Physical Properties of Foods and Food Processing Systems

By M J Lewis

This book is an invaluable introduction to the physical properties of foods and the physics involved in food processing. It provides descriptions and data that are needed for selecting the most appropriate equipment in food technology and for making food processing calculations.

• Language: English
• Publisher: Elsevier Science
• Release date: Jan 1, 1990
• ISBN: 9781845698423

Book preview

Physical Properties of Foods and Food Processing Systems

First Edition

M.J. Lewis

Department of Food Science and Technology

University of Reading, UK

Woodhead Publishing Limited

Cambridge England

Table of Contents

Cover image

Title page

Copyright page

Preface

Dedication

Acknowledgements

1: Units and dimensions

1.1 INTRODUCTION

1.2 FUNDAMENTAL UNITS

1.3 MASS [M] (kg)

1.4 LENGTH [L] (m)

1.5 TIME[T](s)

1.6 TEMPERATURE [θ] (K)

1.7 OTHER FUNDAMENTALS

1.8 PREFIXES IN COMMON USE

1.9 DERIVED UNITS

1.10 AREA [L2] (m2)

1.11 VOLUME [L3] (m3)

1.12 DENSITY [ML− 3] (kg m− 3)

1.13 VELOCITY [LT− 1] (m s− 1)

1.14 MOMENTUM [MLT− 1] (kg m s− 1)

1.15 ACCELERATION [LT− 2] (m s− 2)

1.16 FORCE [MLT− 2](kg m s− 2 or N)

1.17 PRESSURE [ML− 1 T− 2] (kg m− 1 s− 2 or N m− 2)

1.18 WORK [ML2T− 2] (kg m2 s−2 or J)

1.19 POWER [ΜL2T− 3] (kg m2 s− 3 or W)

1.20 ENERGY [ML2T− 2] (J)

1.21 SUMMARY OF THE MAIN FUNDAMENTAL AND DERIVED UNITS

1.22 DIMENSIONAL ANALYSIS

1.23 Concentration

1.24 SYMBOLS

2: Density and Specific Gravity

2.1 INTRODUCTION

2.2 SOLID DENSITY

2.3 BULK DENSITY

2.4 LIQUID DENSITY AND SPECIFIC GRAVITY

2.5 GASES AND VAPOURS

2.6 DENSITY OF AERATED PRODUCTS: OVERRUN

2.7 SYMBOLS

3: Properties of fluids, hydrostatics and dynamics

3.1 INTRODUCTION

3.2 HYDROSTATICS

3.3 ARCHIMEDES’ PRINCIPLE

3.4 FACTORS AFFECTING FRICTIONAL LOSSES

3.5 STREAMLINE AND TURBULENT FLOW

3.6 THE REYNOLDS NUMBER IN AGITATED VESSELS

3.7 THE CONTINUITY EQUATION

3.8 BERNOULLI’S EQUATION

3.9 PRESSURE DROP AS A FUNCTION OF SHEAR STRESS AT A PIPE WALL

3.10 FRICTIONAL LOSSES

3.11 RELATIVE MOTION BETWEEN A FLUID AND A SINGLE PARTICLE

3.12 FLUID FLOW THROUGH PACKED AND FLUIDIZED BEDS

3.13 FLUID FLOW MEASUREMENT

3.14 FLUID TRANSPORTATION AND PUMPING

3.15 VACUUM OPERATIONS

3.16 ASEPTIC OPERATIONS

3.17 AVERAGE RESIDENCE TIME

3.18 DISTRIBUTION OF RESIDENCE TIMES

3.19 CONTINUOUS STIRRED-TANK REACTOR

3.20 FLOWABILITY OF POWDERS

3.21 SYMBOLS

4: Viscosity

4.1 INTRODUCTION

4.2 IDEAL SOLIDS AND LIQUIDS

4.3 SHEAR STRESS AND SHEAR RATE

4.4 NEWTONIAN FLUIDS AND DYNAMIC VISCOSITY

4.5 KINEMATIC VISCOSITY

4.6 RELATIVE AND SPECIFIC VISCOSITIES

4.7 NON-NEWTONIAN BEHAVIOUR

4.8 TIME-INDEPENDENT FLUIDS

4.9 TIME-DEPENDENT FLUIDS

4.10 THE POWER LAW EQUATION

4.11 METHODS FOR DETERMINING VISCOSITY

4.12 ROTATIONAL VISCOMETERS

4.13 VISCOMETER SELECTION

4.14 VISCOSITY DATA

4.15 SOME SENSORY ASPECTS

4.16 SYMBOLS

5: Solid rheology and texture

5.1 INTRODUCTION

5.2 THE PERCEPTION OF TEXTURE

5.3 TEXTURE ASSESSMENT BY SENSORY METHODS

5.4 TEXTURE EVALUATION BY INSTRUMENTAL METHODS

5.5 FUNDAMENTAL PROPERTIES

5.6 VISCOELASTIC BEHAVIOUR

5.7 GELATION

