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Springer handbook of mechanical engineering
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Springer handbook of mechanical engineering

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Springer Handbook

of Mechanical Engineering

Springer Handbooks provide

a concise compilation of approved

key information on methods of

research, general principles, and

functional relationships in physi￾cal sciences and engineering. The

world’s leading experts in the

fields of physics and engineer￾ing will be assigned by one or

several renowned editors to write

the chapters comprising each vol￾ume. The content is selected by

these experts from Springer sources

(books, journals, online content)

and other systematic and approved

recent publications of physical and

technical information.

The volumes are designed to be

useful as readable desk reference

books to give a fast and comprehen￾sive overview and easy retrieval of

essential reliable key information,

including tables, graphs, and bibli￾ographies. References to extensive

sources are provided.

123

Handbook Springer

of Mechanical Engineering

Grote, Antonsson (Eds.)

With DVD-ROM, 1822 Figures and 402 Tables

Editors:

Professor Dr.-Ing. Karl-Heinrich Grote

Department of Mechanical Engineering

Otto-von-Guericke University Magdeburg

Universitätsplatz 2

39106 Magdeburg, Germany

[email protected]

Professor Erik K. Antonsson

Department of Mechanical Engineering

California Institute of Technology (CALTEC)

1200 East California Boulevard

Pasadena, CA 91125, USA

[email protected]

Library of Congress Control Number: 2008934575

ISBN: 978-3-540-49131-6 e-ISBN: 978-3-540-30738-9

All rights reserved. This work may not be translated or copied in whole

or in part without the written permission of the publisher (Springer Sci￾ence+Business Media, LLC New York, 233 Spring Street, New York, NY

10013, USA), except for brief excerpts in connection with reviews or schol￾arly analysis. Use in connection with any form of information storage and

retrieval, electronic adaptation, computer software, or by similar or dissim￾ilar methodology now known or hereafter developed is forbidden. The use

in this publication of trade names, trademarks, service marks, and similar

terms, even if they are not identified as such, is not to be taken as an ex￾pression of opinion as to whether or not they are subject to proprietary rights.

The use of designations, trademarks, etc. in this publication does not imply,

even in the absence of a specific statement, that such names are exempt from

the relevant protective laws and regulations and therefore free for general

use.

Product liability: The publisher cannot guarantee the accuracy of any

information about dosage and application contained in this book. In every

individual case the user must check such information by consulting the

relevant literature.

Production and typesetting: le-tex publishing services oHG, Leipzig

Senior Manager Springer Handbook: Dr. W. Skolaut, Heidelberg

Illustrations: schreiberVIS, Seeheim and Hippmann GbR, Schwarzenbruck

Cover design: eStudio Calamar Steinen, Barcelona

Cover production: WMXDesign GmbH, Heidelberg

Printing and binding: Stürtz GmbH, Würzburg

Printed on acid free paper

SPIN 10934364 60/3180/YL 5 4 3 2 1 0

V

Preface

Mechanical engineering is a broad and complex field

within the world of engineering and has close relations

to many other fields. It is an important economic fac￾tor for all industrialized countries and the global market

allows for wide international competition for products

and processes in this field. To stay up to date with

scientific findings and to apply existing knowledge in

mechanical engineering it is important to renew and

continuously update existing information.

The editors of this Springer Handbook on Mechan￾ical Engineering have worked successfully with 92

authors worldwide to include chapters about all relevant

mechanical engineering topics. However, this Hand￾book cannot claim to cover every aspect or detail of

the mechanical engineering areas or fields included,

and where mechanical engineers are currently present

and contributing their expertise and knowledge towards

the challenges of a better world. However, this Hand￾book will be a valuable guide for all who design,

develop, manufacture, operate, and use mechanical arte￾facts.

We also hope to spark interest in the field of me￾chanical engineering from others. In this Handbook,

high-school students can get a first glance at the options

in this field and possible career moves.

