Fundamentals, Instrumentation and Applications

www.wiley-vch.de

CalorimetryStefan M. Sarge, Günther W. H. Höhneand Wolfgang Hemminger

Sarge • Höhne • H

emm

ingerC

alorimetry

Clearly divided into three parts, this practical book begins by dealing with all funda-mental aspects of calorimetry. The second part looks at the equipment used and new developments. The third and final section provides measurement guidelines in order to obtain the best results. The result is optimized knowledge for users of this technique, supplemented with practical tips and tricks.

Stefan M. Sarge studied chemistry at the Braunschweig University of Technology. Since 1990 he has worked for the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, which is the National Metrology Institute of Germany providing scientific and technical services at the highest level of accuracy and reliability for the benefit of society as a whole, trade and industry, and science. He is the Head of the Working Group on Caloric Quantities and the author of several publications in the fields of thermal analysis, calorimetry and legal metrology. In 1990 and 2004 he received the Netzsch-GEFTA award.

Günther W. H. Höhne studied chemistry, physics and mathematics at the Technical University of Berlin. In 1997 he was appointed Privatdozent (Adj. Professor) after his habilitation in experimental physics. From 1970 until his retirement in 1999 he was Head of the Section for Calorimetry of the University of Ulm, with duties including academic teaching in physics. From 1999 to 2008 he was a visiting professor at the Eindhoven University of Technology. He has published numerous articles and two monographs on calorimetry and its applications. In 2002 he received the science award of the German Society of Thermal Analysis (GEFTA).

Wolfgang Hemminger studied physics at the University of Stuttgart and worked for a couple of years at the Braunschweig University in the field of materials science using calorimetry as one tool of research. In 1981 he joined the PTB and worked in the fields of thermal conductivity and various thermoanalytical methods. In 1989 he was appointed Head of the PTB Division “Thermodynamics and Explosion Protection”. He was co-editor of the journal Thermochimica Acta and is the author of numerous journal articles and books. In 1981 he received the Netzsch-GEFTA award and in 2006 the GEFTA science award.

Stefan M. Sarge

G€unther W. H. H€ohne

Wolfgang Hemminger

Calorimetry

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Stefan M. Sarge, G€unther W. H. H€ohneand Wolfgang Hemminger

Calorimetry

Fundamentals, Instrumentation and Applications

Authors

Dr. Stefan M. SargePhysikalisch-Technische BundesanstaltBundesallee 10038116 BraunschweigGermany

Dr. G€unther W. H. H€ohneMörikeweg 3088471 LaupheimGermany

Dr. Wolfgang HemmingerMalerweg 538126 BraunschweigGermany

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Contents

Preface XIIIList of Quantities and Units XV

Introduction Calorimetry: Definition, Application Fields and Units 1Definition of Calorimetry 1Application Fields for Calorimetry 1First Example from Life Sciences 2Second Example from Material Science 2Third Example from Legal Metrology 2Units 3Further Reading 4References 5

Part One Fundamentals of Calorimetry 7

1 Methods of Calorimetry 91.1 Compensation of the Thermal Effect 91.1.1 Compensation by a Phase Transition 91.1.2 Compensation by Electric Effects 121.2 Measurement of Temperature Differences 131.2.1 Measurement of Time-Dependent Temperature Differences 131.2.2 Measurement of Local Temperature Differences 151.2.2.1 First Example: Flow Calorimeter 151.2.2.2 Second Example: Heat Flow Rate Calorimeter 151.3 Summary of Measuring Principles 16

References 17

2 Measuring Instruments 192.1 Measurement of Amount of Substance 192.1.1 Weighing 202.1.2 Volume Measurement 20

jV

2.1.3 Pressure Measurement 212.1.4 Flow Measurement 212.2 Measurement of Electric Quantities 212.3 Measurement of Temperatures 222.3.1 Thermometers 232.3.1.1 Liquid-in-Glass Thermometers 232.3.1.2 Gas Thermometers 242.3.1.3 Vapor Pressure Thermometers 242.3.1.4 Resistance Thermometers 252.3.1.5 Semiconductors 262.3.1.6 Pyrometers 262.3.2 Thermocouples 272.4 Chemical Composition 29

References 29

3 Fundamentals of Thermodynamics 313.1 States and Processes 313.1.1 Thermodynamic Variables (Functions of State) 313.1.2 Forms of Energy, Fundamental Form, and Thermodynamic

Potential Function 343.1.2.1 Fundamental Form 353.1.2.2 Thermodynamic Potential Function 353.1.3 Equilibrium 383.1.4 Reversible and Irreversible Processes 413.1.5 The Laws of Thermodynamics 423.1.5.1 The Zeroth Law 423.1.5.2 The First Law 423.1.5.3 The Second Law 423.1.5.4 The Third Law 433.1.6 Measurement of Thermodynamic State Functions 433.2 Phases and Phase Transitions 473.2.1 Multiphase Systems 473.2.2 Phase Transitions 503.2.3 Gibbs Phase Rule 523.2.4 Measurement of Variables of State during Phase Transitions 56

References 59

4 Heat Transport Phenomena 614.1 Heat Conduction 614.2 Convection 644.3 Heat Radiation 654.4 Heat Transfer 674.5 Entropy Increase during Heat Exchange 674.6 Conclusions Concerning Calorimetry 68

