(BQ) Part 2 book Food physics (Physical properties – Measurement and applications) presents the following contents: Thermal properties, electrical properties, magnetic properties, electromagnetic properties, optical properties, acoustical properties, radioactivity,...
7 Thermal Properties Most of the food processing operations used to prolong the shelf life of foods involve heating foods to temperatures capable of inactivating microbial and enzymatic activity These heat treatments are based on controlled heat transfer that depends upon thermal properties of the food materials In order to increase the internal temperature of a food product, heat must first be transferred to the outer surface of the food, and then transmitted through the food material in order to reach the center of the food product This is an example of heat transfer In Section 7.6 heat transfer is described in more detail.When heat is added to a material (heating), the temperature of that material will increase so long as it is not undergoing a change in phase The extent of temperature rise is governed by the heat capacity of the material (see Section 7.4) When heat is removed from a material (cooling), and transferred to a surrounding heat exchange medium at a lower temperature, the temperature of the material will decrease Figure 7.1 illustrates these different directions of heat flow In food processing, thermal process operations are very important for food safety Some examples of thermal process operations are listed in Table 7.1 In this chapter we want to focus on thermal properties of foods, such as heat capacity, temperature and enthalpy of phase transition points (melting, freezing, glass transition, chemical reactions, evaporation, etc.), as well as the Figure 7.1 Heat transfer across the interface of a food long-life aseptic packaging – continuous flow / liquids (UHT/HTST) evaporation chilling/freezing cooking/baking frying dehydration removal of water, production of liquid concentrate removal of water, production of dried material with low water activity reactions (proteins,carbohydrates), evaporation of water reactions (proteins,carbohydrates), evaporation of water reducing spoilage reactions, microbial activity inactivation of pathogenic microorganisms for increasing shelf life canned solids and liquids pasteurization/ sterilization – batch purpose operation electricity, hot water, steam (direct or indirect steam) meat, fish, soup, vegetables, fruit, cream cold air, refrigerants, cryogenic fluids (liquid nitrogen) steam, hot air, microwaves hot oil French fries, potatoes, doughnuts catering operations, bread, meat pies, cakes dairy products, meat, fish, fruit, vegetables, frozen desserts 150–250 ◦ C hot air,steam,hot water,electricity 10–0 ◦ C (−18)–(−30) ◦ C (−100)–(−200) ◦ C 100–200 ◦ C 100–150 ◦ C 40–100 ◦ C steam temperature range 63–135 ◦ C milk, fruit and vegetables, coffee, cheese whey milk, potato, vegetables, fruit, meat, fish milk, cream, custard, desserts, soup, fruit, juice, beer, egg long-life milk, cream, fruit juices heat exchange medium food examples Table 7.1 Thermal process operations important in food engineering: 258 Thermal Properties 7.1 Temperature 259 caloric value of foods We will also introduce some methods and techniques for measuring some of these thermal properties 7.1 Temperature The temperature of a system is an indication of the kinetic energy exhibited by the molecular motion taking place within the constituent substances of the system This kinetic energy increases with increasing temperature (molecules move about at greater speed) The mathematical product of absolute temperature T and Boltzmann’s constant k is called the thermal energy E of a system E =k·T (7.1) where E energy in J k Boltzmann’s constant in J · K−1 T temperature in K On a molecular scale, the thermal energy is the kinetic energy of the molecules moving about within a system Recall the ideal gas where there velocity distribution of the gas atoms is a function of the temperature (see Appendix 15.2 about distribution functions) On a macroscopic scale, the thermal energy of a system can be expressed by the temperature of the system So, a high system temperature indicates the molecules have high kinetic energy At a hypothetical zero temperature, the molecules will be completely at rest with no kinetic energy This is the lower limit (zero point) of the absolute temperature scale (thermodynamic temperature scale) It has no upper limit The temperature unit chosen for this scale is K (Kelvin), which is defined as 273.16 of the triple point temperature of water This triple point is the same at any point in the world, and is called a fixed point of the thermodynamic temperature scale Figure 15.8 illustrates the triple point of water as a point in the state diagram that can be exactly defined by the temperature and pressure at which the three phases of