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CHAPTER 29 THERMAL PROPERTIES OF FOODS Commodity Refrigeration Load Data; Enthalpy, Specific Heat, and Thermal Diffusivity; Thermal Conductivity HIS chapter provides data and information for thermal process T (heating, cooling, freezing, and thawing) calculations for foods and food substances. The material was selected and prepared for general usefulness to engineers and others interested in applying these processes to foods in industry, teaching, and research. Since the data selected were considered the best available, discussion of errors, accuracy, and methods for obtaining the data is minimal. References are given, where possible, for those interested in obtaining more detail. Another criterion for data selection was need or potential usefulness. Since comprehensiveness was also sought within this limitation, the amount of data presented in each area reflects the amount of data available. Variability in composition and structure seems to be the major characteristic of food substances to keep in mind in considering their thermal properties. For example, foods are generally nonhomogeneous, varying in composition and structure both within and between products or samples of products. In addition, their chemical and physical (and hence thermal) properties will probably change with time, temperature, and other ambient conditions. If the food is a living commodity, such as a stored fruit or vegetable, it will generate heat, use atmospheric oxygen, and give off carbon dioxide, water vapor, and other gases, all of which affect its ambient surroundings, quality, and storage life. As a specific example, consider conductivity of meat. the composition and structure (fat, lean, bone, moisture, muscle and bone size and shape, fiber direction, etc.) will vary between animals with species, age, feeding, slaughter, and post slaughter conditions, and within a given animal with the particular muscle or muscle part considered. Above freezing, temperature change may cause changes in the conductivity due to changes in the fat; below freezing, the conductivity changes rapidly until the water is substantially frozen. After thawing and refreezing, or a period of above-freezing storage, the conductivity may be different, due to water loss and other changes. Some changes may not be significant, but others are. Care must be taken in measuring and predicting, and in the use of thermal conductivity and other thermal properties. This chapter uses SI units except where other metric units seemed preferable. Some of the most frequently needed conversion factors are given with tables and figures. For more detailed information see Chapter 35. COMMODITY REFRIGERATION LOAD DATA Design of systems for cooling, freezing, or storing foods requires reliable values for thermal properties of various products. Food properties described in this section are specific heat, latent heat of fusion, and heat of respiration. Related properties are freezing point and water content. These data are given in Tables I to 3. Water Content. Although not directly a thermal property, water content significantly influences all thermal properties. The preparation of this chapter is assigned to TC 11.9, Thermal Properties of Foods. In fact, values of specific heat and latent heat of fusion (Table 1) are based on the amount of water in the food. Values for percent water content (Table I) should be considered the average for the commodity. With fruits and vegetables, water content varies with stage of development or maturity when harvested, cultivar, growing conditions, and amount of moisture lost after harvest. Values normally apply to fully mature products shortly after harvest. For fresh meat, water content values are for time of slaughter or after the usual aging period. In cured or processed products, water content depends on the particular process or product. Some foods are hygroscopic, gaining moisture during storage, but most lose water that cannot be recovered. Values for specific heat and latent heat of fusion in Table 1 apply only for the corresponding water content given. Freezing Point. Freezing point values in Table 1 are based on experiments where the product was cooled slowly until freezing occurred. Sensitive temperature indicators, such as thermocouples, were inserted into the product, and a sudden temperature rise caused by ice formation indicated the beginning of freezing. For fruits and vegetables, the highest temperature at which specimens froze is given (Table 1), for they can be seriously damaged by freezing. For other foods, average freezing temperature is shown, largely because initial freezing temperatures are unavailable. Freezing points of foods vary with composition. All apples in a given lot, for example, do not freeze at the same temperature. As a food product is frozen, ice crystals form, concentrating the remaining unfrozen portion and lowering the freezing temperature. Foods packed in high syrup concentrations, or high in sugar content, such as dried fruits, may never be completely frozen, even at frozen food storage temperatures. Also, foods normally low in moisture, such as dried beans and peas, do not freeze at these temperatures. Specific Heat. Siebel's formulas used to calculate listed specific heat values for above and below freezing, are: cp=0.008 a+0.20 (above freezing) (1) cp=0.003 a+0.20 (below freezing) (2) where cp is specific heat in Btu per pound per degree Fahrenheit, or calories per gram per degree Celsius; a is percent water content; and 0.20 is an arbitrary base, assumed to represent the specific heat of the solid constituents. To convert calories to joules, multiply by 4.1868.2 Specific heat is a function of temperature. Siebel's formulas are based on the specific heat of water and ice at O°C of 1.0 and 0.5 cal/(g) (QC), respectively. Specific heat values in Table 1 are for O°C. In nonfrozen foods, specific heat becomes slightly lower as temperatures rise from 0 to 20°C. In frozen foods, there is a large change in specific heat as temperatures decrease. For example, frozen beef at -40°C has a specific heat of 0.49, as compared with 0.35 at -79°C. 3 As mentioned previously, variability in composition is a major characteristic Publica tion of standards in th e fie lds of heat ing, refr igerating, air -cond ition ing and ventilating engineer ing from (ASHRAE: 29.1 American Society o f Hea ting , Refrigerating and Air - Cond itioning Engineers, I nc. Reprinted from ASHRAE handbook Chapter 29 doc081113brev00_11-13-08-thermal_properties_of_foods.doc (1) (2) CHAPTER 29 29.2 1977 Fundamentals Handbook of food substances; this is true for those constituents, particularly water content, that affect specific heat. In calculating specific heat of frozen foods, all the water is assumed to be frozen to ice; the specific heat involved is that of ice. This assumption is not entirely correct. As indicated, freezing of most foods is a gradual process, occurring over a wide temperature range. Specific heat values are subject to error, since freezing may be incomplete, the specimen may not be ice but a mixture of frozen and unfrozen constituents.) Latent Heat of Fusion. Latent heat of fusion is useful in