We, the editors, would like to express our gratitude

and thanks to all of the authors of this Handbook, who

have devoted a considerable amount of time towards

this project. We would like to thank them for their pa￾tience and cooperation, and we hope for a long-lasting

partnership in this ambitious project. We would also

most sincerely like to thank our managers and friends at

Springer and le-tex. The executives at Springer–Verlag

were always most cooperative and supportive of this

Handbook. Without Dr. Skolaut’s continuous help and

encouragement and Ms. Moebes’ and Mr. Wieczorek’s

almost daily requests for corrections, improvements,

and progress reports it would have taken another few

years – if ever – to publish this Handbook. Stürtz has

done a fantastic job in printing and binding. Finally we

would like to thank all the people we work with in our

departments and universities, who tolerated the time and

effort spent on this book.

Finally, we know that there is always room for

improvement – with this Handbook as with most en￾gineering products and approaches. We, as well as the

authors welcome your fair hints, comments, and crit￾icism. Through this Handbook and with the authors’

efforts, we would also like to draw your attention to

what has been accomplished for the benefit of the en￾gineering world and society.

Berlin, Fall 2008 Karl-Heinrich Grote

Pasadena, Fall 2008 Erik K. Antonsson

VII

About the Editors

Dr. Karl-Heinrich Grote is a Professor and Chair of the Department of Mechanical

Engineering – Engineering Design at the Otto-von-Guericke University in Magdeburg,

Germany. He earned his “Diploma in Mechanical Engineering” (Masters of Science in

Mechanical Engineering) in 1979 and his “Dr.-Ing.” (Ph.D. in Engineering) in 1984,

both from the Technical University in Berlin, Germany. After a post doctoral stay

in the USA he joined an automotive supplier as manager of the engineering design

department. In 1990 he followed a call to become full professor at the Mechanical En￾gineering Department at the California State University, Long Beach, USA. In 1992 he

received the TRW Outstanding Faculty award and in 1993 the VDI "Ring of Honor"

for his research on Engineering Design and Methodology. In 1995 he was named

chair of the Engineering Design Department at the Otto-von-Guericke University in

Magdeburg, where he is now Dean of the College of Mechanical Engineering. From

October 2002 to September 2004 he was Visiting Professor of Mechanical Engineer￾ing at the California Institute of Technology (Caltech) USA. Since 1995 he is Editor of

the DUBBEL (Taschenbuch für den Maschinenbau) and author of several books.

Dr. Erik Antonsson is a Professor of Mechanical Engineering at the California Insti￾tute of Technology in Pasadena, where he organized the Engineering Design Research

Laboratory and has conducted research and taught since 1984. He earned a Bachelor

of Science in Mechanical Engineering from Cornell University in 1976, and a PhD in

Mechanical Engineering from the Massachusetts Institute of Technology, Cambridge in

1982. In 1984 he joined the Mechanical Engineering Faculty at the California Institute

of Technology, where he served as the Executive Officer (Chair) from 1998 to 2002.

From September, 2002 through January, 2006, Dr. Antonsson was on leave from Cal￾tech and served as the Chief Technologist at NASA’s Jet Propulsion Laboratory (JPL).

He was an NSF Presidential Young Investigator (1986-1992), won the 1995 Richard

P. Feynman Prize for Excellence in Teaching, and was a co-winner of the 2001 TRW

Distinguished Patent Award. Dr. Antonsson is a Fellow of the ASME, and a member

of the IEEE, AIAA, SME, ACM, and ASEE. He has published over 110 scholarly pa￾pers in the field of engineering design research, has edited two books, and holds eight

U.S. patents.

IX

List of Authors

Gritt Ahrens

Daimler AG X944

Systems Integration and Comfort Electric

71059 Sindelfingen, Germany

e-mail: [email protected]

Seddik Bacha

Université Joseph Fourier

Grénoble Electrical Engineering Laboratory

Saint Martin d’Hères

38402 Grenoble, France

e-mail: [email protected]

Stanley Baksi

TRW Automotive, Lucas Varity GmbH

Carl Spaeter Str. 8

56070 Koblenz, Germany

e-mail: [email protected]

Thomas Böllinghaus

Federal Institute for Materials Research

and Testing (BAM)

Unter den Eichen 87

12205 Berlin, Germany

e-mail: [email protected]

Alois Breiing

Eidgenössische Technische Hochschule Zürich (ETH)

Institut für mechanische Systeme (IMES)