5.8 MODEL SYSTEMS

5.9 OBJECTIVE TEXTURE MEASUREMENT: EMPIRICAL TESTING

5.10 SIZE REDUCTION AND GRINDING

5.11 EXPRESSION

5.12 SYMBOLS

6: Surface properties

6.1 INTRODUCTION

6.2 SURFACE TENSION

6.3 SURFACE ACTIVITY

6.4 TEMPERATURE EFFECTS

6.5 METHODS FOR MEASURING SURFACE TENSION

6.6 INTERFACIAL TENSION

6.7 WORK OF ADHESION AND COHESION

6.8 EMULSIONS

6.9 YOUNG’s EQUATION (SOLID/LIQUID EQUILIBRIUM)

6.10 DETERGENCY

6.11 FOAMING

6.12 WETTABILITY AND SOLUBILITY

6.13 STABILIZATION (DISPERSION AND COLOUR)

6.14 OTHER UNIT OPERATIONS

6.15 SYMBOLS

7: Introduction to thermodynamic and thermal properties of foods

7.1 INTRODUCTION

7.2 CONSERVATION AND CONVERSION OF ENERGY

7.3 THERMAL ENERGY AND THERMAL UNITS

7.4 THERMODYNAMIC TERMS

7.5 THE FIRST LAW OF THERMODYNAMICS

7.6 ENTHALPY

7.7 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS

7.8 DIAGRAMMATIC REPRESENTATION OF THERMODYNAMIC CHANGES

7.9 THE CARNOT CYCLE

7.10 HEAT OR ENERGY BALANCES

7.11 ENERGY VALUE OF FOOD

7.12 ENERGY CONSERVATION IN FOOD PROCESSING

7.13 SYMBOLS

8: Sensible and latent heat changes

8.1 INTRODUCTION

8.2 SPECIFIC HEAT

8.3 RELATIONSHIP BETWEEN SPECIFIC HEAT AND COMPOSITIONS

8.4 SPECIFIC HEAT OF GASES AND VAPOURS

8.5 DETERMINATION OF SPECIFIC HEAT OF MATERIALS (EXPERIMENTAL)

8.6 LATENT HEAT

8.7 BEHAVIOUR OF WATER IN FOODS DURING FREEZING

8.8 LATENT HEAT VALUES FOR FOODS (FUSION)

8.9 ENTHALPY–COMPOSITION DATA

8.10 OILS AND FATS: SOLID–LIQUID TRANSITIONS

8.11 DIFFERENTIAL THERMAL ANALYSIS AND DIFFERENTIAL SCANNING CALORIMETRY

8.12 DILATATION

8.13 SYMBOLS

9: Heat transfer mechanisms

9.1 INTRODUCTION

9.2 HEAT TRANSFER BY CONDUCTION

9.3 STEADY- AND UNSTEADY-STATE HEAT TRANSFER

9.4 THERMAL CONDUCTIVITY

9.5 HEAT TRANSFER THROUGH A COMPOSITE WALL

9.6 THERMAL CONDUCTIVITY OF FOODS

9.7 DETERMINATION OF THERMAL CONDUCTIVITY

9.8 THERMAL DIFFUSIVITY

9.9 PARTICULATE AND GRANULAR MATERIAL

9.10 HEAT TRANSFER BY CONVECTION (INTRODUCTION)

9.11 HEAT FILM COEFFICIENT

9.12 COMBINATION OF HEAT TRANSFER BY CONDUCTION AND CONVECTION

9.13 APPLICATION TO HEAT EXCHANGERS

9.14 DIRECT STEAM INJECTION

9.15 FOULING

9.16 EVAPORATOR DESIGN

9.17 HEAT TRANSFER BY RADIATION

9.18 RADIATION EMITTED FROM HEATED SURFACES

9.19 STEFAN’S LAW

9.20 INFRARED RADIATION

9.21 RADIO-FREQUENCY WAVES

9.22 IRRADIATION

9.23 SYMBOLS

10: Unsteady-state Heat Transfer

10.1 INTRODUCTION

10.2 HEAT TRANSFER TO A WELL-MIXED LIQUID

10.3 UNSTEADY-STATE HEAT TRANSFER BY CONDUCTION

10.4 HEAT TRANSFER INVOLVING CONDUCTION AND CONVECTION

10.5 THERMAL PROCESSING

10.6 COMMERCIAL STERILITY AND F0 EVALUATION

10.7 UHT PROCESSES

10.8 HEAT PENETRATION INTO CANNED FOODS (fh AND fc VALUES)

10.9 FREEZING AND THAWING TIMES

10.10 REFRIGERATION METHODS

10.11 PLATE FREEZERS

10.12 COLD-AIR FREEZING

10.13 IMMERSION FREEZING

10.14 CRYOGENIC FREEZING

10.15 VACUUM COOLING AND FREEZING

10.16 CHILLING

10.17 CONTROLLED-ATMOSPHERE STORAGE AND HEAT OF RESPIRATION

10.8 SYMBOLS

11: Properties of gases and vapours

11.1 INTRODUCTION

11.2 GENERAL PROPERTIES OF GASES AND VAPOURS

11.3 PROPERTIES OF SATURATED VAPOURS

11.4 PROPERTIES OF SATURATED WATER VAPOUR (STEAM TABLES)

