Technical Thermodynamics for Engineers

Achim Schmidt

Technical Thermodynamicsfor EngineersBasics and Applications

123

Prof. Dr.-Ing. Achim SchmidtFakultät Technik und InformatikHAW HamburgHamburg, Germany

ISBN 978-3-030-20396-2 ISBN 978-3-030-20397-9 (eBook)https://doi.org/10.1007/978-3-030-20397-9

© Springer Nature Switzerland AG 2019This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated to my parents.

Preface

Arnold Sommerfeld, the famous physicist, said:

Thermodynamic is a funny subject. The first time you gothrough it, you do not understand it at all. The second timeyou go through it, you think you understand it, except for oneor two small points. The third time you go through it, youknow you do not understand it, but by that time you are soused to it, it does not bother you anymore.

In fact, thermodynamics is probably one of the most difficult and challengingsubjects of mechanical engineering studies. Many students claim that it would be agreat subject—if only it weren’t for the written exam.

Now that I have given the lectures in Technical Thermodynamics I/II for severalsemesters at the University of Applied Sciences in Hamburg, I have decided towrite an accompanying textbook. I believe that my personal gaps of understandinghave become smaller. According to Arnold Sommerfeld, I’m one of those who’vedealt with thermodynamics for at least the third time. Interestingly enough, myfascination for the subject is still growing. In addition, each semester there are acouple of questions from the students that cause me to constantly question thetheory and that give me a new perspective on the subject. I have collected these andmy questions during my studies and tried to summarise the answers as well aspossible in this textbook.

Why another textbook—there are already so many available! During thepreparation of my lectures I had the impression that there are many great textbookson the subject, each with very specific merits. Nevertheless, my approach is tocombine what I find to be best understandable and to go in the depths where it isrequired, always in order not to lose the red, thermodynamic thread. Numerousquestions of the students have been helpful, especially in the context of exampreparations. So this book is a reference guide that has the same structure as mylecture. Although English is not my mother tongue, it was very important to me towrite the book in English: First, I reach a larger readership than if the book were inGerman. Second, linguistic limitations force me to explain even complicated thingsin a simple way.

vii

This book is categorised into three parts: Part I introduces the fundamentals oftechnical thermodynamics. First and second law of thermodynamics will be derivedthat enable us to understand the principle of energy conversion. Fluids are simplytreated as ideal gases or incompressible liquids. The physical description of thesefluids obey equations of state. Thermodynamic cycles will be discussed that convertthermal energy into mechanical energy, e.g. an internal combustion engine.Furthermore, thermodynamic cycles can be utilised to shift thermal energy from alow temperature level to a larger temperature level, e.g. a fridge. In Part II, realfluids will be investigated, i.e. fluids that can change their aggregate state forexample. These fluids cannot be treated as the fluids from Part I. Furthermore,mixtures of fluids are introduced, e.g. humid air as a mixture of dry air and water.Changes of state of these mixtures will be treated as well. However, these mixtureswill not be chemically reactive. Finally, Part III includes chemically reactive fluids.This is required to calculate combustion processes for instance. Combustion pro-cesses are part of many technical applications.

I have tried to find a good mixture of theory, examples and tasks. Since technicaldrawings are the language of the engineer, this book contains a large number ofdetailed illustrations which are intended to clarify even the most difficult aspectsof theory.

Finally, any of your feedback is highly appreciated!

Hamburg, Germany Prof. Dr.-Ing. Achim SchmidtWinter 2018/19

viii Preface

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 How Is This Book Structured? . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Classification of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Technical Thermodynamics . . . . . . . . . . . . . . . . . . . . . 51.2.2 Statistical Thermodynamics . . . . . . . . . . . . . . . . . . . . . 61.2.3 Chemical Thermodynamics . . . . . . . . . . . . . . . . . . . . . 6

1.3 Distinction Thermodynamics/Heat Transfer . . . . . . . . . . . . . . . 61.3.1 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.2 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 History of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4.1 The Caloric Theory Around 1780 . . . . . . . . . . . . . . . . 81.4.2 Thermodynamics as From the 18th Century . . . . . . . . . 91.4.3 Thermodynamics in the 21st Century . . . . . . . . . . . . . 121.4.4 Modern Automotive Applications . . . . . . . . . . . . . . . . 17

Part I Basics & Ideal Fluids

2 Energy and Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.1 Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.1.1 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.1.2 Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.3 Spring Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2 Thermal Energy—Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3 Chemical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.4 Changeability of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.4.1 Joule’s Paddle Wheel . . . . . . . . . . . . . . . . . . . . . . . . . 292.4.2 Internal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

ix

3 System and State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 Classification of Systems . . . . . . . . . . . . . . . . . . . . . . 373.1.2 Permeability of Systems—Open Versus Closed

Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.1.3 Examples for Thermodynamic Systems . . . . . . . . . . . . 43

3.2 State of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2.1 Thermal State Values . . . . . . . . . . . . . . . . . . . . . . . . . 463.2.2 Caloric State Values . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2.3 Outer State Values . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2.4 Size of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2.5 Extensive, Intensive and Specific State Values . . . . . . . 49

4 Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.1 Mechanical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2 Thermal Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.3 Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.4 Local Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . 594.5 Assumptions in Technical Thermodynamics . . . . . . . . . . . . . . . 60

5 Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.1 Gibbs’ Phase Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.1.1 Single-component Systems Without Phase Change . . . . 675.1.2 Single-component Systems with Phase Change . . . . . . 695.1.3 Multi-component Systems . . . . . . . . . . . . . . . . . . . . . . 69

5.2 Explicit Versus Implicit Equations of State . . . . . . . . . . . . . . . . 70

6 Thermal Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.1 Temperature Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.2 Pressure Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.3 Ideal Gas Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

7 Changes of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.1 The p; v-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.1.1 Isothermal Change of State . . . . . . . . . . . . . . . . . . . . . 837.1.2 Isobaric Change of State . . . . . . . . . . . . . . . . . . . . . . . 847.1.3 Isochoric Change of State . . . . . . . . . . . . . . . . . . . . . . 85

7.2 Equilibrium Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 887.2.1 Quasi-Static Changes of State . . . . . . . . . . . . . . . . . . . 897.2.2 Requirement for a Quasi-static Change of State . . . . . . 90

7.3 Reversible Versus Irreversible Changes of State . . . . . . . . . . . . 927.3.1 Mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.3.2 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947.3.3 Chemical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.4 Conventional Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . 96

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8 Thermodynamic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078.1 Equilibrium Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078.2 Transient State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088.3 Thermodynamic Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108.4 Steady State Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.4.1 Open Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1118.4.2 Closed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1128.4.3 Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

9 Process Values Heat and Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159.1 Thermal Energy—Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

9.2.1 Definition of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189.2.2 Volume Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1219.2.3 Effective Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1259.2.4 Systems with Internal Friction—Dissipation . . . . . . . . . 1289.2.5 Dissipation Versus Outer Friction . . . . . . . . . . . . . . . . 1339.2.6 Mechanical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359.2.7 Shaft Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369.2.8 Shifting Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379.2.9 Technical Work Respectively Pressure Work . . . . . . . . 139

10 State Value Versus Process Value . . . . . . . . . . . . . . . . . . . . . . . . . . 14310.1 Total Differential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14510.2 Schwarz’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

11 First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14911.1 Principle of Equivalence Between Work and Heat . . . . . . . . . . 14911.2 Closed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

11.2.1 Systems at Rest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15111.2.2 Systems in Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 15611.2.3 Partial Energy Equation . . . . . . . . . . . . . . . . . . . . . . . 158

11.3 Open Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17611.3.1 Formulation of the First Law of Thermodynamics for

Open Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17811.3.2 Non-steady State Flows . . . . . . . . . . . . . . . . . . . . . . . 18411.3.3 Steady State Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 19111.3.4 Partial Energy Equation . . . . . . . . . . . . . . . . . . . . . . . 194

12 Caloric Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20112.1 Specific Internal Energy u and Specific Enthalpy h for Ideal

Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20212.2 Specific Entropy s as New State Value for Ideal Gases . . . . . . . 204

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12.3 Derivation of the Caloric Equations for Real Fluids . . . . . . . . . 20912.3.1 Specific Internal Energy u . . . . . . . . . . . . . . . . . . . . . . 20912.3.2 Specific Enthalpy h . . . . . . . . . . . . . . . . . . . . . . . . . . 212