determining the amount of refrigeration required to freeze a product. As with specific heat, the values listed are subject to error because they do not take into account the chemical composition other than its water content. They are simply the product of the heat of fusion of water (79.71 cal/g) and the water content expressed in decimal form. Their use is limited to practical applications, being subject to some discrepancy depending on product composition. The following examples show that errors inherent in calculating heat of fusion of foods are not significantly large: of respiration energy is in the form of heat, which must be contended with in cooling and storing these living products. As in all chemical reactions, temperature plays a leading role in the rate of respiration. A 10°C rise in temperature generally causes respiration rates to double or triple in the range of about 0 to 30°C. Higher temperatures usually retard respiration. Fruits, vegetables, flowers, bulbs, florists' greens, and nursery stocks are storage commodities with significant heats of respiration. Dry plant products, such as seeds and nuts have very low respiration rates. Young, actively, growing tissues, like asparagus, broccoli, spinach, and green beans have high rates, as do immature seeds such as green peas and sweet corn. Fast developing fruits like strawberries, raspberries, and blackberries, have much higher respiration rates than fruits that are slow to develop, such as apples, pears, grapes, and citrus fruits (Table 2). Almost all commodities in Table 2 have a low and a high value for heat of respiration at each temperature. When no range is given, the value is an average for the specified temperature, and may be an average of the respiration rates for many days. Example 1: Assume a food of 75°10 moisture content, initially at O°C to -20°C; latent heat of fusion of water, 79.71 cal/lg; specific heat of ice, 0.50 cal/(g) (DC); specific heat of water, 1.01 cal/(g) (DC); specific heat of non-aqueous 25OJo of the food (Eq. 2), 0.20 cal/(g) (DC). Assume only 90OJo of the water present freezes, a good assumption for many foods. 4 Now: Most vegetables, other than root crops, have a high initial rate for the first day or two after harvest. Within a few days, it quickly lowers to what may be called the equilibrium rate. 5 Asparagus is a good example. The first day, heat of respiration of 0ºC is 4900 kcal/(metric ton) (day). Within 3 days, it is down to 2410, and in 16 days to 1 710 (Table 3). Great Lakes lettuce at 0° has a rate of 1040 kcal/(ton)(day) the first day, which falls to 550 in 5 days. Artichokes at 0°C respire at a rate of 2750 kcal/(ton)(day) the first day and by 16 days the heat produced amounts to only 920 kcal/(ton)(day). Sweet corn in the husk at 0ºC produces the first day 3140 kcal/(ton)(day) and in 4 days decreases to 1880 kcal/(ton)(day). Onions are an exception. They increase in respiration with time as the bulbs lose dormancy. The same is true with garlic (Table 3). Fruits present a somewhat different picture than most vegetables. Those that do not ripen in storage, such citrus fruits and grapes, have fairly constant respiration rates. Those that ripen in storage (i.e., apples, pears, peaches, plums, mangos, and avocados) increase in respiration rate. If a fruit can be held at DOC, as most apples can, respiration barely increases, since no ripening takes place. But if held at higher temperatures (10 or 15°C), respiration increases and then decreases (see apples, Table 3). Soft fruits, such as blueberries, figs, and strawberries show a decrease in respiration at O°C with time. If they become infected with decay organisms, however, respiration increases. (a) latent heat of freezing: 79.7IxO.75xO.9 (b) sensible heat to cool the ice: (0. 75xO. 9xO.5)x20 (cY sensible heat to cool unfrozen water: (0.75xO.lx1.01 )x20 (d) sensible heat to cool non-aqueous material: (0.25xO.2)x20 Total =53.8 cal/lg 6.8 call g 1.5 call g 1.0 call g 63.1 Calculated from the freezing of water only, O. 75x79.cal/g 71 =59.8 call g for an error of [(63.1-59.8)/63.I1X 1 00=5.2 O%. Example 2: Assume a food of 50OJo water content. Calculating as above: (a) =35.9 cal/g; (b) =4.5 cal/g; (c) =1.0 calling; and (d)=2.0 calling; the total is 43.4 cal/g. Using heat of fusion of water gives only 39.9 calling for an error of 8.1OJo. Note that in some foods with low water content, very little water will be frozen at -200e This causes a large error if the "90170 freezing" assumption is adhered to. For computing cooling or freezing loads of frozen products, specific heat below freezing and latent heat of fusion are interdependent, and should be used together. For many food products, both freezing and temperature change of frozen material take place simultaneously. This occurs over a temperature range, narrow for foods with low solid matter content, wide for those with high solid matter content. (See Enthalpy, Specific Heat, and Thermal Diffusivity, below.) In Table I, no latent heat of fusion values or specific heat values below freezing are given for products so low in moisture that the water in them does not freeze. Heat of Respiration. All living food products respire. In respiration, a sugar, usually glucose, combines with oxygen by a step process involving enzymes. A simplified formula for the process is: e6H 1206+602--6e02+6H20 +energy (heat and energy of A TP) The end products are CO2, H 2' and energy in the form of heat as well as of adenosine triphosphate (A TP), that the cell can use for growth and development. In most stored plant products, little cell development takes place, and the greater part To use Table 2," select the lower value when estimating respiration heat at the equilibrium state for storage; and the higher value if calculating the heat load for the first day or two, as for precooling and short distance transport. If the storage temperature is 0 or 5°C, respiration increase in fruits, due to ripening, is slight. In fruits that must be held at 10°C or higher, such as mangos, avocados, or bananas, ripening occurs and the higher rates should be used. Vegetables that lose dormancy in storage, like onions, garlic, and cabbage, may increase in heat production after long storage. Not all variations in respiration heat can be attributed to change in rate with time. Broccoli with many flower heads respires faster than if mostly stem tissue. Immature fruits and vegetables usually respire faster than more mature specimens (see potatoes, Table 2). Usually, the early, fast-growing cultivars of fruits and vegetables have higher respiration rates than later, slower developing types. To obtain the values in Tables 2 and 3, the heat of respiration was assumed to be derived from glucose oxidation in the reaction given earlier. One mole of glucose (180 g) is oxidized by 6 moles of oxygen to produce 6 moles of CO2 (264 g). Glucose oxidation produces 673 kcal and 1 g of CO2, therefore represents (673/264)=2.549 kcal; I mg of CO2 represents 2.549 cal. Respiration rate in mg CO2/(kg) (hr)x2.549x24=heat produced/kg in 24 hr. This is equivalent to kcal/(metric ton) (24 hr). To convert heat of respiration to Btu/(ton) (24 hr) from kcal/(metric ton) (24 hr), multiply the latter