11.5 WET VAPOURS

11.6 SUPERHEATED VAPOURS

11.7 THERMODYNAMIC CHARTS

11.8 DIAGRAMMATIC REPRESENTATION OF SOME THERMODYNAMIC PROCESSES

11.9 VAPOUR COMPRESSION REFRIGERATION CYCLE

11.10 INTRODUCTION TO AIR-WATER SYSTEMS

11.11 HUMIDITY CHARTS

11.12 DETERMINATION OF OTHER PROPERTIES FROM HUMIDITY CHARTS

11.13 EXAMPLE OF INTERPRETATION OF CHARTS

11.14 MIXING OF AIR STREAMS

11.15 WATER IN FOOD

11.16 SORPTION ISOTHERMS

11.17 WATER ACTIVITY IN FOOD

11.18 WATER ACTIVITY-MOISTURE RELATIONSHIPS

11.19 SYMBOLS

12: Electrical properties

12.1 INTRODUCTION

12.2 ELECTRICAL UNITS

12.3 ELECTRICAL RESISTANCE AND OHM’S LAW

12.4 ELECTRICAL ENERGY

12.5 MAGNETIC EFFECTS ASSOCIATED WITH AN ELECTRIC CURRENT

12.6 MEASUREMENT OF ELECTRICAL VARIABLES

12.7 RESISTIVITY AND SPECIFIC CONDUCTANCE OF FOODS

12.8 ELECTRICAL SENSING ELEMENTS

12.9 PROCESS CONTROL AND AUTOMATION

12.10 ALTERNATING CURRENT

12.11 AC CIRCUITS

12.12 DIELECTRIC PROPERTIES

12.13 DIELECTRIC PROPERTIES OF FOODS

12.14 POWER FACTOR

12.15 TRANSFORMER ACTION

12.16 THREE-PHASE SUPPLY

12.17 ELECTRIC MOTORS

12.18 SYMBOLS

13: Diffusion and Mass Transfer

13.1 INTRODUCTION

13.2 DIFFUSION

13.3 FICK’S LAW

13.4 GASEOUS DIFFUSION

13.5 DIFFUSIVITY IN LIQUIDS

13.6 SOLID DIFFUSION

13.7 TWO-FILM THEORY

13.8 UNSTEADY-STATE MASS TRANSFER

13.9 SIMULTANEOUS HEAT AND MASS TRANSFER

13.10 PACKAGING MATERIALS

13.11 MEMBRANE PROCESSES

13.12 SYMBOLS

Bibliography and references

Index

Copyright

Published by Woodhead Publishing Limited, Abington Hall, Abington

Cambridge CB1 6AH, England

www.woodhead-publishing.com

First published 1987 Ellis Horwood Limited

Reprinted and issued in paperback 1990

Reprinted 1996 Woodhead Publishing Limited

Reprinted 2002, 2006

© 1996, Woodhead Publishing Limited

The author has asserted his moral rights.

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials. Neither the author nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book.

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British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library.

ISBN-13: 978-1-85573-272-8

ISBN-10: 1-85573-272-6

Printed by Lightning Source, Milton Keynes, England.

Preface

M.J. Lewis

This book has been written in order to fill a need for a text dealing with the physical properties of foods as well as those physical principles involved in food-processing operations.

While many of those connected with or interested in food or the food industry, including students of food science and technology, may well be versed in advanced chemistry or biology, a smaller number seem to be equally qualified and confident in physics or mathematics. For this reason the aim has been to produce a text for those with an ordinary undertanding of physics and mathematics and rudimentary knowledge of the principles of differentiation, integration logarithms and the exponential function.

Although serving as an introduction to the physical properties of foods and the physics involved in food processing, ample references provide pathways to more advanced treatments and authoritative reviews on the subjects.