12.4 Handling of the Caloric State Equations . . . . . . . . . . . . . . . . . . 21912.4.1 Ideal Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21912.4.2 Distinction Between cv and cp for Ideal Gases . . . . . . . 22012.4.3 Isentropic Exponent . . . . . . . . . . . . . . . . . . . . . . . . . . 22512.4.4 Temperature Dependent Specific Heat Capacity . . . . . . 22612.4.5 Incompressible Fluids, Solids . . . . . . . . . . . . . . . . . . . 22912.4.6 Adiabatic Throttle . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

13 Meaning and Handling of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 23713.1 Entropy—Clarification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23713.2 Comparison Entropy Balance Versus First Law of

Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23913.3 Energy Conversion—Why do we Need Entropy? . . . . . . . . . . . 24213.4 The T ; s-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

13.4.1 Benefit of a New State Diagram . . . . . . . . . . . . . . . . . 24513.4.2 Physical Laws in a T ; s-Diagram for Ideal Gases . . . . . 247

13.5 Adiabatic, Reversible Change of State . . . . . . . . . . . . . . . . . . . 25113.6 Polytropic Change of State . . . . . . . . . . . . . . . . . . . . . . . . . . . 25613.7 Entropy Balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

13.7.1 Entropy Balance for Closed Systems . . . . . . . . . . . . . . 26513.7.2 Entropy Balance for Open Systems . . . . . . . . . . . . . . . 26813.7.3 Thermodynamic Mean Temperature . . . . . . . . . . . . . . . 27213.7.4 Entropy and Process Evaluation . . . . . . . . . . . . . . . . . 277

14 Transient Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29314.1 Mechanical Driven Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 29314.2 Thermal Driven Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29914.3 Chemical Driven Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30514.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

15 Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 31315.1 Formulation According to Planck—Clockwise Cycle

Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31315.1.1 The Thermal Engine . . . . . . . . . . . . . . . . . . . . . . . . . . 31515.1.2 Why Clockwise Cycle? . . . . . . . . . . . . . . . . . . . . . . . . 318

15.2 Formulation According to Clausius—Counterclockwise CycleProcesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31915.2.1 The Cooling Machine/Heat Pump . . . . . . . . . . . . . . . . 32015.2.2 Why Counterclockwise Cycle? . . . . . . . . . . . . . . . . . . 323

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15.3 The Carnot-Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32715.3.1 The Carnot-Machine—Clockwise Cycle . . . . . . . . . . . . 32715.3.2 The Carnot-Machine—Counterclockwise Cycle . . . . . . 330

16 Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33316.1 Exergy of Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33516.2 Exergy of Fluid Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34316.3 Exergy of Closed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34616.4 Loss of Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

16.4.1 Closed System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35216.4.2 Open System in Steady State Operation . . . . . . . . . . . . 35416.4.3 Thermodynamic Cycles . . . . . . . . . . . . . . . . . . . . . . . 358

16.5 Sankey-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36516.5.1 Open System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36516.5.2 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

17 Components and Thermodynamic Cycles . . . . . . . . . . . . . . . . . . . . 37517.1 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

17.1.1 Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37517.1.2 Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37917.1.3 Thermal Turbo-Machines in a h; s-Diagram . . . . . . . . . 38217.1.4 Adiabatic Throttle . . . . . . . . . . . . . . . . . . . . . . . . . . . 38317.1.5 Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

17.2 Thermodynamic Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39317.2.1 Carnot Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39417.2.2 Joule Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39517.2.3 Clausius Rankine Process . . . . . . . . . . . . . . . . . . . . . . 39617.2.4 Seiliger Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39817.2.5 Stirling Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39917.2.6 Compression Heat Pump . . . . . . . . . . . . . . . . . . . . . . . 40417.2.7 Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

Part II Real Fluids & Mixtures

18 Single-Component Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42318.1 Ideal Gas Versus Real Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . 42318.2 Phase Change Real Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

18.2.1 Example: Isobaric Vaporisation . . . . . . . . . . . . . . . . . . 42618.2.2 The p; v; T-State Space . . . . . . . . . . . . . . . . . . . . . . . . 42918.2.3 p; T-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43318.2.4 T ; v-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43318.2.5 p; v-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43618.2.6 State Description Within the Wet-Steam Region . . . . . . 439

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18.3 State Values of Real Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . 44218.3.1 Van der Waals Equation of State . . . . . . . . . . . . . . . . . 44318.3.2 Redlich–Kwong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44618.3.3 Peng–Robinson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44618.3.4 Berthelot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44718.3.5 Dieterici . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44718.3.6 Virial Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44818.3.7 Steam Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

18.4 Energetic Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45318.4.1 Reversibility of Vaporisation . . . . . . . . . . . . . . . . . . . . 45318.4.2 Heat of Vaporisation . . . . . . . . . . . . . . . . . . . . . . . . . 45518.4.3 Caloric State Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 45718.4.4 Clausius–Clapeyron Relation . . . . . . . . . . . . . . . . . . . . 466

18.5 Adiabatic Throttling—Joule–Thomson Effect . . . . . . . . . . . . . . 46918.5.1 Ideal Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47018.5.2 Real Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

19 Mixture of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48119.1 Concentration Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . 48119.2 Dalton’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48419.3 Laws of Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

19.3.1 Concentration, Thermal State Values . . . . . . . . . . . . . . 48819.3.2 Internal Energy, Enthalpy . . . . . . . . . . . . . . . . . . . . . . 49119.3.3 Adiabatic Mixing Temperature . . . . . . . . . . . . . . . . . . 49319.3.4 Irreversibility of Mixing . . . . . . . . . . . . . . . . . . . . . . . 495

20 Humid Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50720.1 Thermodynamic State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

20.1.1 Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50820.1.2 Aggregate State of the Water . . . . . . . . . . . . . . . . . . . 50920.1.3 Unsaturated Versus Saturated Air . . . . . . . . . . . . . . . . 511

20.2 Specific State Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51620.2.1 Thermal State Values . . . . . . . . . . . . . . . . . . . . . . . . . 51720.2.2 Caloric State Values . . . . . . . . . . . . . . . . . . . . . . . . . . 52120.2.3 Specific Enthalpy h1þ x . . . . . . . . . . . . . . . . . . . . . . . . 52220.2.4 Specific Entropy s1þ x . . . . . . . . . . . . . . . . . . . . . . . . . 52720.2.5 Overview Possible Cases . . . . . . . . . . . . . . . . . . . . . . 531

20.3 The h1þ x; x-Diagram According to Mollier . . . . . . . . . . . . . . . . 54120.4 Changes of State for Humid Air . . . . . . . . . . . . . . . . . . . . . . . 543

20.4.1 Heating and Cooling at Constant Water Content . . . . . 54320.4.2 Dehumidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54620.4.3 Adiabatic Mixing of Humid Air . . . . . . . . . . . . . . . . . 54820.4.4 Humidification of Air . . . . . . . . . . . . . . . . . . . . . . . . . 553

xiv Contents

20.4.5 Adiabatic Saturation Temperature . . . . . . . . . . . . . . . . 55620.4.6 The h1þ x; x-Diagram for Varying Total Pressure . . . . . 559

21 Steady State Flow Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57121.1 Incompressible Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57321.2 Adiabatic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574

21.2.1 Adiabatic Diffusor . . . . . . . . . . . . . . . . . . . . . . . . . . . 57721.2.2 Adiabatic Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579

21.3 Velocity of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58421.4 Fanno Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58721.5 Rayleigh Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59421.6 Normal Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60421.7 Supersonic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

21.7.1 Flow of a Converging Nozzle . . . . . . . . . . . . . . . . . . . 60521.7.2 Laval-Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

22 Thermodynamic Cycles with Phase Change . . . . . . . . . . . . . . . . . . 62522.1 Steam Power Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626

22.1.1 Clausius-Rankine Process . . . . . . . . . . . . . . . . . . . . . . 62622.1.2 Steam Power Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

22.2 Heat Pump and Cooling Machine . . . . . . . . . . . . . . . . . . . . . . 63722.2.1 Mechanical Compression . . . . . . . . . . . . . . . . . . . . . . 63722.2.2 Thermal Compression . . . . . . . . . . . . . . . . . . . . . . . . . 640

Part III Reactive Systems

23 Combustion Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65523.1 Fossil Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65523.2 Fuel Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658