water are coexisting Because of historic reasons, there are other temperature scales (◦ C, ◦ F, ◦ R) having other units and fixed points For example, the Celsius scale is based on the fixed points for the temperatures at which water will freeze (freezing point) and boil (boiling point) at standard atmospheric pressure The temperature difference between those fixed points was defined to be 100 degrees In a similar manner the Fahrenheit scale was based on two fixed points that could be recognized at the time Zero on the Fahrenheit scale (−17.8 ◦ C = ◦ F) was the lowest temperature that could reached at that time, and the high point of the scale (100 ◦ F) was set at what was believed to be body blood temperature of a healthy person (37 ◦ C = 100 ◦ F) The temperature difference between those fixed points was defined to be 100 degrees Likewise, there exists an absolute temperature scale based on each degree being the same as a Fahrenheit 260 Thermal Properties Table 7.2 Some fixed points for temperature, and related scales T/K # /◦ C # /◦ F # /◦ R absolute zero boiling temperature of N2 freezing temperature of H2 O triple point of H2 O temperature of human body blood boiling temperature of H2 O temperature scale name –273.15 –459.67 77.4 –195.8 –320.4 139.3 273.15 0.0 32.0 491.67 273.16 0.01 32.02 491.69 310.15 37 100 560 373.15 100.0 212.0 672 Kelvin Celsius Fahrenheit Rankine degree This is called the Rankine temperature scale (R), and is a counterpart to the Kelvin temperature scale, but in Fahrenheit degree units (instead of Celsius degree units).Table 7.2 shows an overview.Table 15.17 in the Appendix allows the conversion temperatures between these different scales For industrial use, there is an international temperature scale called ITS-90 (international temperature scale of 1990).It is based on fixed points in the range between 0.7 K and 2500 K, which can be reproduced by many laboratories In Table 7.3 there are some fixed points of ITS-90 shown, which are of interest for food engineers The number of fixed points and their values are adjusted occasionally by international conventions between the national metrological institutes (list of them see Table 2.2) Table 7.3 Some fixed points of the international temperature scale, ITS-90, which are in the temperature range of food processes equilibrium state triple point of water melting point of Gallium melting point of Indium # /◦ C after ITS-90 0.01 29.7646 156.5985 7.2 Heat and Enthalpy Heat is a form of energy Energy exists in many forms (heat, light, work, chemical, e.g in fuel, electricity, etc.), and often changes from one form into another, such as heat into work,chemical (fuel combustion) into heat,etc.(see Table 7.4) Energy per se, however, can neither be created nor destroyed This is known as the first law of thermodynamics, and is often used by engineers as the rule of energy conservation in carrying out energy balance calculations on a system When energy is transformed from one form to another, we have to take into account the efficiency of this transformation Except for heat, all forms of 7.2 Heat and Enthalpy 261 Table 7.4 Different forms of energy energy form mechanic energy electrical energy light energy chemical energy nuclear energy heat energy example: energy in a loaded spring (potential energy) a moving body (kinetic energy) electric power networks light of sun, light from incandescent bulb vegetable oil, mineral oil, potato starch, fuel nucleus of atom emitting radioactivity cooking/heating stove, home heating system energy can be converted to each other with 100% efficiency in theory However, this is not true in reality where we have efficiencies below 100% In the case of heat, the conversion to other energy forms can be 100% displacement only when absolute zero temperature is reached Because of the third law of thermodynamics, this is considered to be impossible So as a consequence, heat cannot be converted to other forms of energy with efficiency of 100% Therefore, heat as a form of energy, has some special character The internal energy U of a thermodynamic system exists in the forms of both heat and work Therefore, two transformations are possible for internal energy Transfer of heat Q and/or transfer of work W So, we can express internal energy in the following way: dU = dQ + dW (7.2) In a thermodynamic system, we treat work only in the form of displacement work W (force–displacement, or pressure–volume) We assume that other forms of work like electric, magnetic, elastic and frictional are not involved dU = dQ + dW (7.3) With the definition of displacement work: dW = −p · dV (7.4) we have dU = dQ − p · dV (7.5) dQ = dU + p · dV (7.6) or where U Q p W W V H internal energy in J heat in J pressure in Pa work in J displacement work in J volume in m3 enthalpy in J 262 Thermal Properties The negative sign in equation (7.4) takes into account that negative