Zentrum für Produkt-Entwicklung (ZPE)

ETH Zentrum, CLA E 17.1, Tannenstrasse 3

8092 Zurich, Switzerland

e-mail: [email protected]

Eugeniusz Budny

Institute of Mechanized Construction and Rock

Mining

Racjonalizacji 6/8

02-673 Warsaw, Poland

e-mail: [email protected]

Gerry Byrne

University College Dublin

School of Electrical, Electronic

and Mechanical Engineering

Belfield, Dublin 4, Ireland

e-mail: [email protected]

Boris Ilich Cherpakov (deceased)

Edward Chlebus

Wrocław University of Technology

Centre for Advanced Manufacturing Technologies

Lukasiewicza 5

50-371 Wrocław, Poland

e-mail: [email protected]

Mirosław Chłosta

IMBiGS – Institute for Mechanized Construction

and Rock Mining (IMBiGS)

ul. Racjonalizacji 6/8

02-673 Warsaw, Poland

e-mail: [email protected]

Norge I. Coello Machado

Universidad Central “Marta Abreu” de Las Villas

Faculty of Mechanical Engineering

Santa Clara, 54830, Cuba

e-mail: [email protected]

Francesco Costanzo

Alenia Aeronautica

Procurement/Sourcing Management Department

Viale dell’Aeronautica

Pomigliano (NA), Italy

e-mail: [email protected]

Carl E. Cross

Federal Institute for Materials Research

and Testing (BAM)

Joining Technology

Unter den Eichen 87

12200 Berlin, Germany

e-mail: [email protected]

X List of Authors

Frank Dammel

Technical University

Department of Mechanical Engineering/Institute

of Technical Thermodynamics

Petersenstr. 30

64287 Darmstadt, Germany

e-mail: [email protected]

Jaime De La Ree

Virginia Tech

Electrical and Computer Engineering Department

340 Whittemore Hall

Blacksburg, VA 24061, USA

e-mail: [email protected]

Torsten Dellmann

RWTH Aachen University

Department of Rail Vehicles and

Materials-Handling Technology

Seffenter Weg 8

52074 Aachen, Germany

e-mail: [email protected]

Berend Denkena

Leibniz University Hannover

IFW – Institute of Production Engineering

and Machine Tools

An der Universität 2

30823 Garbsen, Germany

e-mail: [email protected]

Ludger Deters

Otto-von-Guericke University

Institute of Machine Design

Universitätsplatz 2

39016 Magdeburg, Germany

e-mail: [email protected]

Ulrich Dilthey

RWTH Aachen University

ISF Welding and Joining Institute

Pontstr. 49

52062 Aachen, Germany

e-mail: [email protected]

Frank Engelmann

University of Applied Sciences Jena

Department of Industrial Engineering

Carl-Zeiss-Promenade 2

07745 Jena, Germany

e-mail: [email protected]

Ramin S. Esfandiari

California State University

Department of Mechanical & Aerospace

Engineering

Long Beach, CA 90840, USA

e-mail: [email protected]

Jens Freudenberger

Leibniz-Institute for Solid State and Materials

Research Dresden

Department for Metal Physics

P.O. Box 270116

01171 Dresden, Germany

e-mail: [email protected]

Stefan Gies

RWTH Aachen University

Institute for Automotive Engineering

Steinbachstr. 7

52074 Aachen, Germany

e-mail: [email protected]

Joachim Göllner

Otto-von-Guericke University

Institute of Materials and Joining Technology

Department of Mechanical Engineering

Universitätsplatz 2

39016 Magdeburg, Germany

e-mail:

[email protected]

Timothy Gutowski

Massachusetts Institute of Technology

Department of Mechanical Engineering

Cambridge, MA 02139, USA

e-mail: [email protected]

List of Authors XI

Takeshi Hatsuzawa

Tokyo Institute of Technology

Precision and Intelligence Laboratory

4259-R2-6, Nagatsuta-cho

226-8503 Yokohama, Japan

e-mail: [email protected]

Markus Hecht

Berlin University of Technology

Institute of Land and Sea Transport Systems

Department of Rail Vehicles

Salzufer 17–19

10587 Berlin, Germany

e-mail: [email protected]