References 71

VIj Contents

5 Surroundings and Operating Conditions 735.1 The Isothermal Condition 745.2 The Isoperibol Condition 755.3 The Adiabatic Condition 755.4 The Scanning Condition 76

Reference 79

6 Measurements and Evaluation 816.1 Consequences of Temperature Relaxation within the Sample 816.1.1 First Example: Chemical Reaction 816.1.2 Second Example: Biological System 826.1.3 Third Example: First-Order Phase Transitions 836.2 Typical Results from Different Calorimeters 866.2.1 Adiabatic Calorimeters 866.2.2 Isoperibol Calorimeters 896.2.3 Differential Scanning Calorimeters 936.3 Reconstruction of the True Sample Heat Flow Rate from the

Measured Function 1016.3.1 Reconstruction of the Temperature Field for Negative Times 1016.3.2 The Convolution Integral and Its Validity 1026.3.3 Solution of the Convolution Integral 1056.3.4 Obtaining the Apparatus Function 1066.3.5 Application Limits and Estimation of Uncertainty 1076.4 Special Evaluations 1096.4.1 Determination of the Specific Heat Capacity 1096.4.2 Determination of the Kinetic Parameters of a Chemical Reaction 1096.4.3 Determination of Phase Transition Temperatures 1116.4.4 Determination of Heats of Transition 1126.4.5 Determination of the Purity of a Substance 1146.5 Determination of the Measurement Uncertainty 115

References 121

Part Two Practice of Calorimetry 123

7 Calorimeters 1257.1 Functional Components and Accessories 1257.2 Heating Methods 1267.3 Cooling Methods 1267.4 Comments on Control Systems 1287.5 Thermostats 1317.6 On the Classification of Calorimeters 1317.7 On the Characterization of Calorimeters 1327.8 Isothermal Calorimeters 1347.8.1 Phase Transition Calorimeters 134

Contents jVII

7.8.1.1 First Example: Ice Calorimeter 1357.8.1.2 Second Example: Calorimeter with Liquid–Gas Phase Transition 1377.8.2 Isothermal Calorimeters with Electrical Compensation 1417.8.2.1 First Example: Calorimeter according to Tian 1427.8.2.2 Second Example: Isothermal Titration Calorimeter 1437.8.2.3 Third Example: Isothermal Flow Calorimeter 1447.9 Calorimeters with Heat Exchange between the Sample and

Surroundings 1447.9.1 Isoperibol Calorimeters with Uncontrolled Heat Exchange 1457.9.1.1 First Example: Classic Liquid (or Mixing) Calorimeter 1457.9.1.2 Second Example: Combustion Calorimeter 1487.9.1.3 Third Example: Drop Calorimeter 1517.9.2 Isoperibol Calorimeter with Controlled Heat Exchange 1547.9.2.1 First Example: Activity Monitor 1597.9.2.2 Second Example: Large-Volume Battery Calorimeter 1607.9.2.3 Third Example: Calvet Calorimeter 1617.9.2.4 Fourth Example: Whole-Body Calorimeter 1697.9.3 Isoperibol Flow Calorimeter 1707.9.3.1 First Example: The Picker Calorimeter 1757.9.3.2 Second Example: Flow Calorimeter for High-Pressure and High-

Temperature Measurements 1767.9.3.3 Third Example: Gas Combustion Calorimeter 1777.9.3.4 Fourth Example: Microchip Flow Calorimeter 1777.9.4 Calorimeters with Linear Temperature Change of the

Surroundings 1787.9.4.1 First Example: Heat Flow Differential Scanning Calorimeter 1797.9.4.2 Second Example: Power-Compensated Differential Scanning

Calorimeter 1837.9.4.3 Third Example: Privalov Calorimeter 1857.9.5 Calorimeters with Nonlinear Temperature Change of the

Surroundings 1867.9.5.1 First Example: Temperature-Modulated DSC 1877.9.5.2 Second Example: Stepscan Differential Scanning Calorimetry 1897.9.5.3 Third Example: Advanced Multifrequency TMDSC 1897.10 Adiabatic Calorimeters 1907.10.1 Calorimeters with a Thermally Isolated Sample 1907.10.1.1 First Example: Nernst Calorimeter 1917.10.1.2 Second Example: Low-Temperature Calorimeter 1927.10.1.3 Third Example: AC Calorimeter 1947.10.1.4 Fourth Example: 3v Technique 1957.10.1.5 Nernst’s Method with a Contactless Energy Supply 1967.10.2 Calorimeters with Zero Temperature Difference against the

Surroundings 1977.10.2.1 First Example: Adiabatic Reaction Calorimeter 1987.10.2.2 Second Example: Adiabatic Flow Calorimeter 199

VIIIj Contents

7.10.2.3 Third Example: Adiabatic Whole-Body Calorimeter 1997.10.2.4 Fourth Example: Adiabatic Scanning Calorimeter 2007.10.3 Quasi-adiabatic Calorimetry by Sudden Heat Events 2017.10.3.1 Example: Pulse Heating Calorimeter 2017.11 Other Calorimeters 2027.11.1 Reaction Calorimeters 2027.11.1.1 First Example: Reaction Calorimeter 2037.11.1.2 Second Example: Accelerating Rate Calorimeter (ARC) 2047.11.2 Special Calorimeters 2067.11.2.1 Photocalorimeters 2067.11.2.2 Pressure Calorimeters 2067.11.2.3 Pressure Perturbation Calorimeter 2067.11.2.4 Cement Calorimeter 207