A further objective of the book is to provide numerical values of the properties of foods such as are necessary for solving food-processing calculations or selecting the most appropriate equipment. It will assist in answering the kinds of questions asked by practising technologists or even inquisitive students, such as the following. What is the density of Golden Delicious apples? What is the porosity of rape seed? What is the specific heat of a pork pie? What is the thermal conductivity of beetroot? What is the hardness of spaghetti? What is the viscosity of a custard? What is the spreadability of margarine compared with butter? What is the monomolecular layer moisture value for bananas? What is the water activity of Christmas cake? What is the electrical conductivity of cheese whey? What is the dielectric loss factor of mashed potato? What is the diffusion rate of sulphur dioxide into fresh vegetables? To this end, a wide variety of references are cited to provide published values and equations which relate to the compositional properties of foods as well as to environmental conditions such as temperature, pressure or humidity. Simple experimental methods are also described, to form the basis of informative practical exercises on food materials and to provide answers, where data are not readily available.

While answers to these questions assume importance in food-processing operations and quality control, it is important to realize that the principles and properties described within the text are by no means unique to food. Many of these principles will be applicable to most applied biology subjects, biotechnology and chemical engineering, including soil studies, pharmaceutical products, agricultural produce, fermentation products and enzyme preparations. Therefore, students and practitioners working in these areas may find this book useful.

Finally, it is hoped that this book may stimulate you, the reader, to take a greater interest in the physical properties of the diverse range of foods currently available, and to integrate this with your chemical, biochemical and microbiological knowledge, in order to improve your general appreciation of the field of food studies.

Dedication

This book is dedicated to my mother Nancy and my late father Jack

Acknowledgements

M.J. Lewis

Permission to use material from the following sources is gratefully acknowledged.

Fig. 3.5, George Newnes Ltd, from Turnbull et al. (1962).

Fig. 3.14, Pergamon Press, from Coulson and Richardson (1977).

Fig. 8.6, D. Reidel, from Rha (1975a).

Fig. 9.16, Elsevier Applied Science Publishers, from Lewis (1986a).

Fig. 9.17, The APV Company Ltd, Crawley.

Fig. 9.21, Ellis Horwood Ltd, from Milson and Kirk (1980).

Fig. 10.2, John Wiley & Sons, from Henderson and Perry (1955).

Figs 10.4, 10.5 and 10.6, American Society of Heating, Refrigerating and Air-Conditioning Engineers, from American Society of Heating, Refrigerating and Air-Conditioning Engineers (1985).

Fig. 10.11, The Editor, Refrigeration, Air Conditioning and Heat Recovery, from Ede (1949).

Fig. 11.13, Pergamon Press, from Coulson and Richardson (1977).

Fig. 12.24, The Editor, IEEE Transactions, from Bengtsson and Ohlsson (1974).

Fig. 12.25, The Editor, Journal of Microwave Power, from Bengtsson and Risman (1971).

Table 5.1, Academic Press, from Bourne (1982).

Tables 6.11 and 6.12, Butterworths, from Shaw (1970).

Much of the material presented in this book has been disseminated to students in the Department of Food Science, University of Reading and during lecturing visits to universities in Tanzania and Zimbabwe. I am grateful for the comments and criticism from many of these students over that time period, which have helped to improve the presentation. However, to achieve a comprehensive coverage of the subject, I have had to resort to material which has had no previous public airing and I would like to express my thanks to Dr Ann Walker and Dr David Thomson from the Department of Food Science, University of Reading, for their assistance with some of these topics. I am also grateful to Dr Reg Scott for all his good advice and interest shown in the development of the Department of Food Science since his retirement in 1975 and for his valued suggestions for improving the text.

Finally, I would like to acknowledge the special friendship, support encouragement and patience of Gay Flawley, throughout the preparation of this text.

1

Units and dimensions

1.1 INTRODUCTION

Confusion often arises from the diverse system of weights and measures at present operating in both the UK and overseas. It is possible to buy petrol in gallons (gal) or litres (1), beer in pints, vegetables in pounds (lb) and butter in grams (g). Temperatures are still measured in both degrees Fahrenheit (°F) and degrees Celsius (°C); imagine our surprise if the weather forecaster announced temperatures in kelvins (K). It has been common usage tor pressure to be measured in pounds-force per square inch (lbf in− 2) (often referred to colloquially as psi) e.g. when checking car tyres, but more recently units such as bars and kilograms-force per square centimetre (kgf cm− 2) are becoming more widespread. Electrical energy is measured in kilowatt hours (kWh) units, our gas in therms and the power of our motor vehicles in brake horsepower (hp).