Hamid Hefazi

California State University

Mechanical and Aerospace Engineering

Department of Mechanical and Aerospace

Engineering

1250 Bellflower Boulevard

Long Beach, CA 90840, USA

e-mail: [email protected]

Martin Heilmaier

Technical University

Department of Physical Metallurgy

Petersenstr. 23

64287 Darmstadt, Germany

e-mail: [email protected]

Rolf Henke

RWTH Aachen University

Institute of Aeronautics and Astronautics

Wuellnerstr. 7

52062 Aachen, Germany

e-mail: [email protected]

Klaus Herfurth

Industrial Advisor

Am Wiesengrund 34

40764 Langenfeld, Germany

e-mail: [email protected]

Horst Herold (deceased)

Chris Oliver Heyde

Otto-von-Guericke University

Electric Power Networks and Renewable Energy

Sources

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Andrew Kaldos

AKM Engineering Consultants

31 Tudorville Road

Bebington, Wirral CH632 HT, UK

e-mail: [email protected]

Yuichi Kanda

Toyo University

Department of Mechanical Engineering

Advanced Manufacturing Engineering Laboratory

2100 Kujirai

350-8585 Kawagoe-City, Japan

e-mail: [email protected]

Thomas Kannengiesser

Federal Institute for Materials Research

and Testing (BAM)

Joining Technology

Unter den Eichen 87

12200 Berlin, Germany

e-mail: [email protected]

Michail Karpenko

New Zealand Welding Centre

Heavy Engineering Research Association (HERA)

17–19 Gladding Place

Manukau City, New Zealand

e-mail: [email protected]

Bernhard Karpuschewski

Otto-von-Guericke University

Department of Manufacturing Engineering

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

XII List of Authors

Toshiaki Kimura

Japan Society for the Promotion of Machine

Industry (JSPMI)

Production Engineering Department

Technical Research Institute

1-1-12, Hachiman-cho

203-0042 Tokyo, Japan

e-mail: [email protected]

Dwarkadas Kothari

VIT University

School of Electrical Sciences

Vellore, TN 632 014, India

e-mail: [email protected]

Hermann Kühnle

Otto-von-Guericke University

Institute of Ergonomics

Factory Operations and Automation

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Oleg P. Lelikov

Bauman Moscow State Technical University

2-nd Baumanskaya, 5

Moscow, 105005, Russia

Andreas Lindemann

Otto-von-Guericke University

Institute for Power Electronics

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Bruno Lisanti

AST

Via Dante Alighieri 57

Lonate Pozzolo (VA), Italy

e-mail: [email protected]

Manuel Marya

Schlumberger Reservoir Completions

Material Engineering

14910 Airline Road

Rosharon, TX 77583, USA

e-mail: [email protected]

Surendar K. Marya

GeM-UMR CNRS 6183, Ecole Centrale Nantes

Institut de Recherche en Génie Civil et Mécanique

1 Rue de la Noë

44321 Nantes, France

e-mail: [email protected]

Ajay Mathur

Simon India Limited

Plant Engineering

Devika Tower, 6 Nehru Place

New Delhi, India

e-mail: [email protected]

Klaus-Jürgen Matthes

Chemnitz University of Technology

Institute for Manufacturing/Welding Technology

Reichenhainer Str. 70

09126 Chemnitz, Germany

e-mail: [email protected]

Henning Jürgen Meyer

Technische Universität Berlin

Berlin Institute of Technology

Konstruktion von Maschinensystemen

Straße des 17. Juni 144

10623 Berlin, Germany

e-mail: [email protected]

Klaus Middeldorf

DVS – German Welding Society

Düsseldorf, Germany

e-mail: [email protected]

Gerhard Mook

Otto-von-Guericke University

Department of Mechanical Engineering

Institute of Materials and Joining Technology

and Materials Testing

Universitätsplatz 2

39016 Magdeburg, Germany

e-mail: [email protected]

Jay M. Ochterbeck

Clemson University

Department of Mechanical Engineering

Clemson, SC 29634-0921, USA

e-mail: [email protected]

List of Authors XIII

Joao Fernando G. Oliveira

University of São Paulo

Department of Production Engineering

Av. Trabalhador Sãocarlense, 400

São Carlos, SP 13566-590, Brazil

e-mail: [email protected], [email protected]