by 3.60. If substrates other than glucose are oxidized in the respiration process, as they sometimes are, the heat produced amounts to less when organic acids are the substrate, and considerably more when fats are utilized. C. 29.3 Thermal Properties of Foods ENTHALPY, SPECIFI C HEA T AND THERMAL DIFFUSIVITY When enthalpy is tabulated as a function of temperature, a base temperature must be identified. This base is the temperature at which enthalpy is arbitrarily designated as zero. In this chapter, zero enthalpy is taken at -40°C. Frozen Foods The data shown in Table 1 consist of latent heat, freezing point, and specific heat above and below freezing. This table is used to perform refrigeration load calculations by (1) using specific heat above freezing to compute the sensible heat removed during cooling from the starting temperature to freezing point; (2) using latent heat to compute the heat removed during freezing; and (3) using specific heat below freezing to compute the sensible heat removed during cooling from the freezing point to the final frozen storage temperature. This procedure assumes the latent heat of fusion is removed at constant temperature (the freezing point). Foods do not freeze at constant temperature, however. Beef begins to freeze at about -1°C, but 25070 of the latent heat is still to be removed at -4°C. 4 In haddock muscle, some water is bound to proteins and does not freeze at -40°C. 58 In reviewing problems of measuring specific heat and latent heat of foods, Ref. 59 points out that fresh beef is not completely frozen at -62°C, and orange juice is not completely frozen at -95°C. Ref 60 explains the process of food freezing as follows. When food begins to freeze, the concentration of food solids is increased in the remaining unfrozen water, thereby establishing a lower freezing point for additional change of phase. With additional freezing, there is a gradual depression of the freezing point until all freezable water is frozen. Measurement of heat removed during freezing includes both latent and sensible heat. For this reason, the generally accepted criterion of latent heat {change of phase at constant temperature) cannot be rigorously applied to the process of freezing foods.3 Neither the concept of specific heat nor thermal diffusivity can be applied because there is, as yet, no way to separate the specific heat component from latent heat in a food freezing process. Using Table 1 to compute refrigeration loads can lead to errors, but the errors will always be conservative (i.e., the computed refrigeration load will always be somewhat greater than that actually required). The error diminishes for lower frozen storage temperatures. Conversely, if the product is to be cooled only slightly below the initial freezing temperature, using Table 1 can lead to significant errors because only a small fraction of the latent heat is actually removed from the product. Results from Table 1 assume all latent heat is removed. When the product is to be cooled only slightly below initial freezing temperature, or where greater accuracy is desired for any final frozen storage temperature, the physical quantity employed in frozen food calculations is the total heat content, or enthalpy. 59.61-63 This approach has the additional advantage of yielding estimates of percent water unfrozen. Enthalpy of Meats, Fruits, Vegetables, and Eggs Enthalpy of some frozen foods is in Table 4, as a function of temperature from -40 to O°C. In the temperature range of Table 4, water in the food is never completely frozen, and the percent (by weight) of unfrozen water is also shown as a function of temperature. To identify enthalpy, use: (3) where Q = total heat transferred, kilocalories. W = weight, kilograms. h = enthalpy, kilocalories per kilogram. An example of the use of tabulated enthalpy values follows. Example 3: A quantity of beef (150 kg) is to be frozen to a temperature of 20°C. Initial temperature of the beef is + IO°C, and moisture content is 74.5070. How much heat must be removed, and what is the total weight of unfrozen water at -20°C? The heat removed in cooling from 10 to O°C is calculated from temperatures and specific heat (cp)' From Table 4, specific heat is 0.84 kcal/(kg)(OC), so from 10 to O°C: Q = [(150 kg) x (0.84 kcal)1/[(kg)(°C) x (10°C - O°C)1 = 1260 kcal. ' From the tabulated values in Table 4: h2 at O°C = 73.0 kcal/kg; hi at -20°C = 10.0 kcal/kg. Therefore, from O°C to -20°C: Q = W(h2 - hi) = (150 kg) x (73.0 - 10.0) = 9450 kcal. The total heat to be removed is: QlOtal = 1260 kcal + 9450 kcal = 10,710kcal. The amount of unfrozen water at -20°C is taken directly from Table 4 as II %. The total weight of unfrozen water is (150 kg) x (0.745) x (0.11) = 12.3 kg. Using enthalpy values for beef of various water contents, Ref 4 includes a graph of enthalpy vs water content with connected data points along lines of constant temperature so that enthalpy values can be obtained for beef of any water content. Another graph4 shows percent water frozen vs temperature in beef. These two graphs were combined3 into one using the British Gravitational System of units; the data have been converted to the metric system in Fig. 1. . For a beef sample of known water content, a single vertical line in Fig. I yields enthalpy and percent water unfrozen as a function of temperature. For temperatures below -40°C, the freezing process is nearly complete for beef, and use of specific heat yields reliable results. Table 564 gives specific heat of frozen beef for temperatures between 110 and -40°C. Enthalpy and percent water unfrozen for fruit juices and vegetable juices are given in Fig. 2. Working with twelve juices, Riedel 65 showed that enthalpy data were represented by Fig. 2 within approximately 2070. Fig. 2 exhibits the same general trends as shown in Fig. 1 for beef. However, Fig. 2 has a different range of water content, and isotropic lines of percent water unfrozen are not shown extrapolated to zero enthalpy as in Fig. 1. The effect of soluble solids in the juice on the temperature range over which latent heat is removed is apparent in Fig. 2. For example, a vertical line at a water content of 95070 shows the heat to be removed during freezing. For this high water content, freezing starts at a temperature very close to 0ºC, and the main part of the freezing process occurs over a narrow 29.4 CHAPTER 29 Table 1 Thermal and Related Properties 1977 Fundamentals Handbook Table 1 of Food and Food Materials Specific Heate Highest Food or Food Material Below Latent Water Freezing Above Content, '10 (wO) Point °Ch Freezing cal/(g)("C) heal of 84 -1.2 0.87 0.45 67.0 80 93 89 67 II 88 90 85 92 88 92 88 94 87 74 96 -2.5 -0.6 -0.7 -0.6 0.84 0.94 0.91 0.74 0.29 0.90 0.92 0.88 0.94 0.90 0.94 D.90 0.95 0.90 0.79 0.97 0.44 0.48 0.47 0.40 63.8 74.1 70.9 53.4 0.46 0.47 0.46 0.48 0.46 0.48 0.46 0.48 0.46 0.42 D.49 70.1 71.7 67.8 73.3 70.1 73.3 70.1 74.9 69.3 59.0 76.5 0.48 0.48 0.38 0.46 0.43 0.46 0.47 0.46 0.49 0.47 0.47 0.47 0.46 D.45 0.44 0.42 74.1 74. 