first and the second laws of thermodynamics.
Temperature Scales
Temperature scales enable us to use a common basis for temperature mea-
surements and several have been introduced throughout history. All tem-
perature scales are based on some easily reproducible states such as the
freezing and boiling points of water which are also called the ice point and
the steam point respectively. A mixture of ice and water that is in equilib-
rium with air saturated with vapor at 1 atm pressure is said to be at the ice
point and a mixture of liquid water and water vapor with no air in equilib-
rium at 1 atm pressure is said to be at the steam point.
The temperature scales used in the SI and in the English system today
are the Celsius scale formerly called the centigrade scale in 1948 it was
renamed after the Swedish astronomer A. Celsius 1702–1744 who devised
it and the Fahrenheit scale named after the German instrument maker
G. Fahrenheit 1686–1736 respectively. On the Celsius scale the ice and
steam points were originally assigned the values of 0 and 100°C respec-
tively. The corresponding values on the Fahrenheit scale are 32 and 212°F.
These are often referred to as two-point scales since temperature values are
assigned at two different points.
In thermodynamics it is very desirable to have a temperature scale that
is independent of the properties of any substance or substances. Such a
temperature scale is called a thermodynamic temperature scale which
is developed later in conjunction with the second law of thermodynamics.
The thermodynamic temperature scale in the SI is the Kelvin scale named
after Lord Kelvin 1824–1907. The temperature unit on this scale is the
kelvin which is designated by K not °K the degree symbol was officially
dropped from kelvin in 1967. The lowest temperature on the Kelvin scale
is absolute zero or 0 K. Then it follows that only one nonzero reference
point needs to be assigned to establish the slope of this linear scale. Using
nonconventional refrigeration techniques scientists have approached abso-
lute zero kelvin they achieved 0.000000002 K in 1989.
The thermodynamic temperature scale in the English system is the
Rankine scale named after William Rankine 1820–1872. The tempera-
ture unit on this scale is the rankine which is designated by R.
A temperature scale that turns out to be nearly identical to the Kelvin
scale is the ideal-gas temperature scale. The temperatures on this scale are
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19
CHAPTER 1
measured using a constant-volume gas thermometer which is basically a
rigid vessel filled with a gas usually hydrogen or helium at low pressure.
This thermometer is based on the principle that at low pressures the tem-
perature of a gas is proportional to its pressure at constant volume. That is
the temperature of a gas of fixed volume varies linearly with pressure at suf-
ficiently low pressures. Then the relationship between the temperature and
the pressure of the gas in the vessel can be expressed as
T 5 a 1 bP 1–8
where the values of the constants a and b for a gas thermometer are deter-
mined experimentally. Once a and b are known the temperature of a
medium can be calculated from this relation by immersing the rigid vessel
of the gas thermometer into the medium and measuring the gas pressure
when thermal equilibrium is established between the medium and the gas in
the vessel whose volume is held constant.
An ideal-gas temperature scale can be developed by measuring the pres-
sures of the gas in the vessel at two reproducible points such as the ice
and the steam points and assigning suitable values to temperatures at
those two points. Considering that only one straight line passes through
two fixed points on a plane these two measurements are sufficient to
determine the constants a and b in Eq. 1–8. Then the unknown tempera-
ture T of a medium corresponding to a pressure reading P can be deter-
mined from that equation by a simple calculation. The values of the con-
stants will be different for each thermometer depending on the type and
the amount of the gas in the vessel and the temperature values assigned
at the two reference points. If the ice and steam points are assigned the
values 0°C and 100°C respectively then the gas temperature scale will
be identical to the Celsius scale. In this case the value of the constant a
which corresponds to an absolute pressure of zero is determined to be
2273.15°C regardless of the type and the amount of the gas in the vessel
of the gas thermometer. That is on a P-T diagram all the straight lines
passing through the data points in this case will intersect the temperature
axis at 2273.15°C when extrapolated as shown in Fig. 1–35. This is the
lowest temperature that can be obtained by a gas thermometer and thus
we can obtain an absolute gas temperature scale by assigning a value of
zero to the constant a in Eq. 1–8. In that case Eq. 1–8 reduces to T 5 bP
and thus we need to specify the temperature at only one point to define an
absolute gas temperature scale.
It should be noted that the absolute gas temperature scale is not a thermo-
dynamic temperature scale since it cannot be used at very low temperatures
due to condensation and at very high temperatures due to dissociation and
ionization. However absolute gas temperature is identical to the thermody-
namic temperature in the temperature range in which the gas thermometer
can be used. Thus we can view the thermodynamic temperature scale at
this point as an absolute gas temperature scale that utilizes an “ideal” or
“imaginary” gas that always acts as a low-pressure gas regardless of the
temperature. If such a gas thermometer existed it would read zero kelvin
at absolute zero pressure which corresponds to 2273.15°C on the Celsius
scale Fig. 1–36.
FIGURE 1–35
P versus T plots of the experimental
data obtained from a constant-volume
gas thermometer using four different
gases at different but low pressures.