Antje G. Orths

Energinet.dk

Electricity System Development

Tonne Kjærsvej 65

7000 Fredericia, Denmark

e-mail: [email protected]

Vince Piacenti

Robert Bosch LLC

System Engineering, Diesel Fuel Systems

38000 Hills Tech Drive

Farmington Hills, MI 48331, USA

e-mail: [email protected]

Jörg Pieschel

Otto-von-Guericke University

Institute of Materials and Joining Technology

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Stefan Pischinger

RWTH Aachen University

Institute for Combustion Engines

Schinkelstr. 8

52062 Aachen, Germany

e-mail: [email protected]

Didier M. Priem

École Centrale Nantes

Department of Materials

1 Rue de la Noë, GEM UMR CNRS 6183

44321 Nantes, France

e-mail: [email protected]

Frank Riedel

Fraunhofer-Institute for Machine Tools and

Forming Technology (IWU)

Department of Joining Technology

Reichenhainer Str. 88

09126 Chemnitz, Germany

e-mail: [email protected]

Holger Saage

University of Applied Sciences of Landshut

Faculty of Mechanical Engineering

Am Lurzenhof 1

84036 Landshut, Germany

e-mail: [email protected]

Shuichi Sakamoto

Niigata University

Department of Mechanical and Production

Engineering

Ikarashi 2-8050

950 2181 Niigata, Japan

e-mail: [email protected]

Roger Schaufele

California State University

1250 Bellflower Boulevard

Long Beach, CA 90840, USA

e-mail: [email protected]

Markus Schleser

RWTH Aachen University

Welding and Joining Institute

Pontstr. 49

52062 Aachen, Germany

e-mail: [email protected]

Meinhard T. Schobeiri

Texas A&M University

Department of Mechanical Engineering

College Station, TX 77843-3123, USA

e-mail: [email protected]

Miroslaw J. Skibniewski

University of Maryland

Department of Civil and Environmental

Engineering

1188 Glenn L. Martin Hall

College Park, MD 20742-3021, USA

e-mail: [email protected]

Jagjit Singh Srai

University of Cambridge

Centre for International Manufacturing

Institute for Manufacturing

Cambridge, CB2 1 RX, UK

e-mail: [email protected]

XIV List of Authors

Vivek Srivastava

Corporate Technology Strategy Services

Aditya Birla Management Corporation

MIDC Taloja, Panvel

Navi Mumbai, India

e-mail: [email protected]

Peter Stephan

Technical University Darmstadt

Institute of Technical Thermodynamics

Department of Mechanical Engineering

Petersenstr. 30

64287 Darmstadt, Germany

e-mail: [email protected]

Zbigniew A. Styczynski

Otto-von-Guericke University

Electric Power Networks and Renewable Energy

Sources

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected] or [email protected]

P.M.V. Subbarao

Indian Institute of Technology

Mechanical Engineering Department

HAUS KHAS

New Delhi, 110 016, India

e-mail: [email protected]

Oliver Tegel

Dr.-Ing. h.c. F. Porsche AG

R&D, IS-Management

Porschestr.

71287 Weissach, Germany

e-mail: [email protected]

A. Erman Tekkaya

ATILIM University

Department of Manufacturing Engineering

Incek

Ankara, 06836, Turkey

e-mail: [email protected]

Klaus-Dieter Thoben

University of Bremen

Bremen Institute for Production and Logistics

GmbH

Department of ICT Applications in Production

Hochschulring 20

28359 Bremen, Germany

e-mail: [email protected]

Marcel Todtermuschke

Fraunhofer-Institute for Machine Tools and

Forming Technology

Department of Assembling Techniques

Reichenhainer Str. 88

09126 Chemnitz, Germany

e-mail: [email protected]

Helmut Tschoeke

Otto-von-Guericke University

Institute of Mobile Systems

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Jon H. Van Gerpen

University of Idaho

Department of Biological and Agricultural

Engineering

Moscow, ID, USA

e-mail: [email protected]

Anatole Vereschaka

Moscow State University of Technology “STANKIN”