1 48.6 69.3 59.8 69.3 71.7 67.8 75.7 n.5 71.7 70.9 70.1 67.8 63.0 59.0 -0.8 -0.7 -0.9 -1.1 -1.1 -0.3 -0.5 -0.8 D.94 0.94 0.69 0.90 0.80 D.90 0.92 0.88 0.96 0.93 0.92 0.91 0.90 0.88 0.83 0.79 0.30 0.30 0.94 0.85 0.82 0.75 0.79 0.93 0.96 0.96 0.91 0.83 0.94 0.95 0.88 0.48 0.44 0.43 0.41 0.42 0.47 0.49 0.49 0.47 0.44 0.48 0.48 0.46 73.3 64.6 62.2 55.0 59.0 n.5 75.7 75.7 70.9 63.0 74.1 74.9 67.8 -0.6 -0.5 -0.2 -I.J -0.3 D.94 0.95 0.92 0.94 0.94 0.48 0.48 0.47 0.48 0.48 74.1 74.9 71.7 73.3 74.1 fusion Freezing cal/(g)(OC) cal/gd Vegetables Artichokes, Globe Artichokes, Jerusalem Asparagus Beans, Snap Beans, Lima Beans, Dried Beets, Roots Broccoli Brussels Sprouts Cabbage, Late Carrots, Roots Cauliflower Celeriac Celery Collards Corn, Sweet Cucumbers Eggplant Endive (Escarole) Garlic Ginger, Rhizomes Horseradish Kale Kohlrabi Leeks Lettuce Mushrooms Okra Onions, Green Onions, Dry Parsley Parsnips Peas, Green Peas, Dried Peppers, Dried Peppers, Sweet Potatoes, Early Potatoes, Main Crop Potatoes, Sweet Yams Pumpkins Radishes Rhubarb Rutabagas Salsify Spinach Squash, Summer Squash, Winter Tomatoes, Mature Green Tomatoes, Ripe Turnip Greens Turnip Watercress 93 93 61 87 75 87 90 85 95 91 90 89 88 85 79 74 12 12 92 81 78 69 74 91 95 95 89 79 93 94 85 93 94 90 92 93 -1.1 -0.6 -0.8 -0.9 -1.4 -0.8 -0.9 -0.5 -0.8 -0.6 -0.5 -0.8 -0.1 -0.8 -1.8 -0.5 -1.0 -0.7 -0.2 -0.9 -1.8 -0.9 -0.8 -1.1 -0.9 -0.6 -0.7 -0.6 -0.6 -1.3 (continued) Highest - - Water Freezing Food or Food Content, Material Grapefruit Grapes, American Grapes Lemons Limes Mangos Melons, Casaba Melons, Crenshaw Melons, Honeydew Melons, Persian Melons, Watermelon Nectarines Olives Oranges Peaches, Fresh Peaches, Dried Pears Persimmons Pineapples Plums Pomegranates Prunes Quinces Raisins Raspberries Strawberries Tangerines '10 (wO) 89 82 82 89 86 81 93 93 93 93 93 82 75 87 89 25 83 78 85 86 82 28 85 18 81 90 87 Point °Cb -I.1 -1.6 -2.1 -1.4 -1.6 -0.9 -1.1 -1.1 -0.9 -0.8 -0.4 -0.9 -1.4 -0.8 -0.9 Specific Heat Latent Above Below heal of Freezing Freezing fusion cal/(g)("C) cal/gd 0.47 70.9 0.45 65.4 0.45 65.4 0.47 70.9 0.46 68.6 0.44 64.6 0.48 74.1 0.48 74.1 0.48 74.1 0.48 74.1 0.48 74.1 0.45 65.4 0.43 59.8 0.46 69.3 0.47 70.9 -0.6 -0.8 -1.1 cal/(g)(OC) 0.91 0.86 0.86 0.91 0.89 0.85 0.94 0.94 0.94 0.94 0.94 0.86 0.80 0.90 0.91 0.40 0.86 0.82 0.88 0.89 0.86 0.42 0.88 0.34 0.85 D.92 0.90 78 -2.2 0.82 0.43 62.2 Halibut Herring, Kippered Herring, Smoked Menhaden Salmon Tuna Filets or Steaks 75 70 64 62 64 70 -2.2 -2.2 -2.2 -2.2 -2.2 -2.2 0.80 0.76 0.71 0.70 0.71 0.76 0.43 0.41 0.39 0.39 0.39 0.41 59.8 55.8 51.0 49.4 51.0 55.8 Haddock-Cod Perch Hake· Whiting Pollock Mackerel 80 82 79 57 -2.2 -2.2 -2.2 -2.2 0.84 0.86 0.83 0.66 0.44 0.45 0.44 0.37 63.8 65.4 63.0 45.4 80 83 79 -2.2 -2.2 -2.2 0.84 0.86 0.83 0.44 D.45 0.44 63.8 66.2 63.0 87 80 -2.2 -2.8 0.90 0.84 0.46 0.44 69.3 63.8 49 45 56 67 48 70 -1.7 -2.2 0.59 0.56 0.65 0.74 0.58 0.76 D.35 D.33 0.37 0.40 0.34 0.5 I 39.1 35.9 44.6 53.4 38.3 55.8 66 0.73 O.4D 52.6 19 57 42 37 30 8 49 56 38 0.35 0.66 0.54 0.50 0.44 0.26 D.59 0.65 0.50 D.26 0.37 0.33 0.31 0.29 15.1 45.4 33.5 29.5 23.9 0.35 0.37 0.31 39. J 44.6 30.3 Whole Fish Haddock - Cod Shell Fish Scallop, Meat Shrimp Lobster, American Oysters - Clams, Meat and Liquor Oyster in Shell Beef Carcass (60% Lean) Carcass (54'10 Lean) Sirloin, Retail Cui Round, Retail Cut Dried, Chipped Liver Veal, Carcass (810J0 Lean) -1.6 -2.2 -1.0 -D.8 -3.0 -2.D -1.7 0.45 0.43 0.46 0.46 0.45 66.2 62.2 67.8 68.6 65.4 0.46 67.8 D.44 0.47 0.46 64.6 71.7 69.3 Fruits Apples, Fresh Apples, Dried Apricots Avocados Bananas Blackberries Blueberries Cantaloupes Cherries, Sour Cherries, Sweet Cranberries Currants Dates, Cured Figs, Fresh Figs, Dried Gooseberries 84 24 85 65 75 85 82 92 84 80 87 85 20 78 23 89 -1.1 -1.1 -0.3 -0.8 -D.8 - I .6 -} .2 - 1.7 -1.8 -0.9 - J.O -15.7 -2.4 -1.1 0.87 0.39 0.88 o.80 0.80 0.88 0.86 0.94 0.87 0.84 0.90 0.88 0.36 0.82 0.38 0.91 0.45 67.0 0.46 0.40 0.43 0.46 0.45 0.48 0.45 0.44 0.46 D.46 0.43 67.8 51.8 59.8 67.8 65.4 73.3 67.0 63.8 69.3 67.8 62.2 0.47 70.9 Pork Bacon Ham, Light Cure Ham, Country Cure Carcass (47'10 Lean) Bellies (330J0 Lean) Backfat (IOOO% Fat) Shoulder (67'10 Lean) Ham (74"70 Lean) Sausage, Links or Bulk Sausage, Country Style, Smoked Sausage, Frankfurters Sausage, Polish Style - -2.2 -1.7 50 -3.9 0.60 0.35 39.9 56 -1.7 0.65 0.37 44.6 54 - 0.63 D.36 43.0 29.5 Thermal Properties of Foods Table 1 Food or Food Material Water Content, "10 (wt)" (continued) Highest Freezing Point °Cb Specific HeatC Latent Above Below heat of Freezing Freezing fusion cal/(gWC) cal/(g)(OC) call g Lamb Composite of Cuts (67"10 Lean) Leg (83 "10 Lean) 61 65 1.9 0.69 0.72 0.38 0.40 48.6 51.8 Dairy Products Butter Cheese, Camembert Cheese, Cheddar Cheese, Cottage (Uncreamed) Cheese, Cream Cheese, Limburger Cheese, Roquefort Cheese, Swiss Cheese, Processed American Cream, Half and Half Cream, Table Cream, Whipping, Heavy Ice Cream (10"10 Fat) Milk, Canned, Condensed, Sweetened Milk, Evaporated, Unsweetened Milk, Dried (Whole) Milk, Dried (Nonfat) Milk, Fluid (3.7"10 Fat) Milk, Fluid (Skim) Whey, Dried 16 52 37 -12.9 7 9 1.2 -7.4 51 45 40 39 40 80 72 57 63 -16.3 -10.0 6.9 2.2 27 5.6 -15.0 74 -1.4 2 3 87 -0.6 91 5 0.33 0.62 0.50 0.25 0.36 0.31 12.8 41.4 29.5 0.83 0.61 0.56 0.52 0.51 0.44 0.35 0.33 0.32 0.32 63.0 40.7 35.9 31.9 31.1 0.5 2 0.84 0.78 0.3 9 0.54 0.42 31.9 0.66 0.70 0.37 0.39 45.4 50.2 0.4 2 0.79 0.22 0.22 0.90 0.93 0.24 0.2 8 0.4 2 21.5 0.46 0.47 69.3 72.5 74 88 51 51 50 -0.6 -0.6 -0.6 -3.9 -17.2 4 9 74 64 69 2.8 0.79 0.90 0.61 0.61 0.60 0.23 0.27 0.79 0.71 0.77 63.8 57.4 59. 0 17 33 10 0.7 7 0.42 0.46 0.35 0.35 0.35 0.42 0.39 0.41 59.0 70.1 40.7 40.7 39.9 59.0 51.0 55.0 1 0.21 0.22 0.28 0.34 0.4 1 56. 6 Candy Milk Chocolate Peanut Brittle Fudge, Vanilla Marshmallows 2 1 0 17 Nuts, Shelled Peanuts (with Skins) Peanuts (with Skins, Roasted) Pecans Almonds Walnuts, English Filberts 6 2 3 5 0.2 5 0.22 0.22 0.24 0.23 0.25 a Water contents of fruits and vegetables are from Ref 6, except for Jerusalem artichokes. dried beans and peas, yams, dried apples, figs, peaches, prunes and raisins; the Jatter are from Ref 7. Water contents of meats, dairy and poultry products, miscellaneous candy and nuts are also from Ref 7; water contents of eggs. (yolks, salted) are from Ref 8, while those of fish are from Ref 9 and 10. b Freezing points of fruits and vegetables are from Ref 11, and average freezing points of other food and food materials are from Ref 8,9,10, and 12. c Specific heat was calculated from Siebel's formulas. I d O"C S'C Apples, Y. Transparent 420 740 Latent heat of fusion was obtained by multiplying water content expressed in decimal form by 79.71, the heat of fusion of water in caI/g. 1000C 15"C 2190 2O"C 3440 Apples, Delicious 210 310 Apples, Golden Delicious 220 330 Apples, Jonathan 240 360 Apples, McIntosh 220 330 200 380 320650 8501250 1100- 12001900 2500 110 220 280430 420640 5701200 9001500 140 250 310440 8301890 10302140 320 350 1390 2750 1670 4900 390· 550 680· 1150 13002100 1800· 3200 1950 3670 3340 8340 3340· 47308340 6010 8870 14270 5560- 9740- 1669018640 20030 30600 1220 3780· 4510· 9600 21220 Apples, Early Cultivars Apples, Apples, Average 0 f Many Cultivars Apricots Artichokes, Globe Asparagus C b Bananas, Ripening Beans, Lima Unshelled 820- 12302020C 2700 1350- Cb 25"C Ref 13 6, 1840 Cb Bananas, Green 0.34 0.46 0.28 71 Commodity Avocados Miscellaneous Honey Maple Syrup Popcorn, Unpopped Yeast, Bakers, Compressed Heat of Respiration, kcal per Metric ton per 24 hr, al Late Cultivars Poultry Products Eggs, Whole (Fresh) Eggs, Whites Eggs, Yolks Eggs, Yolks (Sugared) Eggs, Yolks (Salted) Eggs, Dried (Whole) Eggs, Dried (White) Chicken Turkey Duck Table 2 Heat of Respiration of Fresh Fruits and Vegetables Held at Various Temperatures" 18003200 1800 3400 6120 7620 20005000 812010960 14 14 5. 