Measured
data points
P
Gas A
Gas B
Gas C
Gas D
0 –273.15
Extrapolation
T °C
FIGURE 1–36
A constant-volume gas thermometer
would read 2273.15°C at absolute
zero pressure.
Absolute
vacuum
V constant
T °C T K
0 0 – 273.15
P kPa
–275
–250
–225
–200
0
25
50
75
0
40
80
120
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20
INTRODUCTION AND BASIC CONCEPTS
The Kelvin scale is related to the Celsius scale by
TK 5 T8C 1 273.15 1–9
The Rankine scale is related to the Fahrenheit scale by
TR 5 T8F 1 459.67 1–10
It is common practice to round the constant in Eq. 1–9 to 273 and that in
Eq. 1–10 to 460.
The temperature scales in the two unit systems are related by
TR 5 1.8TK 1–11
T8F 5 1.8T8C 1 32 1–12
A comparison of various temperature scales is given in Fig. 1–37.
The reference temperature chosen in the original Kelvin scale was
273.15 K or 0°C which is the temperature at which water freezes or ice
melts and water exists as a solid–liquid mixture in equilibrium under stan-
dard atmospheric pressure the ice point. At the Tenth General Conference
on Weights and Measures in 1954 the reference point was changed to a
much more precisely reproducible point the triple point of water the state
at which all three phases of water coexist in equilibrium which is assigned
the value 273.16 K. The Celsius scale was also redefined at this conference
in terms of the ideal-gas temperature scale and a single fixed point which is
again the triple point of water with an assigned value of 0.01°C. The boil-
ing temperature of water the steam point was experimentally determined
to be again 100.00°C and thus the new and old Celsius scales were in good
agreement.
The International Temperature
Scale of 1990 ITS-90
The International Temperature Scale of 1990 which supersedes the
International Practical Temperature Scale of 1968 IPTS-68 1948
ITPS-48 and 1927 ITS-27 was adopted by the International Commit-
tee of Weights and Measures at its meeting in 1989 at the request of the
Eighteenth General Conference on Weights and Measures. The ITS-90
is similar to its predecessors except that it is more refined with updated
values of fixed temperatures has an extended range and conforms more
closely to the thermodynamic temperature scale. On this scale the unit
of thermodynamic temperature T is again the kelvin K defined as the
fraction 1/273.16 of the thermodynamic temperature of the triple point of
water which is sole defining fixed point of both the ITS-90 and the Kelvin
scale and is the most important thermometric fixed point used in the cali-
bration of thermometers to ITS-90.
The unit of Celsius temperature is the degree Celsius °C which is by
definition equal in magnitude to the kelvin K. A temperature difference
FIGURE 1–37
Comparison of temperature scales.
–273.15
°C
0
273.16 0.01
K
–459.67
°F
0
491.69 32.02
R
Triple
point of
water
Absolute
zero
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21
CHAPTER 1
may be expressed in kelvins or degrees Celsius. The ice point remains the
same at 0°C 273.15 K in both ITS-90 and ITPS-68 but the steam point
is 99.975°C in ITS-90 with an uncertainty of 60.005°C whereas it was
100.000°C in IPTS-68. The change is due to precise measurements made
by gas thermometry by paying particular attention to the effect of sorption
the impurities in a gas absorbed by the walls of the bulb at the reference
temperature being desorbed at higher temperatures causing the measured
gas pressure to increase.
The ITS-90 extends upward from 0.65 K to the highest temperature prac-
tically measurable in terms of the Planck radiation law using monochro-
matic radiation. It is based on specifying definite temperature values on a
number of fixed and easily reproducible points to serve as benchmarks and
expressing the variation of temperature in a number of ranges and subranges
in functional form.
In ITS-90 the temperature scale is considered in four ranges. In the
range of 0.65 to 5 K the temperature scale is defined in terms of the
vapor pressure—temperature relations for
3
He and
4
He. Between 3 and
24.5561 K the triple point of neon it is defined by means of a prop-
erly calibrated helium gas thermometer. From 13.8033 K the triple point
of hydrogen to 1234.93 K the freezing point of silver it is defined by
means of platinum resistance thermometers calibrated at specified sets
of defining fixed points. Above 1234.93 K it is defined in terms of the
Planck radiation law and a suitable defining fixed point such as the freez-
ing point of gold 1337.33 K.
We emphasize that the magnitudes of each division of 1 K and 1°C are
identical Fig. 1–38. Therefore when we are dealing with temperature dif-
ferences DT the temperature interval on both scales is the same. Raising
the temperature of a substance by 10°C is the same as raising it by 10 K.
That is
DTK 5 DT8C 1–13
DTR 5 DT8F 1–14
Some thermodynamic relations involve the temperature T and often the
question arises of whether it is in K or °C. If the relation involves tempera-
ture differences such as a 5 bDT it makes no difference and either can
be used. However if the relation involves temperatures only instead of tem-
perature differences such as a 5 bT then K must be used. When in doubt
it is always safe to use K because there are virtually no situations in which
the use of K is incorrect but there are many thermodynamic relations that
will yield an erroneous result if °C is used.