Although most science subjects in schools are now taught using the International System of Units (SI), it often comes as a shock to students embarking on courses of higher education to be confronted with the centimetre gram second (cgs) or the Imperial system of units (ft lb s). Most textbooks and articles in earlier scientific journals published in the English language are written using Imperial units; it was not until the 1970s that contributions in food science textbooks began to use SI units. Although American textbooks and papers still quote mainly Imperial units, this is now also changing. The food industry is also steeped in tradition and it will take a considerable time period for all instruments, instruction manuals and personnel to be converted to SI units.

In theory, in the UK, the change from Imperial units to the SI system should have been completed by the early 1980s; in practice, this conversion is nowhere near complete and we now have to contend with a mixed system of units. It is necessary for students of applied science to be familiar with the two metric system of units (i.e. cgs and SI) and the Imperial system, in order to derive the maximum benefit from the available literature. This first chapter is written with the first objective in mind. However, throughout the book the major items of theory will be presented in SI units, and relevant conversion factors will be given, where necessary.

1.2 FUNDAMENTAL UNITS

The fundamental dimensions for the main system of measurements are mass [M], length [L], time [T] and temperature [θ]. The fundamental units in the main systems (together with the corresponding abbreviations in parentheses) are summarized in Table 1.1.

Table 1.1

Fundamental units for the three main systems of measurement.

Electric current, luminous intensity and the amount of substance (in units of moles (mol)) are also included amongst the fundamentals the SI system. The Imperial system also includes force F as one of the fundamentals, whereas in the SI system it is included amongst the derived units. The fundamental units will now be discussed in more detail.

1.3 MASS [M] (kg)

Mass is defined as the amount of matter in a body. The international prototype kilogram is a simple cylinder of platinum–iridium alloy, with height equal to diameter, which is kept by the International Bureau of Weights and Measures at Sèvres, near Paris. The mass of this is taken to represent one kilogram (1 kg).

It is important to distinguish between mass and weight. Strictly speaking, weight is defined as the force acting on an object as a result of gravity. Consequently the weight of an object will change as the gravitational force changes, whereas the mass will remain constant. It is often assumed that the acceleration due to gravity is constant at all points on the surface of the Earth and that an object will weigh the same everywhere, for most intents and purposes, this is a reasonable assumption. In practice the mass of an object is determined by comparing the force it exerts with that exerted by a known mass. Consequently we often refer to the weight of an object when we actually mean its mass.

Weight, mass or portion control is extremely important in all packaging and filling operations, where the weight is declared on the label.

1.3.1 Mass balances

In batch processing operations, such as mixing, blending, evaporation and dehydration, the law of conservation of mass applies. This can be used in the form of mass balances for evaluating these processes.

In a batch mixing process it is possible to perform a total mass balance and a mass balance on each of the components, e.g. fat or protein. Sometimes, as in evaporation, all components are grouped together as total solids.

The mass balance states that

Total and component balances will be illustrated by the following example.

1.3.1.1 Example of mass balance

It is required to produce 100 kg of low fat cream (18% fat) from double cream containing 48% fat and milk containing 3.5% fat; all concentrations are given in weight per weight (w/w). (strictly speaking, mass per mass). How much double cream and milk are required? With all such problems it is helpful to represent the process diagrammatically (see Fig. 1.1).

Fig. 1.1 Mass balance in a cream standardization unit.

Let the mass of the milk and the mass of the double cream required be X kg and Y kg, respectively. Then the total balance is

   (1.1)

The component balance on the fat is

   (1.2)

Substituting X from equation (1.1) into equation (1.2) gives

Therefore

The blending operation requires 67.4 kg of milk and 32.6 kg of double cream. Standardization is the name given to the process where the fat content of milk products is adjusted by the addition of cream or skim-milk.

In a continuous process, the same principles apply but an additional term is introduced to account for the fact that some material may accumulate. The equation becomes

However, many continuous food-processing operations take place under steady-state conditions, once they have settled down and can be analysed as such. A steady state is achieved when there is no accumulation of material, i.e.

Such operations are analysed in the same way as batch operations, normally on a time basis (hourly), as in the following example.

1.3.1.2 Mass balances (hourly basis)

If 100 kg h− 1 of liquid containing 12% total solids is to be concentrated to produce a liquid containing 32% total solids, how much water is removed each hour?

Again the process can be represented diagramatically (Fig. 1.2).

Fig. 1.2 Mass balance in an evaporation plant.

Let mass of water removed be m and mass of concentrate produced be C. Therefore the total balance is

and the solids balance is:

It is assumed that the water leaving the evaporator contains no solid. Thus,

Water needs to be removed at the rate of 62.5 kg h− 1. This fixes the evaporative capacity of the equipment. Such calculations involving total solids are extremely useful in evaporation and dehydration processes.