23.2.1 Solid Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65823.2.2 Liquid Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65923.2.3 Gaseous Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

23.3 Stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66023.3.1 Solid/Liquid Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . 66123.3.2 Gaseous Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66823.3.3 Mass Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . 67623.3.4 Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67723.3.5 Setting up a Chemical Equation . . . . . . . . . . . . . . . . . 68023.3.6 Dew Point of the Exhaust Gas . . . . . . . . . . . . . . . . . . 682

23.4 Energetic Balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69323.4.1 Lower Heating Value . . . . . . . . . . . . . . . . . . . . . . . . . 69423.4.2 Conceptual 3-Steps Combustion . . . . . . . . . . . . . . . . . 69623.4.3 Upper Heating Value . . . . . . . . . . . . . . . . . . . . . . . . . 707

Contents xv

23.4.4 Molar and Volume Specific Lower/UpperHeating Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

23.4.5 Combustion Temperature . . . . . . . . . . . . . . . . . . . . . . 71223.5 Combustion Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717

23.5.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71823.5.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718

24 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73324.1 Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73324.2 Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739

24.2.1 Caloric Equations of State . . . . . . . . . . . . . . . . . . . . . 73924.2.2 Open Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74224.2.3 Closed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745

24.3 Gibbs Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75224.3.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75224.3.2 Molar Gibbs Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . 75224.3.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

24.4 Exergy of a Fossil Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75524.5 Chemical Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761

24.5.1 Multi-component Systems . . . . . . . . . . . . . . . . . . . . . . 76124.5.2 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 767

Appendix A: Steam Table (Water) According to IAPWS . . . . . . . . . . . . 771

Appendix B: Selected Absolute Molar Enthalpies/Entropies . . . . . . . . . . 787

Appendix C: Caloric State Diagrams of Water . . . . . . . . . . . . . . . . . . . . 801

Appendix D: The h1þ x; x-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809

xvi Contents

Nomenclature

Roman Symbols

A Areaa Cohesion pressure, see equation 18.38a Mass fraction ashesa Velocity of sounda Accelerationb Co-volume, see equation 18.38_Bx Flux of anergyBðTÞ Virial coefficientBx Anergybx Specific anergyC CapacityC ConstantC Molar heat capacity C ¼ cMC Number of componentsc Mass fraction carbonc Specific heat capacity�c Specific, averaged heat capacitya Velocity of soundc VelocityCðTÞ Virial coefficientci Molarity of a component iDðTÞ Virial coefficientD, d DiameterE EnergyD _Ex;V Flux of loss of exergyDEx;V Loss of exergyDex;V Specific loss of exergy_Ex Flux of exergy

xvii

Exm;F Molar specific absolute exergy of the fuelExm Molar specific absolute exergyEx Exergyex Specific exergyF Degree of freedomF Forcef Specific Helmholtz energyG Gibbs enthalpyg Acceleration of gravity, g ¼ 9:81ms2g Specific Gibbs enthalpyGm Molar specific Gibbs enthalpyH Enthalpyh Mass fraction hydrogenh Specific enthalpyDhv Specific enthalpy of vaporisationD0BHm Molar specific enthalpy of formation at standard conditions

D0RHm Molar specific enthalpy of reaction at standard conditions

Hm Molar specific absolute enthalpyH, h Height in a gravity fieldH0M Molar specific upper heating valueH0v Volume specific upper heating valueH0 Mass specific upper heating valueHUM Molar specific lower heating valueHUv Volume specific lower heating valueHU Mass specific lower heating valuek Heat transition coefficientkB Boltzmann constant, kB ¼ 1:3806� 10�23 J

KkF Spring constantLmin Minimum molar-specific air needlmin Minimum mass-specific air needM Molar massM Torquem Mass_m Mass flux_m00 Mass flux densityMa Mach-numbern Mass fraction nitrogenn Molar quantityn Polytropic exponentn Speed_n Molar flux~n NormalNA Avogadro constant, NA ¼ 6:022 045� 1023 1

mol

xviii Nomenclature

o Mass fraction oxygenOmin Minimum molar-specific oxygen needomin Minimum mass-specific oxygen needP Number of phasesP Powerp Pressurepi Partial pressure of a component iQ Electric chargeQ Heat or thermal energy_Q Heat fluxq Specific heatR Individual gas constantR, r Radius

RM General gas constant, RM ¼ 8:3143 kJkmolK

S Entropy ð JKÞs Mass fraction sulphurDRSm Molar specific entropy of a reaction_Sa Flux of entropy carried with heat_Si Flux of entropy generations Distances Specific entropysa Specific entropy carried with heatsi Specific entropy generationSm Molar specific absolute entropyT Absolute thermodynamic temperaturet Time (s)Tr Reduced thermodynamic temperature according to equation 18.63U Internal energyt Specific internal energyUm Molar specific absolute internal energyV VoltageV Volumet Specific volume_V Volume fluxW Workw Mass fraction waterw Specific workx Coordinatex Molar concentration of a component ix Molar fractionx Vapour ratiox Water contenty Coordinate

Nomenclature xix

y Specific pressure workZ Compressibility factorZ Extensive state valuez Coordinatez Distancez Specific state value, z ¼ Z

m

Greek Symbols

fi Abbreviationfi Anglefi Heat transfer coefficientfl Isobaric volumetric thermal expansion coefficientdh Isenthalpic throttle coefficientdT Isothermal throttle coefficient� Compression ratiog Abbreviationg Efficiency�i Stoichiometric factor of a component ij Isentropic coefficient‚ Air-fuel equivalence ratio„ Chemical potential„i Mass-specific exhaust gas composition of component imi Molar-specific exhaust gas composition of component iΩ Flow function of a nozzleΩ Statistical weight, measure of the probability! Acentric factorΨ Dissipationff Relative saturation_Ψ Flux of dissipationff Specific dissipationff0 Specific dissipation per lengthffi Volume ratio of a component iq Densityqi Partial density of a component iri Volume concentration of a component ie Coefficient of performanceu Relative humidity# Celsius-temperaturen Abbreviationni Mass concentration of a component i

xx Nomenclature

Acronyms

0 Saturated liquid state, saturated humid air00 Saturated vapour stated Process valued State value1P Single-phase2P Two-phaseC CarnotCM Cold machine/fridgecp Critical pointHP Heat pumpHP High pressureHT Heat transferHVAC Heating, ventilation and airconditioning technologyLP Low pressurePr ProductTE Thermal engineTP Triple point

Subscripts

A Air (wet)a Air (dry)a OuterC Cylindercomp Compressioncond. Condensereff EffectiveEG Exhaust gasel Electricenv EnvironmentF Fuelfric. FrictionG Gasgas GasHP High pressureice Icein Inletirrev IrreversibleK Control volumekin Kinetic

Nomenclature xxi

L Liquidliq LiquidLP Low pressurem Meanm MeltingM,m Molarmax MaximumMech Mechanicmin MinimumMP Medium pressuren Narrowest cross sectionout OutletP Pistonp p ¼ const:pot PotentialR Reservoirref Reference staterev ReversibleS Steels Saturatedshift ShiftingSource Source termspr Springswing StrokeSys Systemt TechnicalT T ¼ const:th Thermaltotal TotalV Volumev v ¼ const:V,v VapourW Water

xxii Nomenclature

List of Figures

Fig. 1.1 What is thermodynamics all about? (Tasksof thermodynamics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Fig. 1.2 Distinction thermodynamics (left)/heat transfer (right) . . . . . . . 7Fig. 1.3 Working principle of a steam machine . . . . . . . . . . . . . . . . . . . 12Fig. 1.4 Gas turbine (Schematic working principle) . . . . . . . . . . . . . . . . 14Fig. 1.5 Fossil power plant (left: Schematic working principle, right:

Visualisation in a p; v-diagram, liquid water is supposedapproximately to be incompressible) . . . . . . . . . . . . . . . . . . . . 14