15 5.16 6,1 7 14 14 6401840 1200 2200 1080 2140 1780 3730 Beans, Snap Cb Beets, Red, Roots 330 440 20902140Cb 560580 3340 3560 720830 Berries, Blackberries 960· 1400 17502800 3200- 43005800 8900 Berries, Blueberries 140640 560750 Cb 250280 Berries, Gooseberries 420530 750830 Berries, Raspberries 10801530 t 8902360 1700- 5030- 7000 3400 6200 15000 Berries, Strawberries 7501080 1000 2030 3000 5800 4340- 62505640 11980 10340- 6, 14, 24 12900 Broccoli, Sprouting 11401310 21109790 53820- 6.25,26 34250 Brussels Sprouts 940 147 0 1970 2970 3860 5170 10620· 17010· 20790 20850 5840- 55106530 11630 Beans, Lima Shelled Berries, Cranberries Cabbage, Penn State 5,19 5,2 0 800012000 20903780 14 3170 5340 6701110 13301970 6.2 1 6,2 2 6. 14.23 5.20 7501100 1200- 22001650 2500 14 10801310 17802030 32803500 5.20 9501050 1450- 2250· 34001700 2600 3500 Cabbage, White, Winter 300500 450850 Cabbage. White, Spring 580830 470600 940 6,18 27 580620 Carrots, Roots, Imperator, Texas 7230 7960 5200 5700 1030 1420 1370· 1940 240 Cabbage, Red, Early 12930 16520 6,1 8 1200 4310 1920 2420 14 26 1977 Fundamentals Handbook CHAPTER 29 29.6 Table 2 (continued) Table 2 (continued) Heat of Respiration, keel per metric ton per 24 hr, at Vent of Respiration, kcal per metric ton per 24 hr, lIt Commodity O"C 5"C IO"C 600950 15"C 1320 1730 27 190 410 Cauliflower, Texas 1090 1250 2070 2820 Cauliflower, U.K. 4701470 12001670 25002980 41205010 Celery, 440 670 Celery, U.K. 310440 560780 Celery, Utah, Can. e 310 550 Cherries, Sour 360810 Carrots, Roots Can. Ref. (18°C) 17904050 360740 Main Crop, U.K. 25"C 20 210420 Carrots. Roots, 20"C 2280 26 4910 O° C Commodity C Melons, Watermelon b 5°C 10°C 190250Cb 460 Mushrooms 17202670 4340 Nuts (kind not specified) 50 100 Okra, Clemson 2 0 Onions, Dry, Autumn Spice 3950 f 15°C 1060 1530 1613019360 200 200 300 5340 8920 15970 5801540 140 190 220410 180 210 440 680 6401360 10604170 22103600 40405950 Cb Cb 190 390 750 1280 390 830 1390 280 720 780 690 9201330 12501610 19702620 N.Y. White Cherries, Sweet Corn, Sweet with 250 330 2600 1200 1670 23902560 (18°C) 20 1820 27 780810 16703060 23903060 580860 15302750 17201950 4750 9960 17640 6850 3250 4340 6,28 White Bermuda Onions, Green, New Jersey Olives, Manzanillo Oranges, 6,29,30 24900 Onions, Dry. 26 Oranges, Calif., Husk, Texas 14101770 (13°C) 14702030 19002940 670810 13501410 30003870 34805810 560590 6701670 6101110 970 2000 Cucumbers, Calif. Figs, Mission 31 Valencia Papayas 52005810 6, 32 5,33 Garlic 180670 360590 Grapes, 170 330 80140 190360 500 Grapes, Thompson Seedless 120 290 470 13 Grapes, Ohanez 80 200 440 13 Parsnips, U,K. Parsnips, Canada Hollow Crown 710950 5401070 220500 380940 2360 6,34 Peaches, Alberta 230 400 15301840 6,35 Peaches, Several 250390 390560 Concord Grapes, Emperor 610720 Cultivars Peanuts, Cured I ( 1.70C) Peanuts, Not Cured Virginia Bunch 1 Grapefruit. 560Cb 720 1080 1330 36 420Cb 780 970 1170 36 California Grapefruit, Peanuts, Dixie Spanish Pears, Bartlett 190420 310610 Pears, Late 160 220 360850 160300 450950 Florida Horseradish 500 660 1610 2000 2730 Ripening Kohlrabi Leeks 610 1000 1920 3000 1200 1780 32804170 50607150 Pears, 5801000 5,20 1390 Lemons, Calif Eureka Lettuce, Head Calif. 5601030 8101220 16702450 23602500 3670 Lettuce, Head Texas 640 810 1330 2200 3480 Lettuce Leaf, 1410 5030 (27°C) 5,26 3850 6140 8960 (27°C) 26 1270 2170 2710 4190 6630 26 360640 4201140 9202780 Mangos 2750 45909260 7340 Cantaloupes Melons Honeydew 310530360Cb 610 C b 190310Cb Early Ripening Peas, Green in Pod 18602860 33704670 Peas, Shelled 28904620 48405953 Peppers, Sweet 360 Persimmons 2410 Limes, Persian Melons 36 1790 Texas Lettuce, Romaine, Texas 1590 Pineapple, Mature Green Pineapple, Ripening Plums, Wickson 6,37,38 Potatoes, Calif. White Rose, 950 20602360 27303950 38104370 5,6,26 490 720970 12201460 16102110 6,26,39 13302390 Florida Oranges, Calif., W. Navel 180 240550 Cb 720 120- Immature Potatoes, Calif. White Rose, Mature 360420 20°C 13202830 960 2100 25"C Ref 6,26 6,40 14 (29°C) 26 21110 Thermal Properties of Foods 29.7 Table 2 (continued) Table 3 Change in Respiration Rates with Time Heal of Respiration, kcal per metric ton per 24 hr, at O°C Commodity 5°C 1O°C 15°C Heat of Respiration, 20°C 25°C Ref Days in Commodity potatoes. Calif. White Rose, 1 C b 310420 420 420610 560730 - Storage kcal(metric ton) °C Ref 5 Apples, Grimes 7 180 Very Mature 800 52 (lO°C) Cb potatoes, Katahdin Can. m 240- 480- 260 620 220- 260- potatoes, Kennebec Cb Radishes, 890- 1170- 1890- 4280- 1060 1280 2250 330- 470- 920- 360 500 970 500810 6701110 120- 290- 170 312 with Tops Radishes, Topped Rhubarb, Topped Rutabaga, n Spinach. Texas - Spinach, U.K., Summer Spinach, U.K., Winter Squash. Summer, Yellow, Straight-neck Squash, Winter, - 27 7590- %80- 6 4760 8340 11790 1700- 2920- 4120- 2000 3000 4650 - 18902780 24503480 - 48 - 650- - - 27 - 26 6770 10940 14070 710- 1670- 3580- - 11320- 1310 1970 4590 1070- 1790- 4170- 1550 3850 6320 720780C 8601140C 21402250 Cb Cb Cb Sweet Potatoes, Cb Cb b b 20 13230 118°C) - (18°C) 45905560 1192014900 52005950 800- 980- 1350C 1350 860- 13501410 C C 1960C Cb Cb 430Cb 920C b Cured, Yellow Jersey Sweet Potatoes, Tomatoes. Texas, - Cb 3670 1530 2140 16 920 1590 I 3 16 4900 2410 1710 6430 3980 1840 16 Beans, Lima, 2 1830 2200 18 in Pod 4 1230 1770 6 1080 1620 I 2 440 162 3 350 15 Blueberries, 6 Broccoli, Waltham 29 I 4 8 - 4530- 6 Corn, Sweet, I 3140 2 2250 4 1880 I 800 2 12 730 730 10 30 240 370 550 920 in Husk 49 - - 49 1250 2120 26 1 0 (27°C) 26 1630 2480 2950 (27°C) 26 Figs, Mission 180 Cb - 1310- 1470 1470 1530 Turnip, Roots 530 Watercress 1190- 2680- 5060- 10130- 1610 2980 5660 12520 610 4470 2690 2020 54 - 26 - 32 33104480 Garlic - 53 - - 14702140 - 20 - Tomatoes, Calif. Pearson, Mature Green 580- 2750 4 870Cb Tomatoes, Texas, Ripening Cb I - - Mature Green Cb 670 Blue Crop 1750 Noncured Cb 1070 180 Asparagus, Martha Washington 7470 Cb 180 80 960 2810 Cured, Puerto Rico 30 Artichokes, Globe 550 Butternut Sweet Potatoes, 27 - 260 Laurentian, Can. (day) SOC 18302940 50 Olives, 20 - Lettuce, Great Lakes 860 2020 1040 1220 I 5 550 800 10 490 920 I 55 - 2390 56 (l5eC) Manzanillo - 33 5 1770 - a Column headings indicate temperatures al which respiration rates were determined, within 10 - 1350 1°C except where the actual temperatures are given in parentheses. b The large leaner "C" denotes a chilling temperature. If the temperature is borderline, not Onions, Red damaging 10 some cultivars, or if exposure is short, a value is given. C Rates are for 110 2 mo and 2 10 4 mo storage, the longer storage having the higher rate. except at DOC, where they were the same. d Rates are for I 10 2 mo and 4 to 6 mo storage. respiration increasing with lime only at Plums, Wickson 15°C. e Rates are for J 10 2 mo storage. I 100 30 150 - 57 120 200 2 120 240 6 120 430 18 180 550 47 f Rates arc for 1 to 2 mo and 4 to 6 mo storage; rates increased with time at all temperatures as dormancy was lost. g Rates are for I to 2 mo and 4 10 6 reo; rales increased with time at all temperatures. h Shel1cd peanuts with about 7flJo moisture. Respiration after 60 hr curing was almost 2 Potatoes negligible, even at 30°C. 370 6 - 490 10 - 430 1 1080 1750 2 810 1880 5 810 2020 5 - 51 i Respiralion for freshly dug peanuts, not cured, with about 35 to 40flJo moisture. During curing, peanuts in the shell were dried to about 5 to 6070 moisture, and in roasting are dried further to about 2070 moisture. 