displacement dV represents energy uptake of a system, and has to be counted as a positive contribution (and vice versa) The term enthalpy H now is used for the sum of internal energy and the product pV: H = U +p·V (7.7) So, for a change in enthalpy, we have: dH = dU + p · dV + V · dp (7.8) If we consider only cases where the pressure is constant (dp = 0), then we have: dH = dU + p · dV (7.9) Together with equation (7.6), this means: dH = dQ (7.10) This means that the amount of heat dQ which occurs during an isobaric (constant pressure) process is the same as the change in enthalpy of the system So, when we investigate material properties in a laboratory under constant (e.g normally atmospheric) pressure, we talk about enthalpy instead of energy of a system So the difference between the change in the internal energy dU of a system and the change in its enthalpy dH lies in the work,and with the approximations above, specifically in the displacement work dW = −pdV If in an isobaric process, there is no displacement or it is nearly zero, then the displacement work plays no role in the system, and the distinction between internal energy and enthalpy is no longer important The values of dH and dU are the same (see Table 7.5) When heat is transferred into or out of a system, normally the temperature rises or falls, respectively This type of heat is called sensible heat because we can “sense” the warming or cooling effect by change in temperature But there are also cases where we can transfer heat into or out of a system, but the temperature stays constant This happens during boiling of water as it changes phase from liquid into gas (water vapor) or during freezing water into ice as it changes phase from liquid to solid This type of heat is called latent heat Latent heat is connected with phase transitions in the materials Before going into details about phase transitions, it will be helpful to recall some of the basic principles from thermodynamics in the next section Table 7.5 Heat dQ transferred to/from a system (isobaric cases) general process isobaric process with displacement work isobaric process with displacement work being zero dQ = dU + p · dV + V · dp dQ = dU + p · dV + dQ = dH dQ = dH dQ = dU + + dQ = dH = dU 7.3 Thermodynamics – Basic Principles 263 7.3 Thermodynamics { Basic Principles Thermodynamics is the body of science in which we study the way in which substances are affected by heat, either when being heated or cooled, and especially when heat addition or removal causes a phase change It is no surprise therefore, that thermodynamics is an essential topic that must be well understood by most engineers, and especially food engineers Normally, entire textbooks are devoted solely to a basic primer in thermodynamics Since thermodynamics is not the main topic of this book, only a brief discussion of basic principles will be presented in order to appreciate the importance of thermal properties Measuring thermal properties of materials requires that we conduct experiments to cause thermal effects to occur, and record the results of these effects Most often temperature or quantity of heat are measured and monitored Observing the temperature dependency (like the pressure dependency) of a physical quantity is a common way to study the energetic behavior of a material on a molecular scale 7.3.1 Laws of Thermodynamics In the previous section, we just learned that the law of energy conservation stems directly from thermodynamics, and is called the first law of thermodynamics (equation (7.6)) Recall this equation was derived with the assumption that no work other than displacement work would occur dU = dQ − p · dV (7.6) If we have a system which is thermally insulated so that no heat can cross the system boundary (dQ = 0), we call the system adiabatic (= isentropic) When an adiabatic system shows no displacement work (dV = 0), then the internal energy of the system is constant (dU = 0) When heat dQ is entering or departing a system at a temperature T, the quotient of heat divided by temperature is called change in entropy S of the system: dQrev (7.11) T This definition is valid for a closed system and a completely reversible process When the process of interest is partly or completely irreversible then we have: dS ≡ dQ (7.12) T Equation (7.12) is an expression of the second law of thermodynamics, stating that if a system is not in equilibrium the entropy S tends to increase and to reach a maximum dS > 264 Thermal Properties When we take into consideration reversible processes and reversible displacement work only, the combination of equations (7.6) and (7.11) provides: dU = T · dS − p · dV (7.13) That means that the internal energy of a closed system can be changed only by changing the entropy S or the volume V In thermodynamics there is another“energy term”that is sometimes useful: It is Gibbs’ enthalpy G This is the difference