Fig. 1.6 Cooling machine (left: Schematic working principle, right:Illustration in a T; s-diagram, the compressor is supposedto be isentropic) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Fig. 1.7 Thermoelectric generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Fig. 1.8 Waste heat recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Fig. 2.1 a Definition of work and b power . . . . . . . . . . . . . . . . . . . . . . 24Fig. 2.2 Kinetic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Fig. 2.3 Potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Fig. 2.4 Spring energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Fig. 2.5 Heat as thermal energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Fig. 2.6 Joule’s paddle wheel experiment . . . . . . . . . . . . . . . . . . . . . . . 29Fig. 2.7 Joule’s paddle wheel experiment, state (1) and (2) . . . . . . . . . . 30Fig. 2.8 Sketch to Problem 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Fig. 2.9 Solution Problem 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Fig. 3.1 Definition of a system, (i) indicates the internal state,

(B) the system boundary, that might be permeablefor mass, momentum and energy . . . . . . . . . . . . . . . . . . . . . . . 36

Fig. 3.2 Example of a bank account . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Fig. 3.3 Heterogeneous versus homogeneous systems . . . . . . . . . . . . . . 38Fig. 3.4 Heterogeneous systems—fluidised bed, see [12]. . . . . . . . . . . . 39Fig. 3.5 Heterogeneous systems—diesel spray formation, see [13] . . . . 40Fig. 3.6 Aggregate states from left to right: solid/liquid/gas . . . . . . . . . 40Fig. 3.7 Permeability of systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

xxiii

Fig. 3.8 Cooling machine on the left: thermodynamic cycle on theright: possible system boundaries . . . . . . . . . . . . . . . . . . . . . . . 44

Fig. 3.9 Examples for thermodynamic open systems . . . . . . . . . . . . . . . 45Fig. 3.10 Overview state values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Fig. 3.11 Overview state values for a closed system . . . . . . . . . . . . . . . . 47Fig. 3.12 Extensive and intensive state values . . . . . . . . . . . . . . . . . . . . . 49Fig. 3.13 Extensive state value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Fig. 3.14 Intensive versus specific state value according to Hahne [1]

left: thermodynamic equilibrium possible, though q1\q2right: thermodynamic equilibrium impossible, if p1 6¼ p2 . . . . . 52

Fig. 3.15 Definition of molar mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Fig. 4.1 a Imbalanced system, b system in thermodynamic

equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Fig. 4.2 Calculating the pressure in equilibrium state . . . . . . . . . . . . . . 56Fig. 4.3 Thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Fig. 4.4 Zeroth law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 58Fig. 4.5 Principle of temperature measurement . . . . . . . . . . . . . . . . . . . 59Fig. 4.6 Imbalanced systems in steady state—Example of a heat

conducting wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Fig. 4.7 Assumptions in thermodynamics . . . . . . . . . . . . . . . . . . . . . . . 61Fig. 4.8 Sketch to Problem 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Fig. 4.9 Solution to Problem 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Fig. 4.10 Solution to Problem 4.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Fig. 5.1 p; T-diagram for water—Degrees of freedom . . . . . . . . . . . . . . 70Fig. 6.1 Gay-Lussac law—Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Fig. 6.2 Gay-Lussac law—Results for thermodynamic equilibrium . . . . 75Fig. 6.3 Boyle–Mariotte law—Set-up. . . . . . . . . . . . . . . . . . . . . . . . . . . 76Fig. 6.4 Boyle–Mariotte law—Results for thermodynamic

equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Fig. 7.1 Change of state from one equilibrium state to another . . . . . . . 82Fig. 7.2 Isothermal change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Fig. 7.3 Isobaric change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Fig. 7.4 Isochoric change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Fig. 7.5 Solution to Problem 7.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Fig. 7.6 Quasi-static versus non-quasi-static change of state:

Illustration in a p; v�diagram for gas compression (Thepressure is assumed to be homogeneous. Thus, thegravitational effect has been ignored, see Sect. 7.1.1!) . . . . . . . 89

Fig. 7.7 Path-independent equilibrium state . . . . . . . . . . . . . . . . . . . . . . 91Fig. 7.8 Wire pendulum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Fig. 7.9 Dissipation in a closed systems . . . . . . . . . . . . . . . . . . . . . . . . 93Fig. 7.10 Bouncing ball driven by Dz . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

xxiv List of Figures

Fig. 7.11 Pressure balancing driven by Dp . . . . . . . . . . . . . . . . . . . . . . . 95Fig. 7.12 Cooling down of a liquid driven by DT . . . . . . . . . . . . . . . . . . 95Fig. 7.13 Mixing of gases driven by ni . . . . . . . . . . . . . . . . . . . . . . . . . . 96Fig. 7.14 Overview irreversible/reversible—Example of an adiabatic

compression/expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Fig. 7.15 Analogous model according to [16] . . . . . . . . . . . . . . . . . . . . . 99Fig. 7.16 Approach technical thermodynamics according to [1]. . . . . . . . 100Fig. 7.17 Isobaric change of state—Differential notation . . . . . . . . . . . . . 101Fig. 7.18 p; v- and T ; s-diagram according to Fig. 7.14 . . . . . . . . . . . . . . 106Fig. 8.1 Equilibrium process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Fig. 8.2 Transient state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Fig. 8.3 Thermodynamic cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Fig. 8.4 Stirling cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Fig. 8.5 Steady state flow process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Fig. 8.6 Steady state closed system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Fig. 8.7 Steady state thermodynamic cycle (black box) . . . . . . . . . . . . . 113Fig. 9.1 Thermal equilibrium is achieved by heat flux . . . . . . . . . . . . . . 116Fig. 9.2 Sign convention heat—Advice . . . . . . . . . . . . . . . . . . . . . . . . . 117Fig. 9.3 Definition of work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Fig. 9.4 Sign convention for the process values heat and work . . . . . . . 121Fig. 9.5 Deriving volume work–Expansion (1)! (2). . . . . . . . . . . . . . . 122Fig. 9.6 Specific volume work wv;12—illustration in a p; v-diagram . . . 124Fig. 9.7 Effective work Weff—Illustration and visualisation

in a p;V-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Fig. 9.8 Dissipation in closed (a) and open systems (b) . . . . . . . . . . . . 128Fig. 9.9 Left: Compression to the same volume, right: Expansion

to the same pressure (both adiabatic). ð1Þ ! ð2Þreversible, ð1Þ ! ð20Þ irreversible . . . . . . . . . . . . . . . . . . . . . . . 130

Fig. 9.10 Dissipation in closed systems due to fluid turbulence (left),outer friction (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Fig. 9.11 Illustration of mechanical work . . . . . . . . . . . . . . . . . . . . . . . . 136Fig. 9.12 Shaft work for a closed system . . . . . . . . . . . . . . . . . . . . . . . . 136Fig. 9.13 Shifting work in open systems . . . . . . . . . . . . . . . . . . . . . . . . . 138Fig. 9.14 Technical work—no dissipation, outer energies ignored . . . . . . 139Fig. 9.15 Analogous model for technical work @ pressure decrease,

related to Fig. 9.14b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Fig. 10.1 Process versus state value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144Fig. 10.2 Total differential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Fig. 10.3 Schwarz’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Fig. 11.1 Equivalence of heat and work . . . . . . . . . . . . . . . . . . . . . . . . . 150Fig. 11.2 Converting thermal to mechanical energy. . . . . . . . . . . . . . . . . 151Fig. 11.3 Closed system at rest—supply of heat . . . . . . . . . . . . . . . . . . . 151Fig. 11.4 Closed system at rest—supply of work . . . . . . . . . . . . . . . . . . 152Fig. 11.5 Closed system at rest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

List of Figures xxv

Fig. 11.6 Converting energy in a closed system . . . . . . . . . . . . . . . . . . . 153Fig. 11.7 Closed system—no cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . 155Fig. 11.8 Closed system in motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156Fig. 11.9 First law of thermodynamics for closed systems,

see Sect. 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Fig. 11.10 Partial energy equation for closed systems . . . . . . . . . . . . . . . . 158Fig. 11.11 a Supply of electrical energy in an isochoric system,

b Supply of electrical energy in a non-isochoric system,c Supply of electrical energy with an electrical capacitor . . . . . 159