References 207

8 Recent Developments 2138.1 Microchip Calorimetry 2148.1.1 First Example: Thin-Film Differential Scanning Calorimeter 2168.1.2 Second Example: Low-Temperature AC Nanocalorimeter 2178.2 Ultrafast Calorimetry 2178.2.1 First Example: Ultrafast Nanocalorimeter 2188.2.2 Second Example: Flash Differential Scanning Calorimeter 2208.3 Extreme Ranges of State 2208.3.1 High Pressure 2218.3.1.1 Example: Power-Compensated High-Pressure DSC 2228.3.2 High Temperature 2228.3.2.1 Example: Levitation Calorimetry on Nickel, Iron, Vanadium, and

Niobium 2238.3.3 Strong Magnetic Fields 2248.3.3.1 Example: Influence of Magnetic Fields on Point Defects 2248.3.4 Plasma Surroundings 2248.3.4.1 Example: Calibration Using a Laser Beam 2248.4 Calorimetry as an Analytical and Diagnostic Tool 2258.4.1 First Example: “Artificial Nose” 2258.4.2 Second Example: Infection Diagnostics 225

References 226

9 Calorimetric Measurements: Guidelines and Applications 2299.1 General Considerations 2299.1.1 Sensitivity (DX/Q or DX/DF) 2309.1.2 Noise (dQ or dF) 2309.1.3 Linearity (Xout¼K �Xin) and Linearity Error (dK/K) 2329.1.4 Apparatus Function (fapp(t)) 2329.1.5 Accuracy and Total Error ({Qmeasured – Qtrue}/Qtrue) 2339.1.6 Repeatability and Random Uncertainty (�DQ/Q) 235

Contents jIX

Conclusion 2359.2 Guidelines to Calorimetric Experiments 2359.2.1 Definition of the Problem to be Investigated 2369.2.2 Selection of the Proper Calorimeter 2379.2.2.1 Calorimeter Requirements 2379.2.2.2 Selection of the Calorimeter 2389.2.3 Testing of the Calorimeter 2399.2.3.1 Calibration 2399.2.3.2 Other Testing 2429.2.4 Performing the Experiment 2439.2.4.1 Preparation of the Sample 2439.2.4.2 Calorimetric Measurement 2449.2.4.3 Evaluation of the Measurement 2459.2.5 Interpretation of the Results 2459.2.6 Uncertainty Estimation 2469.3 Calorimetric Applications 2469.3.1 Example from Material Science 2479.3.1.1 Definition of the Problem to be Investigated 2479.3.1.2 Selection of the Calorimeter 2479.3.1.3 Calorimetric Experiments 2489.3.1.4 Evaluation of the Measurements 2489.3.1.5 Interpretation of the Results 2519.3.1.6 Uncertainty Estimation 2529.3.2 Examples from Biology 2569.3.2.1 Definition of the Problem to be Investigated 2569.3.2.2 Selection of the Proper Calorimeter 2569.3.2.3 Calorimetric Experiments 2579.3.2.4 Evaluation of the Results 2589.3.2.5 Calorimetry on Hornets 2589.3.2.6 Uncertainty Estimation 2599.3.3 Example from Medicine 2599.3.3.1 Definition of the Problem to be Investigated 2599.3.3.2 Selection of the Proper Calorimeter 2599.3.3.3 Calorimetric Experiment 2609.3.3.4 Evaluation of the Measurements 2609.3.3.5 Interpretation of the Results 2609.3.3.6 Uncertainty Estimation 2619.3.4 Example from Chemistry 2619.3.4.1 Definition of the Problem to be Investigated 2629.3.4.2 Selection of the Proper Calorimeter 2629.3.4.3 Calorimetric Experiment 2639.3.4.4 Evaluation of the Measurements 2639.3.4.5 Interpretation of the Results 2649.3.4.6 Uncertainty Estimation 2659.3.5 Example from Combustion Calorimetry 265

Xj Contents

9.3.5.1 Definition of the Problem to be Investigated 2659.3.5.2 Selection of the Proper Calorimeter 2659.3.5.3 Calorimetric Experiment 2679.3.5.4 Evaluation of the Measurements 2679.3.5.5 Interpretation of the Results 2689.3.5.6 Uncertainty Estimation 268

References 269

Index 271

Contents jXI

Preface

Fifty years ago, anyone interested in the measurement of heat had to build acalorimeter of his or her own. Thirty years ago, when the book “Calorimetry”1) wasoriginally published, the change from self-made calorimeters to instruments that areproduced commercially had just begun. This change has now been completed.Today a large variety of instruments are commercially available. Owing to newproduction techniques and particularly to the development of electronics andcomputers, these calorimeters permit accurate and reliable measurements withinshort intervals of time. It is not surprising, therefore, that calorimetry has become astandard measuring procedure in many branches of natural science as well as inproduction and quality control.This book is intended to help readers to understand the basics of calorimetry and