2070 moisture. Strawberries, Shasta j Harvested 98 days after planting. 51 24 k 51 Harvested 126 days after planting. I Harvested 141 days after planting. 51 Tomatoes, Pearson, m Rates are for J to 2 mo and 4 to 6 mo with rate declining with time at 5°C but increasing at 15°C as sprouting started. n Rates are for J to 2 and 4 to 6 mo; rates increased with rime, especially at 15°C where sprouting occurred. Mature Green 1960 (20°C) 15 20 - 1710 1470 50 1977 Fundamentals Handbook CHAPTER 29 29.8 Table 4 Enthalpy of Frozen Foodsa Water Coolant Product Mean Specific Heal h 4 tu 32°C. kcal/(kg1 (dog C1 Temperature ºC -40-JO-20-1S-)6-J4-12 -10 Enthalpy, kcal/kg u;'() water nonfrozen c 2 4 6 9 10 12 Enthalpy, 10 I 070 (wI) -9 8 -7 6 23 19 24 27 23 29 27 31 21 7 18 7 19 20 21 -4 Fruits and Vegetables Applesauce Asparagus. Peeled 82.8 Y2.6 0.89 0.95 kcal/kg 1 8 20 1417 12 1315 56 water unfrozen Blueberries 85. 1 0.90 Entha1py, kcal/kg IJ/o 11 1213 7 8 1517 911 20 14 11 12 13 7 8 15 1 7 911 20 14 water unfrozen Carrots 87.5 Enthalpy, calk 0"10 water unfrozen Cucumbers 95.4 10 11 15 0.96 Enthalpy, kcal/kg fJfo 85.5 0.91 22 15 17 water unfrozen Peaches. 85. 1 0.90 83.8 0.89 without stones 1719 1416 22 18 12 13 16 8 9 I1 Entha1py, kcal/kg 070 1719 1316 121416 9 10 12 Enthalpy, keeling 070 Plums, without 80.3 0.87 stones Raspberries 22 18 0.89 Strawberries 90.2 89.3 0.93 0.94 o 131618 1 4 16 1 8 water frozen o I1 7 20 23 20 23 12 14 89 water unfrozen I1 1618 1013 12 1314 6 Sweet Cherries, 77.0 water unfrozen 10 12 13 Tomato Pulp 75.8 o water unfrozen 0.85 0.96 16 7 1416 18 79 11 14 16 18 21 24 1 5 1 7 1 9 21 26 23 19 10 11 Entha1py, kcal/kg 070 1 8 20 1618 23 21 12 1 315 17 5 6 7 water unfrozen 24 21 28 29 21 17 12 29 32 water unfrozen 18 8 Eggs Egg White 86.5 0.91 Enthalpy, kcal/kg 0 Egg Yolk Whole Egg with 50.0 66.4 0.74 0.79 Enthalpy, kcal/kg 0 070 water unfrozen - Enthalpy, kcal/kg 4 9 10 11 1214 - 10 - 070 water unfrozen 0 4 9 10 11 13 14 - 4 9 10 11 15 12 13 26 18 21 24 30 18 26 20 1 8 1 9 2 1 25 28 3 35 33 16 34 37 31 25 20 1 9 18 9 2 1 14 32 36 22 1 6 35 40 27 26 80.3 0.88 Haddock 83.6 0.89 Perch 79. 1 0.86 74.5 0.84 Beef. Lean Fresh Beef, Lean, Dried 26. 1 0.59 Enthalpy, kcal/kg 070 water unfrozen Entha1py, kcal/kg % water unfrozen 0 5 10 11 13 10 10 11 12 0 8 Enthalpy, kcal/kg O7owaterunfrozcn Enthalpy, kcal/kg 070 water, unfrozen Entha1py, kcal/kg water unfrozen 12 5 10 1 I 13 8 9 JO 1416 18 J314 16 0 5 10 11 12 1415 17 10 10 II 12 12 13 14 15 0 5 10 11 12 1416 17 4 10 12 13 1415 1516 43 16 17 96 96 97 98 99 JOO 30 22 13 20 11 27 20 24 18 39 47 45 55 36 33 39 24 2 10 1 17 18 22 17 18 14 21 20 23 23 26 28 20 21 22 22 24 27 19 21 23 33 15 16 17 1 9 20 21 25 28 18 19 23 27 34 20 21 23 25 28 33 15 16 2 1 1 8 1 7 19 19 14 17 18 1 8 1 6 19 21 21 23 18 1 8 20 20 24 31 24 27 31 22 26 32 ~ 27 n ~ 31 40 22 20 18 23 22 17 1 37.3 0.62 Entha1py, Whole Wheat Bread 42.4 0.64 Enthalpy, kca1/kg kcal/kg 9 10 10 12 14 16 18 1I 13 15 1 21 9 a Above -4()OC. To convert from kcal/kg to Btu/lb, multiply by 1.80. Adapted from Ref 4,65,66,81,82 and Ref 8. Temperature range limited to 0 to 20°C for meats. C Total weight of unfrozen water = (total weight of food)(% water content/ 100)(070 Water unfrozen/ I (0). Calculated for a weight composition of 58% white (86.5070 water) and 32070 yolk (50fJio water). C Date for chicken, veal, venison very nearly matched the data for beef of the same water content.8 40 40 16 1 9 18 Bread White Bread 39 38 27 27 23 32 29 28 1 SO 38 42 1 9 14 17 13 10 10 11 12 13 0 35 29 15 1416 II 12 II 35 3 1 1 8 1 6 29 31 28 2 6 Fish and Ideal Cod 1 28 26 23 18 33 30 1 34 25 26 22 23 2 6 7 24 30 26 1 9 Shelled 29 25 23 13 16 1 22 17 23 f170 12 24 27 33 25 Enthalpy, kcal/kg 1 7 24 27 29 121416 10 12 14 23 15 10 20 19 Entha1py, kcal/kg 070 water unfrozen 92.9 20 16 Entha1py, kcal/kg 070 withou1 Stones Tall Peas 26 27 Enthalpy, kcal/kg fJ!o 5-6 0.86 22 19 4 33 6 20 Enthalpy, kcal/kg % Spinach 1 7 19 1417 water unfrozen Entha1py, kea1/kg % 82.7 1 5 water unfrozen Pears, Bank-II 22 17 15 12 13 15 8 10 12 Enthalpy, kea1/kg 070 8 2 1 \.,'atcr unfrozen Onions 36 37 44 2 1 1214 30 20 22 25 23 2 5 28 28 32 E. D. F. Thermal Properties of Foods 29.9 90 70 60E :''":: ~ 50 '" ,,: a. ...J 40 <t :r: >z UJ 30 WATER CONTENT. % (by weight) Fig. 1 Enthalpy of Beef (Adapted from Ref 4) temperature range. Conversely, for a 60070 water content, freezing starts at a much lower temperature, and appreciable freezing occurs over a greater temperature range; because of the lower water content, however, the energy associated with freezing is significantly less. Fig. 2 does not give enthalpy of whole fruits and vegetables G. H. 130 because of the effect of solids (fibers, rind, membranes, stems, and seeds), which are not a part of the juice, and do not participate in the change of phase. From data for 16 fruits and vegetables, Riedel 65 obtained the following correlation between enthalpy of fruits and vegetables, enthalpy of juice (Fig. 2), and percent solids-not-juice (solids other than those present in the juice). where !J.h = enthalpy difference, kilocalories per kilogram. X snj = solids-not-juice, percent by weight. !J.hj = enthalpy difference of juice from Fig. 2, kilocalories per kilogram. !J.T = temperature difference, degrees Celsius. Eq 4 and Fig. 2 have been used to calculate enthalpy of the fruits and vegetables investigated, with results shown in Table 4. Except for plums and onions, enthalpy of fruits and vegetables, Table 4, differs from Riedel's measured values by less than 5% of enthalpy at DoC. Maximum deviation for plums and onions is 12%. Using measured enthalpy values for egg white, yolk, and shell, Riedel66 calculated enthalpy of whole egg with shell. These calculated values are shown in Table 4. Also in Table 4: enthalpy of frozen egg products. Enthalpy of frozen egg yolk of various water contents is shown in Fig. 3. Fresh Foods Specific Heat. Above freezing, specific heat may be used instead of enthalpy. Specific heat of fruits, vegetables, juices, meats, breads, and eggs are shown in Table 4; selected data are shown as a function of water content in Fig. 4. For juices, variation of specific heat with water content is uniform (Fig. 4) and closely matches the equation: WATER CONTENT. % (by weight) Fig.2 Enthalpy of Fruit Juices and Vegetable Juices (Adapted from Ref 65) CHAPTER 29 29.10 1977 Fundamentals Handbook Table 5 Specific Heat of Beef at Temperatures Below 64 40oe 1. 0 Temperature, 0.8 0. 6 °C Beef, Chuck -110 - 80 - 50 0.24 0.35 0.44 40 0.49 0.4 WHOLE EGG 0.2 L- EGG YOLK WHOLE WHEAT BREAD WHITE BREAD foods are nonhomogeneous and anisotropic; however, Eq 6 has been used to find the thermal behavior of foods. 