EXAMPLE 1– 4 Expressing Temperature Rise in Different Units
During a heating process the temperature of a system rises by 10°C. Express
this rise in temperature in K °F and R.
SOLUTION The temperature rise of a system is to be expressed in different
units.
FIGURE 1–38
Comparison of magnitudes of various
temperature units.
1°C 1 K 1.8°F 1.8 R
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22
INTRODUCTION AND BASIC CONCEPTS
Analysis This problem deals with temperature changes which are identical
in Kelvin and Celsius scales. Then
DTK 5 DT8C 5 10 K
The temperature changes in Fahrenheit and Rankine scales are also iden-
tical and are related to the changes in Celsius and Kelvin scales through
Eqs. 1–11 and 1–14:
DTR 5 1.8 DTK 5 1.810 5 18 R
and
DT8F 5 DTR 5 188F
Discussion Note that the units °C and K are interchangeable when dealing
with temperature differences.
1–9
■
PRESSURE
Pressure is defined as a normal force exerted by a fluid per unit area.
Normally we speak of pressure when we deal with a gas or a liquid. The
counterpart of pressure in solids is normal stress. Note however that pres-
sure is a scaler quantity while stress is a tensor. Since pressure is defined
as force per unit area it has the unit of newtons per square meter N/m
2
which is called a pascal Pa. That is
1 Pa 5 1 N/m
2
The pressure unit pascal is too small for most pressures encountered in
practice. Therefore its multiples kilopascal 1 kPa 5 10
3
Pa and megapas-
cal 1 MPa 5 10
6
Pa are commonly used. Three other pressure units com-
monly used in practice especially in Europe are bar standard atmosphere
and kilogram-force per square centimeter:
1 bar 5 10
5
Pa 5 0.1 MPa 5 100 kPa
1 atm 5 101325 Pa 5 101.325 kPa 5 1.01325 bars
1 kgf / c m
2
5 9.807 N/cm
2
5 9.807 3 10
4
N/m
2
5 9.807 3 10
4
Pa
5 0.9807 bar
5 0.9679 atm
Note the pressure units bar atm and kgf/cm
2
are almost equivalent to each
other. In the English system the pressure unit is pound-force per square
inch lbf/in
2
or psi and 1 atm 5 14.696 psi. The pressure units kgf/cm
2
and lbf/in
2
are also denoted by kg/cm
2
and lb/in
2
respectively and they are
commonly used in tire gages. It can be shown that 1 kgf/cm
2
5 14.223 psi.
Pressure is also used on solid surfaces as synonymous to normal stress
which is the force acting perpendicular to the surface per unit area. For
example a 150-pound person with a total foot imprint area of 50 in
2
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23
CHAPTER 1
exerts a pressure of 150 lbf/50 in
2
5 3.0 psi on the floor Fig. 1–39. If the
person stands on one foot the pressure doubles. If the person gains exces-
sive weight he or she is likely to encounter foot discomfort because of the
increased pressure on the foot the size of the bottom of the foot does not
change with weight gain. This also explains how a person can walk on
fresh snow without sinking by wearing large snowshoes and how a person
cuts with little effort when using a sharp knife.
The actual pressure at a given position is called the absolute pressure
and it is measured relative to absolute vacuum i.e. absolute zero pressure.
Most pressure-measuring devices however are calibrated to read zero in
the atmosphere Fig. 1–40 and so they indicate the difference between
the absolute pressure and the local atmospheric pressure. This difference is
called the gage pressure. P
gage
can be positive or negative but pressures
below atmospheric pressure are sometimes called vacuum pressures and
are measured by vacuum gages that indicate the difference between the
atmospheric pressure and the absolute pressure. Absolute gage and vacuum
pressures are related to each other by
P
gage
5 P
abs
2 P
atm
1–15
P
vac
5 P
atm
2 P
abs
1–16
This is illustrated in Fig. 1–41.
Like other pressure gages the gage used to measure the air pres-
sure in an automobile tire reads the gage pressure. Therefore the com-
mon reading of 32.0 psi 2.25 kgf/cm
2
indicates a pressure of 32.0 psi
above the atmospheric pressure. At a location where the atmospheric
pressure is 14.3 psi for example the absolute pressure in the tire is
32.0 1 14.3 5 46.3 psi.
In thermodynamic relations and tables absolute pressure is almost always
used. Throughout this text the pressure P will denote absolute pressure
unless specified otherwise. Often the letters “a” for absolute pressure and
“g” for gage pressure are added to pressure units such as psia and psig to
clarify what is meant.
FIGURE 1–39
The normal stress or “pressure” on
the feet of a chubby person is much
greater than on the feet of a slim
person.
150 pounds
A
feet
50 in
2
P
3 psi P
6 psi
300 pounds
W
––––
A
feet
150 lbf
––––––
50 in
2
P
n
3 psi s
FIGURE 1–40
Some basic pressure gages.
Dresser Instruments Dresser Inc. Used by
permission
FIGURE 1–41
Absolute gage and vacuum pressures.
Absolute
vacuum
Absolute
vacuum
P
abs
P
vac
P
atm
P
atm
P
atm
P
gage
P
abs
P
abs
0
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