Fig. 11.12 a Reversible, adiabatic compression, b Irreversible,adiabatic compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Fig. 11.13 Partial energy equation for closed systems . . . . . . . . . . . . . . . . 164Fig. 11.14 Partial energy equation for closed systems . . . . . . . . . . . . . . . . 164Fig. 11.15 Solution Problem 11.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Fig. 11.16 Solution to Problem 11.8—isobaric change of state . . . . . . . . . 170Fig. 11.17 Solution Problem 11.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Fig. 11.18 Numerical solution to Problem 11.9 . . . . . . . . . . . . . . . . . . . . . 177Fig. 11.19 Compression process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Fig. 11.20 Schematic diagram (analogous model) . . . . . . . . . . . . . . . . . . . 178Fig. 11.21 From closed to open systems . . . . . . . . . . . . . . . . . . . . . . . . . . 179Fig. 11.22 Energy balance open system. . . . . . . . . . . . . . . . . . . . . . . . . . . 179Fig. 11.23 Energy within an open system . . . . . . . . . . . . . . . . . . . . . . . . . 180Fig. 11.24 Energy crossing the system boundary of an open system . . . . . 183Fig. 11.25 Energy crossing system boundary of an open system . . . . . . . . 184Fig. 11.26 Sketch to Problem 11.10, see also Fig. 9.15. . . . . . . . . . . . . . . 185Fig. 11.27 Sketch to Problem 11.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190Fig. 11.28 Open systems with multiple inlets/outlets . . . . . . . . . . . . . . . . . 194Fig. 11.29 Technical work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195Fig. 11.30 What does technical work mean? . . . . . . . . . . . . . . . . . . . . . . . 196Fig. 11.31 Specific pressure work y12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Fig. 12.1 Joule expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Fig. 12.2 Isobaric (Case A) versus isochoric (Case B) change

of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221Fig. 12.3 Solution for Problem 12.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Fig. 12.4 Temperature dependency of the specific heat capacity . . . . . . . 227Fig. 12.5 Sketch to Problem 12.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Fig. 12.6 Sketch to Problem 12.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232Fig. 13.1 Mechanism of entropy in a closed systems. . . . . . . . . . . . . . . . 239Fig. 13.2 Balance of entropy in a closed system . . . . . . . . . . . . . . . . . . . 241Fig. 13.3 Balance of energy in a closed system. . . . . . . . . . . . . . . . . . . . 241Fig. 13.4 Power plant as a block-box . . . . . . . . . . . . . . . . . . . . . . . . . . . 243Fig. 13.5 T ; s-diagram: principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

xxvi List of Figures

Fig. 13.6 T ; s-diagram: reversible (left) and irreversible (right) . . . . . . . . 247Fig. 13.7 T ; s-diagram: isochore and isobar . . . . . . . . . . . . . . . . . . . . . . . 248Fig. 13.8 Isobar and isochore in a T ; s-diagram (ideal gas) . . . . . . . . . . . 250Fig. 13.9 Adiabatic, reversible change of state. . . . . . . . . . . . . . . . . . . . . 251Fig. 13.10 Reversible compression of an ideal gas: isothermal versus

adiabatic according to Problem 13.8. . . . . . . . . . . . . . . . . . . . . 254Fig. 13.11 Polytropic change of state for an ideal gas in

a p; v-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256Fig. 13.12 Polytropic change of state for an ideal gas in a p; v- and

in a T ; s-diagram according to [1] . . . . . . . . . . . . . . . . . . . . . . 258Fig. 13.13 Overview ideal gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260Fig. 13.14 Polytropic change of state for an ideal gas–Compression

(closed system), see Problem 13.8 . . . . . . . . . . . . . . . . . . . . . . 261Fig. 13.15 Polytropic change of state for an ideal gas–Expansion

(closed system), see Problem 13.9 . . . . . . . . . . . . . . . . . . . . . . 262Fig. 13.16 Sketch of the compressor, see Problem 13.10. . . . . . . . . . . . . . 263Fig. 13.17 Energy and entropy balance for a closed system . . . . . . . . . . . 265Fig. 13.18 Isothermal irreversible compression of an ideal gas . . . . . . . . . 267Fig. 13.19 Energy and entropy balance—open system. . . . . . . . . . . . . . . . 269Fig. 13.20 Entropy balance—steady state flow system, multiple

inlets/outlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Fig. 13.21 Thermodynamic mean temperature—steady state flow

system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Fig. 13.22 Thermodynamic mean temperature—closed system . . . . . . . . . 276Fig. 13.23 Lifting a crate of beer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278Fig. 13.24 Sketch to Problem 13.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281Fig. 13.25 Left: compression to the same volume, right: expansion

to the same pressure (both adiabatic) . . . . . . . . . . . . . . . . . . . . 283Fig. 13.26 Sketch to Problem 13.17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284Fig. 13.27 System boundaries for Problem 13.17 . . . . . . . . . . . . . . . . . . . 286Fig. 13.28 Massless boundary, Problem 13.17e . . . . . . . . . . . . . . . . . . . . . 288Fig. 14.1 Wire pendulum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Fig. 14.2 Sketch to Problem 14.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297Fig. 14.3 Wall—Heat conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Fig. 14.4 Heat transfer between two homogeneous systems. . . . . . . . . . . 302Fig. 14.5 Thermal balancing process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303Fig. 14.6 Sketch to Problem 14.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307Fig. 14.7 Sketch to Problem 14.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308Fig. 14.8 Sketch to Problem 14.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311Fig. 15.1 Contradiction to the second law according to Planck . . . . . . . . 314Fig. 15.2 Thermal engine without cooling . . . . . . . . . . . . . . . . . . . . . . . . 315Fig. 15.3 Thermal engine in black box notation . . . . . . . . . . . . . . . . . . . 316Fig. 15.4 Thermal engine in a p;V-diagram . . . . . . . . . . . . . . . . . . . . . . 318Fig. 15.5 Contradiction to the second law according to Clausius. . . . . . . 320

List of Figures xxvii

Fig. 15.6 Cooling machine/heat pump in black box notation . . . . . . . . . . 321Fig. 15.7 Cooling machine/heat pump in a p;V-diagram . . . . . . . . . . . . . 324Fig. 15.8 Solution to Problem 15.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325Fig. 15.9 Clockwise Carnot process—Thermal engine. . . . . . . . . . . . . . . 328Fig. 15.10 Clockwise Carnot process—T ; s-diagram . . . . . . . . . . . . . . . . . 329Fig. 15.11 Counterclockwise Carnot process—Cooling machine/heat

pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331Fig. 16.1 Evaluation of thermal energy sources . . . . . . . . . . . . . . . . . . . . 334Fig. 16.2 Gaining work from heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335Fig. 16.3 Energy-in-exergy-and-anergy-decomposition-machine . . . . . . . 336Fig. 16.4 Heat at constant temperature ! evaluation of the exergy

of the heat q@ T with a Carnot-machine . . . . . . . . . . . . . . . . . 337Fig. 16.5 Exergy of heat at isothermal expansion according to [2] . . . . . 338Fig. 16.6 Non-isothermal heat supply (1) ! (2) . . . . . . . . . . . . . . . . . . . 339Fig. 16.7 Exergy of heat—influence of the environmental temperature

according to [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Fig. 16.8 Sign of exergy of heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Fig. 16.9 Exergy of a fluid flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Fig. 16.10 Change of state (1) ! (env) with p10 [ penv, according

to [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Fig. 16.11 Change of state (1) ! (env) with p10\ penv, according

to [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346Fig. 16.12 Exergy of a closed system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347Fig. 16.13 Change of state (1) ! (env) with p10 [ penv . . . . . . . . . . . . . . 348Fig. 16.14 Change of state (1) ! (env) with p10\ penv . . . . . . . . . . . . . . . 348Fig. 16.15 Closed system: balance of exergy. . . . . . . . . . . . . . . . . . . . . . . 352Fig. 16.16 Overview closed system: balance of energy (a), entropy

(b) and exergy (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354Fig. 16.17 Open system: balance of exergy . . . . . . . . . . . . . . . . . . . . . . . . 355Fig. 16.18 Overview open system: balance of energy (a), entropy

(b) and exergy (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357Fig. 16.19 Balance of exergy: a Clockwise cycle, b Counterclockwise

cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Fig. 16.20 Overview clockwise cycle: balance of energy (a), entropy