of enthalpy H and product of temperature T and entropy S G = H −T ·S (7.14) With equation (7.7) G = U +p·V −T ·S (7.15) any change in Gibbs’ enthalpy is dG = dU + p · dV + V · dp − S · dT − T · dS (7.16) Then, with equations (7.6) and (7.11) this becomes: dG = V · dp − T · dS (7.17) When we consider an equilibrium situation,such as water vapor above a surface of liquid water at a given temperature, with dQ = T · dS = 0: dG = V · dp (7.18) dG =V dp (7.19) or If we treat water vapor under the given conditions like an ideal gas, we get: dG R · T = dp p (7.20) dG = R · T · d ln p (7.21) or Because water vapor is not an ideal gas,we can adjust the water vapor properties to account for its nonideal behavior by using the fugacity f of the vapor, instead of the pressure p dG = R · T · d ln f (7.22) This shows that Gibbs’ energy of a simple system can be calculated by measuring the vapor pressure i.e the fugacity f , only The dimensionless relative fugacity is called the activity of the chemical compound In the case of water, we recognize this quantity as water activity (Chapter 1): 7.4 Heat Capacity aW = 265 f f0 (7.23) When Gibbs’ enthalpy is dependent on a chemical compound, the partial derivative of dG over dn is called chemical potential i ≡ ıG ıni (7.24) S,p,nj(j=i) The chemical potential indicates the ability of a component to undergo a reaction In terms of our example of water vapor, the chemical potential indicates the ability of water to act as part of a chemical reaction We see now, that what we learned about water activity being an indicator of bound or available water in order to support various reactions has a sound thermodynamic basis It tells us, that if we want to know the ability of water to undergo reactions (i.e want to know the chemical potential), then we should measure water vapor pressure p (more exactly the fugacity f ) That is what we in measuring the water activity The water activity is nothing more than a relative measure of the chemical potential of water d = R · T · d ln f (7.25) with equation (7.8) d = function (aW ) where G Gibbs energy in J n substance in mol f fugacity in Pa chemical potential in J · mol−1 S entropy in J · K−1 aW water activity 7.4 Heat Capacity The heat capacity of a material is a thermal property that indicates the ability of the material to hold and store heat It can be quantified by specifying the amount of heat that is needed to raise the temperature by a specified amount Mathematically, it is the quotient of heat divided by temperature: dQ dT respectively, C= C= Q T (7.26) (7.27) 266 Thermal Properties When heat capacity is defined only in this way, it will also depend upon the mass of the material sample, and serves as a property only of the specific sample size measured For this reason, we normally measure and report the heat capacity on the basis of a common unit of mass When we this, we call it the specific heat capacity Sometimes this property is called specific heat of the material but this should be avoided because dQ/dm = q is specific heat c= C m (7.28) c= dq dQ · = m dT dT (7.29) In order to help better understand heat capacity, let us assume we wish to determine how much heat is needed to raise the temperature of one liter of water at 21 ◦ C up to 23 ◦ C (by K) When we this, we measure the heat required to be 8.36 kJ When heat is added to a system like this (liter of water), the water molecules experience an increase in their kinetic energy They move in both rotational and translational motion at faster rates If we insert our finger (or a thermometer) into this liter of water, we can sense this increased thermal energy level by a warming sensation on our finger, and a rise in the temperature scale on the thermometer Therefore, we use temperature as a measure of increased thermal energy In this case, the temperature increase was T = K Table 7.6 Heat capacity terms p = const V = const Cp = dH dT (7.30) CV = dU dT (7.31) cp = dH · m dT (7.32) cV = dU · m dT (7.33) cp = dh dT (7.34) cV = du dT (7.35) where C c Q q T m H h U u heat capacity in J · K−1 specific heat capacity in J · kg−1 · K−1 heat in J specific heat in J · kg−1 temperature in K mass in kg enthalpy in J specific enthalpy in J · kg−1 internal energy in J specific internal energy in J · kg−1 ... triple point of H2 O temperature of human body blood boiling temperature of H2 O temperature scale name 2 73.15 –4 59.67 77.4 –1 95.8 –3 20 .4 139.3 27 3.15 0.0 32. 0 491.67 27 3.16 0.01 32. 02 491.69 310.15... desserts 15 0 2 50 ◦ C hot air,steam,hot water,electricity 1 0–0 ◦ C (−18 )–( −30) ◦ C (−100 )–( 20 0) ◦ C 10 0 2 00 ◦ C 10 0–1 50 ◦ C 4 0–1 00 ◦ C steam temperature range 6 3–1 35 ◦ C milk, fruit and vegetables,... medium food examples Table 7.1 Thermal process operations important in food engineering: 25 8 Thermal Properties 7.1 Temperature 25 9 caloric value of foods We will also introduce some methods and