to find their way in the ever-growingmarket of commercial instruments. During thethree decades that have passed, huge progress in calorimetry has been madeconcerning the techniques and the instrumentation alike. Because of missingspecial literature or textbooks, there developed an increasing desire for anotherbasic monograph about calorimetry that would take these developments intoaccount. In the present book, we describe the state of the art of modern calorimetryand today’s instrumentation almost completely. Despite the risk that some of thecalorimeters described here will be obsolete in a few years, we decided not to denyreaders basic and concise information about all the apparatus that they can buytoday. Another objective of the new book is to promote the application of calorimetricprocedures in various fields of research, providing practical advice and examples forthis purpose.In accordance with these considerations, this book is intended for scientists

considering the use of calorimeters, senior students engaged in heat measurements,and technicians working in the field of thermal analysis or calorimetry.To achieve these objectives, we have written all the chapters and sections in such a

way as to emphasize principles and problems. The measuring examples andinstruments described were selected in accordance with this view. Crucial items,such as the evaluation of measuring curves, are treated in detail and with referenceto particular commercial calorimeters. Readers are instructed about criteria for the

1) Hemminger, W., H€ohne, G. (1984) Calorimetry. Fundamentals and Practice, Verlag Chemie, Weinheim.

jXIII

evaluation of calorimeters to enable them to select the ones that best suit theirpurposes. Sometimes we have included in our discussion classical calorimeters thatare no longer marketed as such but are perhaps available in an improved version.We have done this when necessary in order to explain certain principles or toshow special applications.For the same reason, numerous self-made calorimeters are described, and some

hints for their construction are given. For further details, readers are referred to theliterature. The information provided may be of value when certain experimentalrequirements are not met by commercial instruments or these instruments areoversized for the work involved.Because of the rapid progress of electronic measuring and control techniques as

well as data processing, we have made no attempt to cover these aspects in detail.We have not attempted to provide a comprehensive review of the special literature,but it is our hope that we have not overlooked any important instruments orprocedures. Regrettably, non-English literature could only be partly considered.

Braunschweig and Laupheim, 2013 Stefan M. SargeG€unther W. H. H€ohneWolfgang Hemminger

XIVj Preface

List of Quantities and Units

(Bold symbols describe vector quantities.)

Symbol Name Unit

a (Relative) activity 1a Reciprocal heat capacity K J�1

A Area m2

A Helmholtz energy JA Preexponential factor (m3 mol�1)n�1 s�1

b Half-width sc Constant (general) Dependsc Specific heat capacity J g�1 K�1

ci Sensitivity coefficient Output unit/input unitC Electric capacitance FC Heat capacity J K�1

Cc Convection coefficient W m�2 K�1

Cht Coefficient of heat transfer W m�2 K�1

d Degree of freedomd Distance me Error Same as corresponding quantitye Specific energy J kg�1

E Energy Jf Frequency s�1

f Force NF Fraction melted 1g Acceleration due to gravity

(9.81 m s�2)m s�2

G Gibbs energy JG Thermal conductance W K�1

h Specific enthalpy J kg�1

H Enthalpy JHs,V Volumetric superior calorific value kWh m�3

jXV

I Electric current AJ Heat flux W m�2

Jq Heat flux field W m�2

k Coverage factork Rate constant (m3 mol�1)n�1 s�1

k0 Preexponential factor (m3 mol�1)n�1 s�1

K Calibration factor Output unit / input unitK Missing heat of fusion JK12 Empirical radiation exchange

coefficientm�2

KF Heat flow calibration factor 1 or W K�1

KQ Heat calibration factor 1 or J K�1 s�1

l Length mL Angular momentum J sm Mass kgM Molar mass kg mol�1

n Amount of substance moln Order of reaction 1N Number of entities 1NGr Grashof number 1p Pressure Pap Momentum kg m s�1

P Power Wq Electric charge Cq Specific heat J kg�1

Q Electric charge CQ Heat Jr Correlation coefficient 1r Position vector mR Electric resistance V

R Molar gas constant((8.3144621�0.0000075)J K�1 mol�1)

J K�1 mol�1

Rth Thermal resistance K W�1

s Standard deviation Same as corresponding quantityS Entropy J K�1

S Seebeck coefficient V K�1

t Time sT Temperature K (or �C)u Uncertainty Same as corresponding quantityU Voltage VU Internal energy Jv flow rate m3 s�1

v Velocity m s�1

XVIj List of Quantities and Units

V Volume m3 (or l)wc Degree of cystallinity 1W Work Jx Mole fraction 1x Position coordinate (general) m

Greek Symbols

a Cubic expansion coefficient K�1

a Degree of reaction 1b Heating rate K s�1 (or K min�1)hdyn Dynamic viscosity Pa sl Thermal conductivity W m�1 K�1

m Chemical potential J mol�1

w Phase shift radf Electric potential VF Heat flow rate WP Peltier coefficient Vr Density kg m�3 (or g cm�3)s Standard deviation Same as corresponding quantitys Surface tension J m�2

sB Stefan–Boltzmann constant((5.670373�0.000021)� 10�8 W m�2 K�4)

Wm�2 K�4

q Temperature �CQ Temperature �Ct Time constant sv Angular velocity rad s�1

v Angular frequency rad s�1

Indices and Subscripts

A Amplitudeact Activationam Amorphapp ApparatusC Containercal Calorimeterclb Calibrationcomb Combustioncond Condensatecryst Crystallizedeff Effective