Department of Mechanical Engineering Technology

and Institute of Design and Technological

Informatics

Laboratory of Surface Nanosystems

Russian Academy of Science

Vadkovsky pereulok 1

Moscow, 101472, Russia

e-mail: [email protected]

Detlef von Hofe

Hohen Dyk 106

47803 Krefeld, Germany

e-mail: [email protected]

List of Authors XV

Nikolaus Wagner

RWTH Aachen University

ISF Welding and Joining Institute

Pontstr. 49

52062 Aachen, Germany

e-mail: [email protected]

Jacek G. Wankowicz

Institute of Power Engineering

ul. Mory 8

01-330 Warsaw, Poland

Ulrich Wendt

Otto-von-Guericke University

Department of Materials and Joining Technology

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Steffen Wengler

Otto-von-Guericke University

Faculty of Mechanical Engineering

Institute of Manufacturing Technology

and Quality Management

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Bernd Wilhelm

Volkswagen AG

Sitech Sitztechnik GmbH

Stellfelder Str. 46

38442 Wolfsburg, Germany

e-mail: [email protected]

Patrick M. Williams

Assystem UK

1 The Brooms, Emersons Green

Bristol, BS16 7FD, UK

e-mail: [email protected]

Lutz Wisweh

Otto-von-Guericke University

Faculty of Mechanical Engineering

Institute of Manufacturing Technology

and Quality Management

Universitätsplatz 2

39106 Magdeburg, Germany

e-mail: [email protected]

Johannes Wodara

Schweißtechnik-Consult

Hegelstr. 38

39104 Magdeburg, Germany

e-mail: [email protected]

Klaus Woeste

RWTH Aachen University

ISF Welding and Joining Institute

Pontstr. 49

52062 Aachen, Germany

e-mail: [email protected]

Hen-Geul Yeh

California State University

Department of Electrical Engineering

1250 Bellflower Boulevard

Long Beach, CA 90840-8303, USA

e-mail: [email protected]

Hsien-Yang Yeh

California State University Long Beach

Department of Mechanical and Aerospace

Engineering

1250 Bellflower Boulevard

Long Beach, CA 90840, USA

e-mail: [email protected]

Shouwen Yu

Tsinghua University

School of Aerospace

Beijing, 100084, P.R. China

e-mail: [email protected]

XVII

Contents

List of Abbreviations ................................................................................. XXIII

Part A Fundamentals of Mechanical Engineering

1 Introduction to Mathematics for Mechanical Engineering

Ramin S. Esfandiari ................................................................................. 3

1.1 Complex Analysis........................................................................... 4

1.2 Differential Equations.................................................................... 9

1.3 Laplace Transformation ................................................................. 15

1.4 Fourier Analysis ............................................................................. 24

1.5 Linear Algebra............................................................................... 26

References .............................................................................................. 33

2 Mechanics

Hen-Geul Yeh, Hsien-Yang Yeh, Shouwen Yu ............................................ 35

2.1 Statics of Rigid Bodies ................................................................... 36

2.2 Dynamics ...................................................................................... 52

References .............................................................................................. 71

Part B Applications in Mechanical Engineering

3 Materials Science and Engineering

Jens Freudenberger, Joachim Göllner, Martin Heilmaier, Gerhard Mook,

Holger Saage, Vivek Srivastava, Ulrich Wendt............................................ 75

3.1 Atomic Structure and Microstructure............................................... 77

3.2 Microstructure Characterization...................................................... 98

3.3 Mechanical Properties ................................................................... 108

3.4 Physical Properties ........................................................................ 122

3.5 Nondestructive Inspection (NDI) ..................................................... 126

3.6 Corrosion ...................................................................................... 141

3.7 Materials in Mechanical Engineering .............................................. 157

References .............................................................................................. 218

4 Thermodynamics

Frank Dammel, Jay M. Ochterbeck, Peter Stephan...................................... 223

4.1 Scope of Thermodynamics. Definitions ........................................... 223

4.2 Temperatures. Equilibria ............................................................... 225

4.3 First Law of Thermodynamics ......................................................... 228

4.4 Second Law of Thermodynamics ..................................................... 231

4.5 Exergy and Anergy......................................................................... 233

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