72-75 Thermal diffusivity may also be defined: ORIEO Bm o I o 10 20 I I [ 30 40 50 I 60 70 I 80 90 Specific heat, kcal/(kg)(deg C) Product 100 WATER CONTENT. Fig. 4 Specific Heat of Food in the Temperature Range of 4 to 32°e (0 to 200e for Meats) a = 0.0143 klQcp (7) where a = thermal diffusivity, square centimeters per minute. Cp = 0.40 + 0.006[O?owater (wt)1 (5) where cp = specific heat at constant pressure, kilocalories per (kilogram)(degree Celsius). When data are needed for juices not in Fig. 4, Eq 5 yields reasonably accurate specific heat values. For other foods, the correlation with Eq 5 is not as precise because of distorting effects of the solids-not-juice content (fats, fibers, rind, membranes, stems, and seeds). However, deviations are not great and, when data are lacking, Eq 5 may be used to estimate specific heat. In comparing data from Table I and Fig. 4, slight differences in specific heat values may be noted for the same food product, particularly at low moisture contents. This is because Table 1 data were computed using Siebel's formulas I which, in its time, represented the best information available for foods generally; while Eq 5 is based on more recent experiments. Data for meats (Fig. 4) were obtained in the temperature range of 0 to 20°C; caution is recommended in extrapolating the data into the range of 20 to 50°C, particularly for meats with high fat content. For beef fat, the change in enthalpy from 20 to 50°C is more than double67 the change in sensible heat due to specific heat alone; the additional heat is required to melt the fat. At temperatures between -40 and O°C, the specific heat of beef fat is constant at 0.40 kcal/(kg)(°C).67 Above 50°C, it is constant at 0.45 kcal/(kgWC). Between 0 and 50°C, the energy required for a unit change in temperature is highly variable, because beef fat components change state at different temperatures. Similar data are available for 26 additional fats and oils. 67 Thermal Diffusivity. For non steady state heat transfer, the important property is thermal diffusivity, a, defined by the Fourier equation: where x,y,z = rectangular coordinates. T = temperature, degrees Celsius. T = time, minutes. a = thermal diffusivity, square centimeters per minute. Eq 6 has been solved for numerous conditions, and graphical solutions are available. 68-73 Use of Eq 6, however, is limited to temperatures above freezing; and, from a mathematically rigorous point of view, is restricted to homogeneous, isotropic substances. Generally, k = thermal conductivity, milli-watts per (centimeter)(degree Celsius). Q = density, grams per cubic centimeter. cp = specific heat at constant pressure, kilocalories per (kilogram)( degree Celsius). The constant 0.0143 is required because of the units in which k, Q, and Cp are defined. The denominator on the right-hand side of Eq 7 denotes heat absorbing ability; the numerator, ability of the material to conduct heat through itself. Schneider 76 interprets thermal diffusivity in terms of heating time: "In a transient heating process the thermal capacity of the conducting material dictates the quantity of heat absorbed and the thermal conductivity of the conducting material sets the rate of this heat addition. The reciprocal of the diffusivity, I/", = min/cm2, is a measure of the time required to heat this material to some required temperature level and evidently this time is directly proportional to the square of the conducting path length." Thermal diffusivity data for foods are scarce; but reasonable estimates can be obtained from Eq 7, using values of thermal conductivity, specific heat, and density, given elsewhere in this chapter. A few experimental values are available (Table 6). Like other thermal properties of foods, thermal diffusivity strongly depends on water content, as shown by Riedel's correlation: 77 a = 0.053 + (aw - 0.053)[% water (wt)1 (8) where a = thermal diffusivity, square centimeters per minute. a w = thermal diffusivity of water at the desired tem- perature, square centimeters per minute. Thermal diffusivity of water as a function of temperature is available elsewhere. 3 When data are lacking, Eq 8 may be used to estimate thermal diffusivity of foods; but its use must be limited to water contents above 40% by weight. For water contents below 40%, there is some question whether the water represents the continuous phase. If another constituent (such as fat-usually a dispersed phase) replaces the water as the continuous phase, there would be an abrupt drop in thermal conductivity and thermal diffusivity. Meats. Eq 8 applies to foods with variable amounts of water, fat, and fiber; if the water content is reduced, it is assumed that the water is replaced with fat. For this reason, the thermal diffusivity of 0.053 cm2/min, obtained from Eq 6 for zero water content, is reasonably close to a computed value for fat (from Eq 7). Thus, Eq 8is applicable only where a reduction in water content is compensated for by an increase in fat content. Eq 8 cannot, for example, be used for freeze dried samples, where a reduction in water content is compensated for by an increase in air content. Thermal Properties of Foods 29.11 Table 6 Product Apple, Whole, Red Deliciousa Applesauce Bananas, Flesh Cherries, Flesh b Peaches b Potatoes, Whole Potatoes, Mashed, Cooked Strawberries, Flesh Sugar Beets Codfish HalibutC Beef, Chuckd Beef, Round d Beef, Tongued Corned Beef Ham, Smoked Ham, Smokedd Water Thermal Diffusivity of Some Foods Water content, 0/0 (wt) 85 37 37 80 80 76 76 78 78 92 Fat content, %(wt) 81 81 76 66 71 68 65 65 64 64 - I 16 4 13 - Apparent density, (g/cm3) 0.84 - - Temperature, °C o to 30 5 65 5 65 5 65 0 to 30 2 to 32 o to 70 5 65 5 o to 60 5 65 40 to 65 40 to 65 40 to 65 40 to 65 5 65 5 40 to 65 30 - - 1.05 0.96 1.04 to 1.07 - 1.07 1.06 1.09 1.06 1.09 - 14 - Thermal diffusivity, cm2/min 0.082 0.063 0.067 0.073 0.084 0.071 0.085 0.079 0.084 0.080 0.074 0.087 0.076 0.076 0.073 0.085 0.088 0.074 0.080 0.079 0.068 0.079 0.071 0.083 0.089 0.096 Ref 83 77 77 77 77 77 77 84 85 86, 87 77 77 77 75 77 77 88 88 88 88 77 77 77 88 3 3 a Data is applicable only to raw whole apple. bFreshly harvested. cStored frozen and thawed prior to test. d Data is applicable only where the juices extruded during heating remain in the food samples. Table 7 Thermal Properties of Food Container Materials (0 to 80°C) Product Stainless Steel (302) Type 18-8 Austenitic Glass, borosilicate Nylon, Type 6/6c Polyethylene, High Density C Polyethylene, Low Density C PolypropyleneC Polytetrafluoroethylene C Thermal conductivity, m W /(cm) (deg C) 160 Specific heat, kcal/(kg) (deg C) 0.12 Apparent density, g/ cm 3 7.9 Thermal diffusivity, b (cm2/min) 2.4 II 2.4 4.8 0.20 0.40 0.55 2.2 1.1 0.96 0.36 0.078 0.13 90 91 91 3.3 0.55 0.93 0.092 91 1.2 2.6 0.46 0.25 0.91 2.1 0.041 0.071 91 91 Ref 89 aTo obtain: W I(m) (deg C). multiply by 0.1; cal/(cm) (sec) (deg C). multiply by 2.39 x to -4; BlU/(hr) (rt) (F), multiply by 0.0578; kcal/(hr) (m) (deg C), multiply by 0.0856. bCa1culated; a ~ 0.0143 k/QCp)' To obtain in2/min, multiply by 0.155. COata applicable only to monolayer materials. When