List of Quantities and Units jXVII

el Electricexp ExperimentalF Furnace (surroundings)F Final statefin Final statefus Fusiong Glass transitionI InflectionI Initial Statein Inletini Initial stateliq LiquidM Measuring systemm Molarmax Maximumn Standard conditionsout Outputp At constant pressurer Reactionref Reference stateR ReferenceRp Responses SuperiorS SampleS Surfacesln SolutionT At constant temperatureth Thermaltrs TransitionV At constant volumevap Vapor, vaporizationw WaterW Wall

XVIIIj List of Quantities and Units

IntroductionCalorimetry: Definition, Application Fields and Units

Definition of Calorimetry

Calorimetry means the measurement of heat. In the past, the term heat wasassociated with various concepts. Nowadays one no longer speaks of differentenergies (e.g., heat energy, electrical energy, and kinetic energy) coexisting in asubstance or system independent of one another. According to the modern view,there is only one single energy (the internal energy) stored in a body, which – onlyduring an exchange – appears in a variety of energy forms such as heat energy,electrical energy, or kinetic energy. Accordingly, the form of energy known as heatcan only be conceived as coupled with a change of energy. Heat is always associatedwith a heat flow. In other words, heat is the amount of energy exchanged within agiven time interval in the form of a heat flow. Calorimeters are the instruments usedfor measuring this heat.

Application Fields for Calorimetry

Calorimetry has been well known for centuries as a very effective method innatural sciences. The precise measurement of heat capacity, heat of fusion,heat of reaction, heat of combustion, and other caloric quantities has built thebasis for progress in thermodynamics and classical physical chemistry. Theclassical methods of calorimetry have not changed very much during the pastcentury, and the scientific interest in and the knowledge about them havedropped accordingly. Only the progress in microelectronics and computerscience during the past few decades has made it possible to develop new typesof calorimeters and open new fields of application. As a result, there is now anincreasing interest in calorimetry as a very easy and powerful method fordifferent kinds of investigation.Modern calorimetry is successfully used in many fields, such as material science,

life sciences (biology, medicine, and biochemistry), pharmacy, and food science, forquality control, safety investigations, and the determination of the energy contentof fuels. Some examples illustrating this are presented below.

Calorimetry: Fundamentals, Instrumentation and Applications, First Edition.Stefan M. Sarge, G€unther W. H. H€ohne, and Wolfgang Hemminger.� 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.

1

First Example from Life Sciences

Disregarding, for example, frictional heat, every living organism produces heatbecause of the chemical reactions involved in the metabolism of the cells.Depending on the temperature and other parameters (atmosphere, nutrients, andrespiration), the heat production differs. If the temperature and the surroundingsare kept constant, the heat production remains constant, too. Different micro-biological organisms such as microbes and bacteria may produce differentamounts of heat, but a single cell produces – under the above conditions – acharacteristic amount of heat. If this quantity is known for certain organisms – say,bacteria – it is possible with a microcalorimeter to determine the amount ofbacteria in a sample from the heat flow rate they produce (approximately 1–3 pWper cell, James, 1987). Furthermore, it was shown that the heat flow–time profilesof bacteria in a suitable nutrient solution are very specific and can be used toidentify a bacterial species with a microcalorimeter much faster (within 15–24 h)than with a traditional culture medium (Trampuz et al., 2007). Possible applicationsof this calorimetric method could be the quick testing of the possible contamina-tion of donated blood products or the faster identification of the bacterium causingblood poisoning and the more successful treatment of very dangerous sepsis.

Second Example from Material Science

Polymer processing frequently implies molding of nonamorphous polymers thatoften crystallize partially on cooling. Unfortunately, crystallization changes thematerial properties of certain polymers dramatically for the worse and shouldtherefore be avoided. This can be achieved by quick cooling into a supercooledstate (below the crystallization range). To investigate the crystallization behaviorof such polymers, quick heating and quick cooling are required. Unfortunately,the heating and cooling rates of differential scanning calorimeters (DSCs) arelimited to less than 100 Kmin�1 because of the thermal inertia of theequipment. For many polymers, this is not fast enough to avoid crystallizationand to come to a really amorphous state. To overcome this problem, so-calledchip calorimeters have recently been developed with the help of modern chipprocessing technology. Such ultrasmall calorimeters have a very small mass andvery good thermal conductivity and, therefore, nearly no thermal inertia. Thevery low time constants of such calorimeter chips together with very small (1 ng)and very thin (10 mm) samples allow heating and cooling rates up to 106 K s�1

(Minakov et al., 2007). At heating and cooling rates higher than 103 K s�1,recrystallization can be avoided for several polymers, and the melting kineticsalong with the superheating behavior and their influence on material propertiescan be investigated with such a chip calorimeter.