(b) and exergy (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360Fig. 16.21 Overview counterclockwise cycle: balance of energy (a),

entropy (b) and exergy (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362Fig. 16.22 Illustration of energy fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . 365Fig. 16.23 Sankey-diagram of an open system . . . . . . . . . . . . . . . . . . . . . 366Fig. 16.24 Heat transfer (wall) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Fig. 16.25 Sketch for the solution to Problem 16.4 . . . . . . . . . . . . . . . . . . 368Fig. 16.26 Sketch for the solution to Problem 16.4 . . . . . . . . . . . . . . . . . . 370Fig. 16.27 Sketch for the solution to Problem 16.5 . . . . . . . . . . . . . . . . . . 371Fig. 16.28 Sketch for the solution to Problem 16.5 . . . . . . . . . . . . . . . . . . 373

xxviii List of Figures

Fig. 17.1 Turbine: a First law, b Second Law, c Exergy . . . . . . . . . . . . . 376Fig. 17.2 Adiabatic turbine: Illustration in a T; s-diagram (ideal

and real gases) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378Fig. 17.3 Compressor: a First law, b Second Law, c Exergy. . . . . . . . . . 379Fig. 17.4 Adiabatic compressor: Illustration in a T ; s-diagram (ideal

and real gases) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382Fig. 17.5 Thermal turbo-machines in a h; s-diagram . . . . . . . . . . . . . . . . 383Fig. 17.6 Adiabatic throttle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384Fig. 17.7 Symbols for heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . 388Fig. 17.8 Countercurrent heat exchanger . . . . . . . . . . . . . . . . . . . . . . . . . 388Fig. 17.9 Countercurrent heat exchanger . . . . . . . . . . . . . . . . . . . . . . . . . 388Fig. 17.10 Wall—Heat conduction (heat exchanger is supposed

to be adiabatic to the environment) . . . . . . . . . . . . . . . . . . . . . 389Fig. 17.11 Entropy balance (heat exchanger is supposed to be adiabatic

to the environment) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390Fig. 17.12 Entropy balance (System C) . . . . . . . . . . . . . . . . . . . . . . . . . . . 392Fig. 17.13 Overall entropy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392Fig. 17.14 Carnot process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394Fig. 17.15 Joule process—Layout clockwise cycle . . . . . . . . . . . . . . . . . . 395Fig. 17.16 Joule process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396Fig. 17.17 Clausius Rankine process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397Fig. 17.18 Clausius Rankine process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397Fig. 17.19 Seiliger process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399Fig. 17.20 Stirling process—Technical principle . . . . . . . . . . . . . . . . . . . . 400Fig. 17.21 Stirling process—p; v- and T ; s-diagram . . . . . . . . . . . . . . . . . . 401Fig. 17.22 Compression heat pump—Layout. . . . . . . . . . . . . . . . . . . . . . . 403Fig. 17.23 Compression heat pump: Sketch and illustration in a T;

s-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404Fig. 17.24 Sketch of the layout to Problem 17.1 . . . . . . . . . . . . . . . . . . . . 406Fig. 17.25 p; v- and T ; s-diagram to Problem 17.1 . . . . . . . . . . . . . . . . . . . 407Fig. 17.26 Sketch to Problem 17.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409Fig. 17.27 Sketch to Problem 17.2: a Compressor in a p; v-diagram,

b Heat exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410Fig. 17.28 Sketch to Problem 17.2c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411Fig. 17.29 Sketch to Problem 17.3e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414Fig. 17.30 Sketch to Problem 17.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417Fig. 17.31 Sketch to Problem 17.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419Fig. 18.1 Compressibility factor Z for air according to [3] . . . . . . . . . . . 425Fig. 18.2 Changes of aggregation state . . . . . . . . . . . . . . . . . . . . . . . . . . 425Fig. 18.3 Isobaric evaporation—schematic illustration . . . . . . . . . . . . . . . 426Fig. 18.4 Isobaric evaporation—schematic illustration in a

p; v-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428Fig. 18.5 The p; v; T-diagram: a Real fluid, b Ideal gas. . . . . . . . . . . . . . 430Fig. 18.6 The p; v; T-diagram: examples . . . . . . . . . . . . . . . . . . . . . . . . . 432

List of Figures xxix

Fig. 18.7 Possible projections of the p; v; T-state space . . . . . . . . . . . . . . 434Fig. 18.8 The p; T-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435Fig. 18.9 The p; T-diagram: a Water, b Non-water fluid . . . . . . . . . . . . . 435Fig. 18.10 The T ; v-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436Fig. 18.11 The p; v-diagram for water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437Fig. 18.12 Closed system—Isothermal expansion . . . . . . . . . . . . . . . . . . . 438Fig. 18.13 Isothermal expansion (1) to (4) in a p; v-diagram . . . . . . . . . . . 438Fig. 18.14 Lever rule of the quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . 441Fig. 18.15 Van der Waals approach for CO2 . . . . . . . . . . . . . . . . . . . . . . . 444Fig. 18.16 Isobaric vaporisation: a reversible, b irreversible . . . . . . . . . . . 454Fig. 18.17 Isobaric vaporisation of water. . . . . . . . . . . . . . . . . . . . . . . . . . 456Fig. 18.18 Specific enthalpy of vaporisation Dhv of water. . . . . . . . . . . . . 458Fig. 18.19 T ; s-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459Fig. 18.20 T ; s-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460Fig. 18.21 h; s-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460Fig. 18.22 log p; h-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461Fig. 18.23 Technical work in the h; s-diagram. . . . . . . . . . . . . . . . . . . . . . 461Fig. 18.24 Isobaric, isothermal, reversible change of state . . . . . . . . . . . . . 463Fig. 18.25 Isochoric change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464Fig. 18.26 Adiabatic change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466Fig. 18.27 Clausius–Clapeyron relation . . . . . . . . . . . . . . . . . . . . . . . . . . . 466Fig. 18.28 Vapour pressure curve of water . . . . . . . . . . . . . . . . . . . . . . . . 468Fig. 18.29 Adiabatic throttling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469Fig. 18.30 Adiabatic throttling (Joule Thomson effect) . . . . . . . . . . . . . . . 472Fig. 18.31 Adiabatic throttling of air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Fig. 18.32 Solution to Problem 18.11e . . . . . . . . . . . . . . . . . . . . . . . . . . . 478Fig. 18.33 Solution to Problem 18.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479Fig. 19.1 Isobaric, isothermal mixing of two gases according

to Dalton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484Fig. 19.2 Gas constant of a mixture of ideal gases . . . . . . . . . . . . . . . . . 489Fig. 19.3 Adiabatic mixing closed system—Exemplary for n ¼ 3

components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493Fig. 19.4 Adiabatic mixing open system—Exemplary for n ¼ 3

components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494Fig. 19.5 Irreversibility of mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496Fig. 19.6 Irreversibility of mixing—Analogous model. . . . . . . . . . . . . . . 496Fig. 19.7 Thought experiment for a reversible, isothermal mixing,

pistons replace separating wall in Fig. 19.1 . . . . . . . . . . . . . . . 496Fig. 19.8 Sketch to Problem 19.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504Fig. 20.1 Humid air—composition of the gaseous mixture of dry

air and vapour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508Fig. 20.2 p; T-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509Fig. 20.3 Humid air—Example 1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515Fig. 20.4 Humid air—Example 2/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

xxx List of Figures

Fig. 20.5 How to treat the water in humid air—vapour . . . . . . . . . . . . . . 525Fig. 20.6 How to treat the water in humid air—liquid. . . . . . . . . . . . . . . 525Fig. 20.7 How to treat the water in humid air—ice . . . . . . . . . . . . . . . . . 526Fig. 20.8 How to treat the water in humid air—vapour . . . . . . . . . . . . . . 530Fig. 20.9 How to treat the water in humid air—liquid. . . . . . . . . . . . . . . 530Fig. 20.10 How to treat the water in humid air—ice . . . . . . . . . . . . . . . . . 531Fig. 20.11 Unsaturated humid air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532Fig. 20.12 Saturated humid air and liquid water . . . . . . . . . . . . . . . . . . . . 533Fig. 20.13 Saturated humid air and solid water . . . . . . . . . . . . . . . . . . . . . 533Fig. 20.14 Saturated humid air, liquid and solid water . . . . . . . . . . . . . . . 534Fig. 20.15 Solution to Problem 20.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536Fig. 20.16 Sketch to Problem 20.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536Fig. 20.17 Mollier h1þ x; x-diagram—schematic . . . . . . . . . . . . . . . . . . . . . 542Fig. 20.18 Heating ð1Þ ! ð2Þ and cooling ð1Þ ! ð3Þ at constant water