In some cases, chemical or biological reactions take place and an extra term for the production of new components will need to be considered.

Mass balances can also be used for evaluating losses occurring during food processing. For example, a large creamery may process 1,000,0001 of milk a day producing butter and skim-milk powder. If the amount and composition of milk processed are known together with the amounts and compositions of butter and skim-milk powder, it is possible to determine the processing losses; most of this will end up in the effluent stream and require extra expensive treatment.

For example, let us evaluate the losses occurring during the conversion of 10⁶ l of full cream milk to 40 000 kg of butter and 92 000 kg of skim-milk powder. The input is as follows (note that kg m− 3 is equivalent to gl− 1): milk, 10⁶ l; fat, 35 kg m− 3; milk solids not fat (MSNF), 90 kg m− 3. The output is as follows: butter, 40 000 kg (fat, 84%; MSNF, 1%; water, 15% (w/w)); skim-milk powder, 92 000 kg (fat, 1%; MSNF, 95%, water, 4% (w/w)). The losses occurring are shown in Table 1.2. This table shows that 480 kg of fat and 2200 kg of MSNF are not recovered in these products.

Table 1.2

Loss during conversion of full cream milk.

Some of the MSNF will be retained in the butter-milk, which is an additional byproduct. Such accounting procedures rely on being able to measure volumes, volumetric flow rates and concentrations accurately. Further examples of mass balances have been given in Earle (1983), Toledo (1980) and Blackhurst et al. (1974).

1.4 LENGTH [L] (m)

One metre (1 m) was originally the length between two marks on a specially constructed bar of platinum-iridium, kept st Sèvres, near Paris (see section 1.3). In the age of atomic physics it has been defined more precisely; the wavelength of orange light emitted by a discharge lamp containing a pure isotope of krypton (⁸⁶Kr) at 63 Κ is 6.058 × l0− 7 m. However, such conditions are not so easy to reproduce and, for a manufacturer interested in producing accurate metre rules, it is quite obvious which of the two standards would be most useful. Instruments used for measuring small distances accurately are vernier calipers, micrometers and travelling microscopes.

1.5 TIME[T](s)

One mean solar second was based on astronomical observations and was equal to 1/86 400 of a mean solar day. It is now based on the duration of the electromagnetic radiation emitted from ¹³³Cs and is the time required for 9 192 631 770 wavelengths to pass a stationary observer, i.e. 1 s = 9 192 631 770 periods.

1.6 TEMPERATURE [θ] (K)

Temperature is defined as the degree of hotness of a body. In a spontaneous change, heat (energy) is always transferred from an object at a high temperature to one at a lower temperature, until thermal equilibrium is achieved (i.e. the temperatures are equal). To set up a scale of temperature it is necessary to use some reproducible fixed points, which are normally the melting point or boiling point of pure substances, and some easily measured property of a substance that changes in a uniform manner, as the temperature changes.

The two scales of temperature most commonly encountered are the Fahrenheit and Celsius scales. The Fahrenheit system is still widely used and favoured by the ‘older generation’ of food technologists and American publishing houses.

The fixed points most easily reproduced are the melting and boiling points of pure water at atmospheric pressure (Table 1.3).

Table 1.3

Melting and boiling points of pure water at atmospheric pressure.

Temperature conversions can be achieved by the following equations or by reference to Table 1.4:

Table 1.4

Temperature conversion chart.

A temperature of −

− 40 marks the point where the two scales coincide, i.e. −

− 40 °C = − 40 °F.

The interval, one degree Celsius (1 degC), is 1/100 times the temperature difference between the boiling point and freezing point of water, whereas the interval, one degree Fahrenheit (1 degF), is 1/180 times this temperature difference. Therefore, it is more precise to record temperatures to ± 1 degF than ± 1 degC.

Conversion of temperature differences is made by the use of the following equations:

It will be seen in Chapter 9 that heat transfer rates are proportional to temperature difference. There may be many cases where it is necessary to convert temperature differences as well as temperatures. It should be noted that the Ζ value for an organism, which is a measure of how the heat resistance of an organism changes with temperature, is a temperature difference rather than a temperature. Most heat-resistant spores have a Ζ value equal to l0 degC (18 degF), i.e. an increase in temperature of l0 degC (18 degF), will decrease the processing time required by a factor of 10 (see section 10.5.1).

Other fixed points which are used are the boiling point of oxygen (− 182.97 °C), the boiling point of sulphur (444.6 °C) and the melting points of antimony (630.5 °C), silver (960.8 °C) and gold (1063.0 °C).