Third Example from Legal Metrology

The commercial value of fuels in general and fuel gases in particular dependson the amount of energy contained in a given amount of fuel. Traditionally, thisamount of energy per unit amount, the calorific value, has been determined bygas calorimetry (Hyde and Jones, 1960). In recent times, gas chromatography

2 Introduction Calorimetry: Definition, Application Fields and Units

has been used to infer the calorific value of natural gas from its composition.But biogases and other nonconventional fuel gases such as landfill gas andshale gas contain components not included in natural gas. As a consequence,gas chromatography fails or becomes prohibitively expensive. As a simple,quick, and cheap method for the determination of the calorific value of suchgases, gas calorimetry is again applied, this time computer controlled and fullyautomatically (Haug and Mrozek, 1998). In this particular calorimeter, fuel gasflow and combustion airflow are controlled by nozzles. The two gas streams aremixed and burned. The resulting heat is transferred to a constant flow of air,whose temperature is measured at the entrance and the exit of the heatexchanger. This temperature increase is a measure of the energy content of thegas. To account for the influence of different fuel gas properties on the flowthrough the nozzle, the density of the gas is measured and used for convertingthe primary output of the calorimeter, the Wobbe number, to the desiredquantity, the inferior calorific value of the fuel gas.

Units

As illustrated by the earlier examples, there is no direct method for themeasurement of heat. Consequently, heat has to be determined by means of itseffects. The older unit quantity of heat – the calorie – was therefore defined interms of a measurement instruction:One 15 �C calorie (cal15� ) is the amount of heat required to raise the temperature

of 1 g of water from 14.5 to 15.5 �C under standard atmospheric pressure.1)

Because heat is merely one form of energy, as are the electrical and mechanicalenergies (Mayer, 1842; Joule, 1843; Colding, 1843, according to Dahl, 1963), aspecial unit for heat is unnecessary. Today, in the International System of Units(SI), heat is expressed in the unit of energy:

1 J ¼ 1 Nm ¼ 1Ws

Conversion between the old unit (cal) and new SI unit (J) is made as follows:

1 cal ¼ 4:1868 J; 1 J ¼ 0:2388459 cal

The latter is the International Steam Table calorie (calIT), one of the two “calories”still in use of a number of older calories (e.g., the “15 �C water calorie”corresponding to 0.9996801 calIT) (Stille, 1961).The second calorie still in use in some parts of the world is the US National

Bureau of Standards calorie (calNBS or calthermochem):

1 calNBS ¼ 4:1840 J ðexactlyÞ; 1 J ¼ 0:239006 calNBS

1) Temperature is treated here as a directly measurable quantity, which, strictly speaking, is not thecase.

Introduction Calorimetry: Definition, Application Fields and Units 3

Further Reading

Numerous monographs on calorimetry have beenpublished:

Brown, M.E. (ed.) (1998)Handbook of ThermalAnalysis and Calorimetry, vol. 1, Principles andPractice, Elsevier, Amsterdam.

Brown, M.E. and Gallagher, P.K. (eds) (2003)Handbook of Thermal Analysis and Calorimetry,vol. 2, Applications to Inorganic andMiscellaneous Materials, Elsevier, Amsterdam.

Brown, M.E. and Gallagher, P.K. (eds) (2008)Handbook of Thermal Analysis and Calorimetry,vol. 5, Recent Advances, Techniques andApplications, Elsevier, Amsterdam.

Calvet, E. and Prat, H. (1963) Recent Progress inMicrocalorimetry, Pergamon Press, Oxford.

Cheng, S.Z.D. (ed.) (2002)Handbook ofThermal Analysis and Calorimetry, vol. 3,Applications to Polymers and Plastics, Elsevier,Amsterdam.

Eder, F.X. (1983) Arbeitsmethoden derThermodynamik, Bd. II, Thermische undkalorische Stoffeigenschaften, Springer, Berlin.

Eucken, A. (1929) Energie- und W€armeinhalt,inHandbuch der Experimentalphysik, Band 8,1. Teil (eds W. Wien and F. Harms),Akademische Verlagsgesellschaft,Leipzig.

Goodwin, A.R.H., Marsh, K.N., and Wakeham,W.A. (eds) (2003) ExperimentalThermodynamics, vol. 6, Measurement of theThermodynamic Properties of Single Phases,Elsevier, Amsterdam.

Haines, P.J. (ed.) (2002) Principles of ThermalAnalysis and Calorimetry, The Royal Societyof Chemistry, Cambridge.

H€ohne, G.W.H., Hemminger, W.F., andFlammersheim, H.-J. (2003) DifferentialScanning Calorimetry, 2nd edn, Springer,Berlin.

Hyde, C.G. and Jones, M.W. (1960)Gas Calorimetry, 2nd edn, Ernest Benn,London.

Kemp, R.B. (ed.) (1999)Handbook of ThermalAnalysis and Calorimetry, vol. 4, FromMacromolecules to Man, Elsevier, Amsterdam.

LeNeindre, B. and Vodar, B. (eds) (1975)Experimental Thermodynamics, vol. 2,Experimental Thermodynamics of Non-ReactingFluids, Butterworths, London.

Marsh, K.N. and O’Hare, P.A.G. (eds) (1994)Experimental Thermodynamics, vol. 4, Solution

Calorimetry, Blackwell Scientific Publications,Oxford.

McCullough, J.P. and Scott, D.W. (eds) (1968)Experimental Thermodynamics, vol. 1,Calorimetry of Non-Reacting Systems,Butterworths, London.

Rossini, F.D. (ed.) (1956) ExperimentalThermochemistry. Measurement of Heats ofReaction. Interscience Publishers, New York.

Roth, W.A. and Becker, F. (1956)Kalorimetrische Methoden zur Bestimmungchemischer Reaktionswärmen, FriedrichVieweg & Sohn, Braunschweig.