content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544Fig. 20.19 Dehumidification of air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547Fig. 20.20 Adiabatic mixing of humid air . . . . . . . . . . . . . . . . . . . . . . . . . 549Fig. 20.21 Adiabatic mixing of humid air, h1þ x; x-diagram. . . . . . . . . . . . 550Fig. 20.22 Adiabatic mixing of humid air, h1þ x; x-diagram. . . . . . . . . . . . 552Fig. 20.23 Humidification of air with pure water. . . . . . . . . . . . . . . . . . . . 553Fig. 20.24 Humidification of air with pure water. . . . . . . . . . . . . . . . . . . . 555Fig. 20.25 Adiabatic saturation temperature. . . . . . . . . . . . . . . . . . . . . . . . 557Fig. 20.26 Adiabatic saturation temperature. . . . . . . . . . . . . . . . . . . . . . . . 559Fig. 20.27 Psychrometer (wet-and-dry-bulb thermometer) . . . . . . . . . . . . . 560Fig. 20.28 The h1þ x; x–diagram - p 6¼ 1 bar . . . . . . . . . . . . . . . . . . . . . . . 561Fig. 20.29 Solution to Problem 20.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564Fig. 20.30 Technical layout to Problem 20.11 . . . . . . . . . . . . . . . . . . . . . . 564Fig. 20.31 Solution to Problem 20.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565Fig. 21.1 Steady state flow process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572Fig. 21.2 Incompressible flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574Fig. 21.3 Adiabatic flow with A 6¼ const. . . . . . . . . . . . . . . . . . . . . . . . . 576Fig. 21.4 Adiabatic flow with A 6¼ const. . . . . . . . . . . . . . . . . . . . . . . . . 576Fig. 21.5 Adiabatic diffusor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577Fig. 21.6 Adiabatic diffusor in a h; s-diagram . . . . . . . . . . . . . . . . . . . . . 579Fig. 21.7 Adiabatic nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580Fig. 21.8 Adiabatic nozzle in a h; s-diagram . . . . . . . . . . . . . . . . . . . . . . 581Fig. 21.9 Velocity of sound a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584Fig. 21.10 Adiabatic, frictional tube flow (A ¼ const.) . . . . . . . . . . . . . . . 589Fig. 21.11 Subsonic Fanno-curves, ideal gas with j ¼ const. . . . . . . . . . . 590Fig. 21.12 Subsonic Fanno-curves for one mass flux density, ideal

gas with j ¼ const. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591Fig. 21.13 Supersonic Fanno-curves, ideal gas with j ¼ const. . . . . . . . . 591Fig. 21.14 Supersonic Fanno-curves for one mass flux density, ideal

gas with j ¼ const. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592

List of Figures xxxi

Fig. 21.15 Non-adiabatic, frictionless tube flow (A ¼ const.). . . . . . . . . . . 597Fig. 21.16 Subsonic Rayleigh-curves for heating, ideal gas

with j ¼ const. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598Fig. 21.17 Subsonic Rayleigh-curves for one mass flux density

and heating, ideal gas with j ¼ const. . . . . . . . . . . . . . . . . . . . 598Fig. 21.18 Rayleigh correlation (subsonic), p; v-diagram . . . . . . . . . . . . . . 599Fig. 21.19 Polytropic exponent—a subsonic, b supersonic . . . . . . . . . . . . 599Fig. 21.20 Supersonic Rayleigh-curves for heating, ideal gas

with j ¼ const. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600Fig. 21.21 Supersonic Rayleigh-curves for one mass flux density

and heating, ideal gas with j ¼ const. . . . . . . . . . . . . . . . . . . . 601Fig. 21.22 Rayleigh correlation (supersonic), p; v-diagram . . . . . . . . . . . . 602Fig. 21.23 Normal shock, adiabatic tube flow . . . . . . . . . . . . . . . . . . . . . . 605Fig. 21.24 Steady flow from vessels according to [1] . . . . . . . . . . . . . . . . 606Fig. 21.25 Local flow function Ω for j ¼ 1:4, state (0) in rest . . . . . . . . . 611Fig. 21.26 Converging nozzle scenarios I/II . . . . . . . . . . . . . . . . . . . . . . . 611Fig. 21.27 Converging nozzle scenarios II/II . . . . . . . . . . . . . . . . . . . . . . . 612Fig. 21.28 Overview subsonic/supersonic flows . . . . . . . . . . . . . . . . . . . . 617Fig. 21.29 Steady flow from vessels using a Laval-nozzle. . . . . . . . . . . . . 618Fig. 21.30 Pressure characteristic Laval-nozzle . . . . . . . . . . . . . . . . . . . . . 618Fig. 21.31 (a) Venturi-nozzle, (f) Supersonic flow . . . . . . . . . . . . . . . . . . 621Fig. 21.32 Supersonic exit Laval-nozzle (a) isentropic,

(b) polytropic/adiabatic, i.e. with friction . . . . . . . . . . . . . . . . . 622Fig. 21.33 Supersonic exit Laval-nozzle, T; s-diagram. . . . . . . . . . . . . . . . 623Fig. 21.34 Laval-diffusor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623Fig. 22.1 Clockwise Carnot process: thermal engine . . . . . . . . . . . . . . . . 626Fig. 22.2 Clausius-Rankine cycle: sketch. . . . . . . . . . . . . . . . . . . . . . . . . 627Fig. 22.3 Clausius-Rankine cycle: a p; v-diagram, b T; s-diagram . . . . . . 627Fig. 22.4 Steam power process: boiler . . . . . . . . . . . . . . . . . . . . . . . . . . . 630Fig. 22.5 Steam power process: T ; s-diagram. . . . . . . . . . . . . . . . . . . . . . 631Fig. 22.6 Steam power process: h; s-diagram . . . . . . . . . . . . . . . . . . . . . . 631Fig. 22.7 Steam power process—expansion in the wet-steam region . . . . 634Fig. 22.8 Steam power process—reheating . . . . . . . . . . . . . . . . . . . . . . . 635Fig. 22.9 Steam power process—reheating . . . . . . . . . . . . . . . . . . . . . . . 635Fig. 22.10 Steam power process—a No feed water preheating,

b Regenerative feed water preheating . . . . . . . . . . . . . . . . . . . . 636Fig. 22.11 Steam power process—regenerative feed water preheating . . . . 636Fig. 22.12 Compression heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639Fig. 22.13 Compression heat pump—layout (left), T ; s-diagram

(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640Fig. 22.14 Compression heat pump—log p; h-diagram . . . . . . . . . . . . . . . 640Fig. 22.15 Absorption heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642Fig. 22.16 Solar cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642Fig. 22.17 Sketch to Problem 22.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643

xxxii List of Figures

Fig. 22.18 h; s-diagram to Problem 22.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 643Fig. 22.19 Entropy balance to Problem 22.1 . . . . . . . . . . . . . . . . . . . . . . . 648Fig. 22.20 a Sketch of the plant, b T; s-diagram to Problem 22.2 . . . . . . . 648Fig. 22.21 a Energy balance, b Entropy balance for the condenser . . . . . . 651Fig. 23.1 Fossil fuels according to [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . 656Fig. 23.2 Combustion process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657Fig. 23.3 Example of a solid fossil fuel . . . . . . . . . . . . . . . . . . . . . . . . . . 661Fig. 23.4 Exemplary gaseous fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669Fig. 23.5 Exemplary gaseous fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679Fig. 23.6 Condensing product water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683Fig. 23.7 Energy balance—Combustion chamber . . . . . . . . . . . . . . . . . . 694Fig. 23.8 Definition of the lower heating value HU . . . . . . . . . . . . . . . . . 695Fig. 23.9 Combustion—step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697Fig. 23.10 Combustion—step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698Fig. 23.11 Combustion—step 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699Fig. 23.12 Combustion—summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700Fig. 23.13 Condensation of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700Fig. 23.14 HUðT0Þ ! HUðTÞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703Fig. 23.15 Combustion with unsaturated humid air—summary . . . . . . . . . 704Fig. 23.16 Combustion with saturated humid air—summary . . . . . . . . . . . 705Fig. 23.17 Definition of the upper heating value H0 . . . . . . . . . . . . . . . . . 708Fig. 23.18 Combustion with saturated humid air—applying