On the Celsius and Fahrenheit scales the numerical value attached to a particular temperature appears to be rather arbitrary and in both scales it is possible to achieve temperatures below zero. However, as temperatures is reduced, a point is reached at which all molecular motion stops and the kinetic energy of the molecule becomes zero. The temperature at this point is known as absolute zero or zero kelvin (0 K); this is the lower fixed point on the absolute scale of temperature. A second ‘easily’ reproducible fixed point is the triple point of water, the temperature at which ice, liquid water and water vapour are all in equilibrium. This occurs at a temperature of 273.16 K. Therefore the interval 1 Κ is equal to 1/273.16 of the temperature difference between the triple-point temperature and absolute zero.

On the absolute scale the freezing point and boiling point of water are 273.15 K and 373.15 K, respectively. Thus the interval 1 K is equal to the interval 1 degC. Temperature conversions can be made using the following equation:

Lord Kelvin later showed that the work produced from an ideal heat engine taking heat in at a source temperature θ1 and rejecting it a sink temperature θ2 was proportional to the temperature difference and that the efficiency of heat engine working between two fixed temperatures would always be the same, regardless of the working fluid. The efficiency of the heat engine, which is a measure of the conversion of heat to work, is termed the Carnot efficiency CE.

This represents the maximum conversion efficiency of heat to work. Thus the efficiency of such an ideal engine, which depends only on the temperature of the source and the sink, can be used to define the thermodynamic scale of temperature (section 7.9).

Unfortunately, this is not a convenient scale for determining temperatures experimentally. To set up a practical scale, use is made of a property of a material which is easy to measure and which varies with temperature in a simple fashion. Examples of such properties are listed in Table 1.5.

Table 1.5

Types of thermometer commonly used.

Measurement of these properties at two fixed points is often sufficient to establish a scale of temperature. For example, let the heights h of mercury and electrical resistances R at the ice point, steam point and unknown temperature be given as follows: at the ice point (0 °C), h0 and R0; at the steam point (100 °C), h100 and R100; at the unknown temperature (θ°C), hθ and Rθ.

Then the temperature θ on each of the scales can be determined from

However, there is no reason why the different types of thermometer should record exactly the same temperature when immersed in the same fluid. For this reason the International Scale of Temperature states which thermometers should be used for different temperature ranges. Other types of thermometer have been discussed by Jones (1974a).

1.6.1 Food-processing temperatures

The most common thermometers use in food-processing operations are mercury-in-steel thermometers, resistance thermometers and thermocouples. Mercury-in-glass thermometers are not used because they are easily broken and the resulting mercury is extremely toxic. A wide range of temperatures are encountered, ranging from − 196 °C, when using liquid nitrogen for freezing, to 1300 °C when using direct flame techniques for the sterilization of canned products. However, the usual range is between − 40 °C and 250 °C. Table 1.6 shows typical temperatures for a range of food-processing operations.

Table 1.6

Typical temperatures used for processing and storing foods.

It can be seen that the food processer has a wide range of temperatures to deal with. Furthermore, accurate temperature control is essential in the canning of low-acid products (a temperature error of 2 degC can lead to considerable under processing (see the lethality table in section 10.6) and in the storage of chilled and frozen produce to ensure optimum retention of quality. Recommendations for chilled storage of perishable products are given in an International Institution of Refrigeration publication (1979) and in section 10.16. In large-scale equipment, such as retorts and ovens, it is important to ensure that there are no temperature fluctuations and, when measuring physical properties of food such as viscosity and surface tension, it is essential to have accurate temperature control.

It is very important to check the accuracy of thermometers at regular intervals both at the fixed points and over the temperature range in which they are most often used. It may also be necessary to record temperatures during certain processing operations, e.g. pasteurization, canning and to keep records for inspection by the local health authorities. Electrical thermometers are extremely useful for this purpose.

The food processer still works mainly in temperatures on the Fahrenheit and Celsius scales. However, when certain equations such as the ideal gas equations (pV = RT) or the Arrhenius equation (k = A exp (− E/RT)) are used, it is essential that the temperature be substituted in absolute temperatures, expressed in kelvin or degrees Rankine (°R):

(note that °R is how the absolute temperature is expressed on the Fahrenheit scale). Further details have been provided by Gruenwedel and Whitaker (1984).

1.7 OTHER FUNDAMENTALS

The fundamental units in the SI system are completed with the addition of electric current, luminous intensity, and the amount of substance (units of mole) (mol). These will now be defined.

1.7.1 Electric current (A)

Electric current is a measure of the flow of electrons. One ampere (1 A) is that flow of electrons which, when flowing down two long parallel conductors, of negligible cross-sectional area, placed 1 metre apart in a vacuum produces between the two wires a force of 2 × 10− 7 Ν per metre of the length (see section 12.2).