Sengers, J.V., Kayser, R.F., Peters, C.J., andWhite, H.J., Jr. (eds) (2000) ExperimentalThermodynamics, vol. 5, Equations of State forFluids and Fluid Mixtures, Elsevier,Amsterdam.

Skinner, H.A. (ed.) (1962) ExperimentalThermochemistry, vol. II, IntersciencePublishers, New York.

Sorai, M. (ed.) (2004) Comprehensive Handbookof Calorimetry and Thermal Analysis, JohnWiley & Sons, New York.

Sunner, S. and Ma�nsson, M. (eds) (1979)

Experimental Chemical Thermodynamics,vol. 1, Combustion Calorimetry, PergamonPress, Oxford.

Swietoslawski, W. (1946)Microcalorimetry,Reinhold Publishing Corp.,New York.

Wakeham, W.A., Nagashima, A., andSengers, J.V. (eds) (1991) ExperimentalThermodynamics, vol. 3, Measurementof the Transport Properties of Fluids,Blackwell Scientific Publications, Oxford.

Weber, H. (1973) Isothermal Calorimetry, PeterLang, Frankfurt.

Weir, R.D. and de Loos, Th.W. (eds) (2005)Experimental Thermodynamics, vol. 7,Measurement of the Thermodynamic Propertiesof Multiple Phases, Elsevier, Amsterdam.

White, W.P. (1928) The Modern Calorimeter,American Chemical Society MonographSeries No. 42, The Chemical CatalogCompany, New York.

Zielenkiewicz, W. and Margas, E. (2002) Theoryof Calorimetry, Kluwer, Academic Publ.Dordrecht.

Many physics books contain separate chaptersdedicated to calorimetry:

4 Introduction Calorimetry: Definition, Application Fields and Units

Magli�c, K.D., Cezairliyan, A., and Peletsky, V.E.(1984) Compendium of ThermophysicalProperty Measurement Methods, vol. 1, Surveyof Measurement Techniques, Plenum Press,New York, pp. 457–685.

Magli�c, K.D., Cezairliyan, A., andPeletsky, V.E. (1992) Compendium ofThermophysical Property MeasurementMethods, vol. 2, Recommended MeasurementTechniques and Practices, PlenumPress, New York, pp. 409–545.

Oscarson, J.L. and Izatt, R.M. (1986)Calorimetry, in Physical Methods of Chemistry,vol. VI, Determination of ThermodynamicProperties (eds B.W. Rossiter and R.C.Baetzold), 2nd edn, Wiley-Interscience,New York, pp. 573–620.

Spink, H. and Wads€o, I. (1976) Calorimetry asan analytical tool in biochemistry and biology,in Methods of Biochemical Analysis, vol. 23 (ed.D. Glick), John Wiley & Sons, New York,pp. 1–159.

Warrington, S.B. and H€ohne, G.W.H. (2008)Thermal analysis and calorimetry,in Ullmann’s Encyclopedia of IndustrialChemistry, Wiley-VCH, Weinheim.

Monographs on calorimetry with referenceto special topics:

Beezer, A.E. (ed.) (1980) BiologicalMicrocalorimetry, Academic Press,London.

KaletunSc , G. (ed.) (2009) Calorimetry in FoodProcessing: Analysis and Design of FoodSystems, Wiley-Blackwell, Ames.

Koch, E. (1977) Non-IsothermalReaction Analysis, Academic Press,London.

Kubaschewski, O. and Alcock, C.B. (1979)Metallurgical Thermochemistry, 5th edn,Pergamon Press, Oxford.

Ladbury, J.E. and Doyle, M.L. (eds) (2004)Biocalorimetry 2: Applications of Calorimetry inthe Biological Sciences, John Wiley & Sons,New York.

Three series of international conferences dedicatedto calorimetry take place regularly. Theirpresentations are partly published in special issuesof different journals or as separate proceedings:

The European Conference on ThermalAnalysis and Calorimetry.

The International Conference on ChemicalThermodynamics (until 2006 known asIUPAC Conference on ChemicalThermodynamics).

The International Conference on ThermalAnalysis and Calorimetry.

Several journals publish original contributions onthermal analysis, calorimetry, and experimentalthermodynamics:

International Journal of Thermophysics(Springer, Berlin).

Journal of Thermal Analysis and Calorimetry(Springer, Berlin).

Journal of Chemical Thermodynamics (Elsevier,Amsterdam).

Netsuo Sokutei (Calorimetry and ThermalAnalysis) (Nihon Netsu Sokutei Gakkai,Tokyo).

Thermochimica Acta (Elsevier,Amsterdam).

References

Dahl, F. (1963) Ludvig A. Colding andthe conservation of energy. Centaurus,8, 174–188.

Haug, T. and Mrozek, C. (1998)Temperaturstabilit€at undAnzeigegeschwindigkeit beiVerbrennungskalorimetern, gwf-GasErdgas, 139, 7–12. Union Instruments(2009) Data Sheet CWD20 05 w ww.u nion-instrume nts.com/ fi leadmi n/docum ents/Analysi s%20s yste ms/Data sheets /

CWD200 5_en_data sheet_ 2009_0 3.pdf(October 10, 2010).

Hyde, C.G. and Jones, M.W. (1960)Gas Calorimetry, 2nd edn, Ernest Benn,London.