the specific upper heating value . . . . . . . . . . . . . . . . . . . . . . . . 710Fig. 23.19 h; #-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715Fig. 23.20 Adiabatic flame temperature (dry air) . . . . . . . . . . . . . . . . . . . . 717Fig. 23.21 Combustion chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719Fig. 23.22 Combustion chamber—variation of ‚ . . . . . . . . . . . . . . . . . . . . 719Fig. 23.23 Influence of fuel-air equivalence ratio and air preheating

on the adiabatic flame temperature for oil according to [6] . . . 720Fig. 23.24 Solution to Problem 23.4b . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722Fig. 23.25 Sketch to Problem 23.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726Fig. 24.1 Enthalpy of reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743Fig. 24.2 Enthalpy of reaction at T0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743Fig. 24.3 Entropy and irreversibility of a reaction . . . . . . . . . . . . . . . . . . 745Fig. 24.4 First law of thermodynamics reactive closed system. . . . . . . . . 746Fig. 24.5 Second law of thermodynamics reactive closed system . . . . . . 749Fig. 24.6 Sketch to Problem 24.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 750Fig. 24.7 Gibbs enthalpy—Closed system . . . . . . . . . . . . . . . . . . . . . . . . 754Fig. 24.8 Gibbs enthalpy—Open system . . . . . . . . . . . . . . . . . . . . . . . . . 755Fig. 24.9 Exergy of a fossil fuel—Energy balance . . . . . . . . . . . . . . . . . 756Fig. 24.10 Exergy of a fossil fuel—Entropy balance . . . . . . . . . . . . . . . . . 759Fig. 24.11 Exergy of a fossil fuel—Exergy balance . . . . . . . . . . . . . . . . . 759Fig. 24.12 Mixing of two ideal gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767Fig. 24.13 Dynamic chemical reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 769

List of Figures xxxiii

Fig. 24.14 Chemical balancing driven by „i . . . . . . . . . . . . . . . . . . . . . . . 769Fig. C.1 log p; h-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802Fig. C.2 T ; s-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803Fig. C.3 h; s-diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804Fig. D.1 h1þ x; x-diagram (atmospheric airþwater) . . . . . . . . . . . . . . . . 806

xxxiv List of Figures

List of Tables

Table 3.1 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Table 3.2 Molar masses of relevant elements . . . . . . . . . . . . . . . . . . . . . 54Table 5.1 Exemplary combinations of state values for ideal gases in

thermodynamic equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 12.1 Isentropic exponent for ideal gases at standard conditions,

i.e. temperature # ¼ 0 °C according to DIN 1343 . . . . . . . . . . 226Table 12.2 Temperature dependency of an ideal gas according to

Problem 12.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Table 13.1 Polytropic change of state—Technical meaning for ideal

gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257Table 17.1 Overview thermodynamic cycles . . . . . . . . . . . . . . . . . . . . . . . 406Table 18.1 Triple/critical point of water . . . . . . . . . . . . . . . . . . . . . . . . . . 435Table 18.2 Further equations of state for real fluids . . . . . . . . . . . . . . . . . 442Table 20.1 Properties—Humid air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532Table 23.1 Simplified composition of dry, atmospheric air . . . . . . . . . . . . 663Table 23.2 Lower heating value HU (Solids and Liquids)

at #0 ¼ 25 °C, see [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696Table 23.3 Lower heating value HU (Gases) at #0 ¼ 25 °C, see [7] . . . . . 696Table 23.4 Averaged specific heat capacity cpj#0 in kJ

kgK, according

to [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702Table 23.5 Upper heating values H0 at #0 ¼ 25 °C, according to [7] . . . . 709Table 23.6 Upper heating values H0 (Gases) at #0 ¼ 25 °C, according

to [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 710Table 23.7 Composition of the combustion air . . . . . . . . . . . . . . . . . . . . . 723Table 23.8 Averaged specific heat capacities cpj#0 in kJ

kgK . . . . . . . . . . . . . . 723Table 23.9 Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725Table 24.1 Chemical composition of the standard atmosphere . . . . . . . . . 756Table A.1 Saturated liquid and saturated steam . . . . . . . . . . . . . . . . . . . . 771Table A.2 Specific volume v of water in m3

kg 1/2 . . . . . . . . . . . . . . . . . . . 775

xxxv

Table A.3 Specific volume v of water in m3

kg 2/2 . . . . . . . . . . . . . . . . . . . 777

Table A.4 Specific enthalpy h of water in kJkg 1/2. . . . . . . . . . . . . . . . . . . 779

Table A.5 Specific enthalpy h of water in kJkg 2/2. . . . . . . . . . . . . . . . . . . 781

Table A.6 Specific entropy s of water in kJkgK 1/2 . . . . . . . . . . . . . . . . . . 783

Table A.7 Specific entropy s of water in kJkgK 2/2 . . . . . . . . . . . . . . . . . . 785

Table A.8 Specific heat capacity cp of water in kJkgK 1/2 . . . . . . . . . . . . . 785

Table A.9 Specific heat capacity cp of water in kJkgK 2/2 . . . . . . . . . . . . . 786

Table B.1 Molar enthalpy and entropy of H2 at p0 ¼ 1 bar . . . . . . . . . . . 787Table B.2 Molar enthalpy and entropy of H at p0 ¼ 1 bar . . . . . . . . . . . . 788Table B.3 Molar enthalpy and entropy of O2 at p0 ¼ 1 bar . . . . . . . . . . . 788Table B.4 Molar enthalpy and entropy of O at p0 ¼ 1 bar . . . . . . . . . . . . 789Table B.5 Molar enthalpy and entropy of OH at p0 ¼ 1 bar . . . . . . . . . . 789Table B.6 Molar enthalpy and entropy of H2O(liq) . . . . . . . . . . . . . . . . . 790Table B.7 Molar enthalpy and entropy of H2O(g) at p0 ¼ 1 bar.

Water vapour is treated as an ideal gas . . . . . . . . . . . . . . . . . . 790Table B.8 Molar enthalpy and entropy of N2 at p0 ¼ 1 bar . . . . . . . . . . . 791Table B.9 Molar enthalpy and entropy of N at p0 ¼ 1 bar . . . . . . . . . . . . 791Table B.10 Molar enthalpy and entropy of NO at p0 ¼ 1 bar . . . . . . . . . . 792Table B.11 Molar enthalpy and entropy of NO2 at p0 ¼ 1 bar . . . . . . . . . . 792Table B.12 Molar enthalpy and entropy of CO at p0 ¼ 1 bar. . . . . . . . . . . 793Table B.13 Molar enthalpy and entropy of CO2 at p0 ¼ 1 bar . . . . . . . . . . 793Table B.14 Molar enthalpy and entropy of CGraphite at p0 ¼ 1 bar . . . . . . . 794Table B.15 Molar enthalpy and entropy of S at p0 ¼ 1 bar . . . . . . . . . . . . 794Table B.16 Molar enthalpy and entropy of S2 at p0 ¼ 1 bar . . . . . . . . . . . 795Table B.17 Molar enthalpy and entropy of SO at p0 ¼ 1 bar . . . . . . . . . . . 795Table B.18 Molar enthalpy and entropy of SO2 at p0 ¼ 1 bar . . . . . . . . . . 796Table B.19 Molar enthalpy and entropy of CH4 at p0 ¼ 1 bar . . . . . . . . . . 796Table B.20 Molar enthalpy and entropy of C2H6 at p0 ¼ 1 bar . . . . . . . . . 797Table B.21 Molar enthalpy and entropy of C3H8 at p0 ¼ 1 bar . . . . . . . . . 797Table B.22 Molar Enthalpy and Entropy of C2H5OH at p0 ¼ 1 bar . . . . . . 798Table B.23 Molar enthalpy and entropy of C2H5OH(liq). . . . . . . . . . . . . . 798Table B.24 Molar enthalpy and entropy of CH3OH at p0 ¼ 1 bar . . . . . . . 799Table B.25 Molar enthalpy and entropy of CH3OH(liq) . . . . . . . . . . . . . . 799Table B.26 Molar enthalpy and entropy of air at p0 ¼ 1 bar . . . . . . . . . . . 800

xxxvi List of Tables