1.7.2 Luminous intensity (cd)

One candela (1 cd) is the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 m² of a perfect radiator (black body) at the temperature of freezing platinum (1772 °C) under a pressure of one standard atmosphere (1 atm) or 1.013 bar.

1.7.3 Amount of substance (mol)

One mole (1 mol) is the amount of substance of a system which contains as many elementary entities as there are atoms in 12 × 10− 3 kg of ¹²C. When the mole is used, the elementary entity must be specified and may be atoms, molecules, ions, electrons, other particles or specified groups of such particles.

Kaye and Laby (1973) make some interesting comments about the use of these definitions of the given fundamental dimensions for setting up practical scales of measurement.

1.8 PREFIXES IN COMMON USE

The prefixes given in Table 1.7 are commonly used with the metric system of units, but not with the Imperial system.

Table 1.7

Prefixes in common use before units.

Compound prefixes (e.g. mμ) are not allowed.

1.9 DERIVED UNITS

Measurements such as volume [L³], density [ML− 3], velocity [LT− 1] and pressure [ML− 1 T− 1] are termed derived units, because they are made up of combinations of the fundamental units. Derived units can be expressed in two alternative forms, e.g. m/s or m s− l. Both forms of presentation are commonly encountered; in this book, the second form will be used. Let us consider as an example of a derived unit the velocity of an object which is measured by dividing the distance covered by the time. The dimensions are [LT− l], which remain constant regardless of the system of units being used.

The respective units of velocity in the different systems are m s− 1 (or cm s− 1) and ft s− 1.

All equations must be dimensionally consistent, i.e. the dimensions on both sides of the equation must be the same. If an equation is not dimensionally consistent, it cannot be correct.

The important derived units will now be covered.

1.10 AREA [L²] (m²)

Area is defined as the product of two lengths. Therefore the dimensions of area are [L²] and in the SI system the unit is the square metre (m²), where

Common areas encountered are as follows:

where r and D are the radius and the diameter, respectively.

Thus the total surface area of a can of radius r and length h is equal to 2πrh + 2πr² = 2πr(r + hin. Table 1.8 lists some common can sizes at present used in the UK, with equivalent metric dimensions.

Table 1.8

Sizes of some common UK round open-top cans.

Adapted from Hersom and Hulland (1980).

In many physical and chemical processes the rate of reaction is proportional to the surface area. Therefore it is often desirable to maximize the surface area. This is so in drying operations and in aerobic fermentations. Food, in either a solid or a liquid form, is prepared in strips or cubes or in the form of a spray to increase the drying rate, and air is broken into bubbles to increase the oxygen transfer rate. For homogenization of milk the fat globule is reduced in size to prevent separation from taking place; in this case the increased surface area may be a disadvantage as oxidation reaction rates will increase.

The approximate surface areas for a variety of fruit have been quoted by Mohsenin (1970), i.e. apples, 17.2–25.2 in²; plums, 5.4–7.0 in²; pears, 22.2–23.0 in².

In the design of food-processing equipment, it is necessary to be able to predict the surface area required for such pieces of equipment as heat exchangers, evaporators, driers and filtration equipment.

The size and shape of argicultural produce are used for grading purposes and for separating and sifting material. Sieves are commonly used for this purpose.

The particle size distribution of milled or ground commodities such as flour, coffee, oil seeds and other materials needs to be known and controlled for ensuring that subsequent processing and handling is optimized.

Some of these factors have been discussed in more detail by Mohsenin (1970) and Arthey (1975).

1.11 VOLUME [L³] (m³)

Volume is the product of three lengths, with dimensions [L³]. The SI unit of volume is the cubic metre (m³). However, this is a very large unit of volume and is often more conveniently subdivided into litres (l) (dm³) and ml (or cubic centimetres (cm³)):

In Imperial units, volumes are measured in gallons (gal) where 4.541 = 1 gal. Note that the British (Imperial) gallon (gal) is larger than the American gallon (US gal):

The output of breweries is still often quoted in barrels, where one standard barrel is equal to 36 gal. Barrels can be subdivided into kilderkins (18 gal) and firkins (9 gal) (4 firkins = 1 barrel); a larger measure containing 63 gal is called a hogshead.

The capacity of food-processing equipment which handles fluids is often expressed as a volumetric flow rate, in terms of gallons per hour (gal h− 1) or litres per hour (1 h− 1). Thus, pilot plant pasteurizers may process milk at the rate of 200 l h− 1, whereas the larger-scale pasteurizers in dairies or breweries may be capable of handling up to 50 000 l h− 1. In this text,