James, A.M. (1987) Calorimetry, past, present,future, in Thermal and Energetic Studies ofCellular Biological Systems (ed. A.M. James),Wright, Bristol, p. 4.

Joule, J.P. (1843) On the calorific effects ofmagneto-electricity, and on the mechanical

References 5

value of heat. Philos. Mag., 23, 263–276,347–355, 435–443.

Mayer, J.R. (1842) Bemerkungen €uber dieKr€afte der unbelebten Natur. Ann. Chem.Pharm., 42, 233–240.

Minakov, A.A., van Herwaarden, A.W.,Wien, W., Wurm, A., and Schick, C. (2007)Advanced nonadiabatic ultrafastnanocalorimetry and superheatingphenomenon in linear

polymers. Thermochim. Acta, 461,96–106.

Stille, U. (1961)Messen und Rechnen in derPhysik, 2nd edn, Springer, Braunschweig,p. 113.

Trampuz, A., Salzmann, S., Antheaume, J., andDaniels, A.U. (2007) Microcalorimetry:a novel method for detection of microbialcontamination in platelet products.Transfusion, 47, 1643–1650.

6 Introduction Calorimetry: Definition, Application Fields and Units

Part One

Fundamentals of Calorimetry

Calorimetry: Fundamentals, Instrumentation and Applications, First Edition.Stefan M. Sarge, G€unther W. H. H€ohne, and Wolfgang Hemminger.� 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.

7

1

Methods of Calorimetry

This chapter provides a brief outline of the principles of heat measurement. Aclassification scheme will be developed on the basis of simple examples. A moredetailed treatment of the procedures and calorimeters involved can be found in thesecond part of the book.

1.1

Compensation of the Thermal Effect

The heat released from a sample during a process flows into the calorimeter andwould cause a temperature change of the latter as a measuring effect; this thermaleffect is continuously suppressed by compensating the respective heat flow. Themethods of compensation include the use of “latent heat” caused by a phasetransition, thermoelectric effects, heats of chemical reactions, a change in thepressure of an ideal gas (Ter Minassian and Milliou, 1983), and heat exchange witha liquid1) (Regenass, 1977). Because the last three methods are confined to specialcases, only the compensation by a physical heat of transition and by electric effectsare briefly discussed here.

1.1.1

Compensation by a Phase Transition

Around 1760, Black2) (Robison, 1803) realized that the heat delivered to melting iceserves for a transition from the solid to the liquid state at a constant temperature.Indeed, although the melting of ice requires a steady supply of heat, thetemperature of the ice–water mixture only begins to rise after all the ice has melted.Black is said to have been the first to have used this “latent heat of fusion” of ice forthe measurement of heat. His “phase transition calorimeter” was very simple. Heplaced a warm sample in a cavity inside a block of ice and sealed the cavity with an

1)For example, “Bench Scale Calorimeter” developed by Ciba-Geigy Ltd., Switzerland, andcommercialized by Mettler-Toledo (Schweiz) GmbH, Switzerland, as Reaction Calorimeter RC1.

2)Black only reported his findings verbally; see Encyclopaedia Britannica (2003) or Ramsay (1918).

9

Calorimetry: Fundamentals, Instrumentation and Applications, First Edition.Stefan M. Sarge, G€unther W. H. H€ohne, and Wolfgang Hemminger.� 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.

ice sheet. After the sample had assumed the temperature of ice, he determined themass of the melted ice by weighing.The principle of this method is that the heat DQ exchanged with the calorimeter

is not measured as a heat flow but causes a phase transition in a suitable substance(e.g., ice). If the specific heat of transition qtrs of the respective substance is known,the heat involved can be determined because it is proportional to the mass of thetransformed substance Dm:

DQ ¼ qtrs � DmThe mass of the transformed substance Dm is determined either directly byweighing or indirectly (e.g., by measuring the volume change due to the differencebetween the densities of the two phases).The first usable calorimeter involving a phase transition – the “ice calori-

meter” – was developed by Lavoisier and Laplace (1780). Figure 1.1 schemati-cally shows the design of this device. The sample chamber is completelysurrounded by a double-walled vessel containing pieces of ice. This inner icejacket is surrounded by a second double-walled vessel filled with an ice–watermixture (outer ice jacket). The whole system is in thermal equilibrium at 0 �C.The basic idea in this calorimeter is that the measuring system proper (i.e., theinner ice jacket) is insulated by the outer jacket, in which any disturbinginfluence of heat from the environment on the inner ice jacket is compensatedby an ice–water phase transition in the outer jacket. Only heat released insidethe sample chamber serves for the melting of ice in the inner ice jacket. Becausethere is no temperature difference between the inner and outer jackets, no heatexchange between them takes place. Lavoisier and Laplace designated themeasured heat as the “mass of melted ice.” The specific heat capacities of solidsand liquids, as well as heats of combustion and the production of heat byanimals, were measured this way. These measurements were carried out in

Working equation:

ΔQ = qtrs

· Δm

ΔQ Heat produced by

the sample

Δm Mass of molten ice

qtrs

Specific heat of

fusion of ice

To be determined ΔQ

To be measured Δm

Known qtrs

Air in Air out

Figure 1.1 Calorimeter of Lavoisier and Laplace (according to Kleiber, 1975).

10 1 Methods of Calorimetry