meat samples are heated to temperatures in the range of 40 to 65°C, juices sometimes exude, and heat transfer rates may be altered significantly, depending on whether the exuded juices remain in the sample and contribute to heat transfer, or drain away from the meat and significantly lower thermal conductivity. The data in Table 6 for the temperature range of 40 to 65°C apply only where juices remain in the meat sample. Fruits. Most data for fruits (Table 6) apply to the flesh of the fruit; for products such as apples, cherries, and peaches, the data can be used for the whole fruit (with rind) because the very thin rind neither improves nor inhibits heat transfer. Conversely, the relatively thick rind of grapefruits, oranges, and lemons, has a pronounced effect on heat transfer rates, even though thermal diffusivity of the rind is about the same as that of the juice vesicle.78 It may seem that these equal thermal diffusivities should result in equal heat transfer rates through both components, But, the problem arises because the thermal conductivity of the rind is only half that of the juice vesicle.79 The rind has a spongy layer of loosely arranged cells with many gas-filled intercellular spaces, producing an insulating effect. Because of these spaces, the rind density is only 0.5 that of the juice vesicle.78 The lower density compensates for the lower thermal conductivity, leaving thermal diffusivity essentially unchanged (Eq 7). The rind's insulating effect results from the lower thermal conductivity and correspondingly higher temperature gradient, which reduces heat transfer rates through the rind. If the rind had a thermal diffusivity and thermal conductivity equal to that of the juice vesicle, there would be no insulating effect. Data are available on the "effective" thermal diffusivity of whole grapefruits, oranges, and lemons.71,74.78-80 However, because of the rind's insulating characteristics, the reported 1977 Fundamentals Handbook CHAPTER 29 29.12 values (except in Ref 74) are significantly lower than expected for a food of high water content. These values do represent an empirical coefficient for any given experiment, and may be used to estimate heating and cooling times. They are dependent, however, on rind thickness, fruit size, and time of harvest. 78 Since the data do not meet the criteria of a basic thermal property, they are not listed in Table 6. Food Container Materials In calculating heat transfer in foods, it may be necessary to consider the effect of the food container. Thermal properties of some food container materials are given in Table 7. In much the same way as a thick rind insulates the flesh of fruit, a food container may insulate food. Thermal diffusivities and conductivities of glass and stainless steel are significantly greater than those of foods (Tables 7 and 8). Consequently, these two materials will not significantly delay heat transfer in foods. Thermal diffusivity of low density polyethylene is considerably lower than that of glass or stainless steel, but about the same as that of beef (Table 6). A container fabricated from polyethylene 0.3 mm thick has about the same effect on heat transfer as an additional 0.3 mm thickness of the food, provided there is intimate contact between food and container, thereby preventing accumulation of air spaces on the inside surface of the container. Thermal conductivity of low density polyethylene is somewhat lower than that of beef, and, if the container wall is thick enough, it could reduce heat transfer rates to the food; but the effect is negligible when the container diameter is greater than about 10 em and wall thickness less than about 0.4 mm. The data for plastics (Table 7) apply. only for monolayer materials, and not for plastic laminates. Thin plastic films can have a thermal resistance much greater than indicated by their thermal conductivities, due to imperfect contact between laminated films and gas bubble buildup on the hydrophobic surface of the plastic. THERMAL CONDUCTIVITY Heat conduction (as opposed to convection and radiation) can be described as the transfer of heat associated with motion of the particles (molecules, atoms, electrons) of a substance without appreciable displacement or flow of those particles. This mode of heat transfer depends on a property of substances called coefficient of thermal conductivity: the quantity of heat that flows in unit time through a plate of unit thickness and unit area having unit temperature difference between its faces. For food refrigeration, this is commonly expressed as MW /(cm)(°C). The U.S. customary unit is [(Btu)(ft)/(hr)(ft2)(deg F)1; and the SI unit for thermal conductivity is [(watt per square meter) per (Kelvin per meter of thickness)1, written watt per (meter)(Kelvin), or, in symbols, W/(m' K). Thermal conductivity depends on many factors, including: kind of substance (metal, dielectric, crystalline, amorphous, solid, liquid, gas); composition (impurities, mixtures); structure and structural orientation; temperature; and pressure. Thus, accurate measurement and prediction of thermal conductivity may be difficult for many foods, although a large amount of experimental data is available, and estimations or predictions sufficiently accurate for practical purposes can be made for many food materials. Thermal Conductivity of Mixtures Thermal conductivity for mixtures of 60/0 gelatin gel and butterfat arranged in several ways are shown in Fig. 5, which was adapted from a more detailed study. 94 Since the ratio of o 20 4 0 60 8 0 10 0 BUTTERFAT IN MIXTURE, % (VOLUME) Fig.5 Thermal Conductivity of Gelatin Gel 16% (wO1-Butterfat Mixtures at 4°C. A. Alternate parallel layers parallel to direction of heat f/ow (calculated). B. Small spherical particles of butterfat dispersed in gelatin gel (calculated using Maxwell-Eucken equation). I. As for (2) but experimentally determined values up to 52"70 butterfat. D. Alternate parallel layers perpendicular to direction of heat f/ow (calculated). NOTE: Experimentally determined values for thermal conductivity of butterfat (1.76) and gelatin gel (5.91) are used in calculations. thermal conductivities of butterfat and 6% gelatin gel is roughly the same as for fat and lean portions of meat, the curves give some indication of the variability to be expected in the thermal conductivity of meat. Conductivity is maximum for layers arranged parallel to the direction of heat flow (Curve A) and minimum for perpendicular layers (Curve D); other arrangements fall in between. Curves B (calculated) and C (experimental) give values for small spherical butterfat particles dispersed in the gel. The calculated curve was obtained using Eucken's adaptation95 of Maxwell's equation96 for conductivity of a mixture composed of small spheres of one substance dispersed in another: k = k 1 - [1 - a(kd/kc)1b c 1 + (a - l)b (9) where k = conductivity of the mixture. kc = conductivity of the continuous phase. kd = conductivity of the dispersed phase. a = 3kc/(2kc + kd)· b = Vd/(Vc + Vd)· Vd = volume of dispersed phase. Vc = volume of continuous phase. The derivation of this equation assumes the dispersed particles are sufficiently separated for their effects in disturbing heat flow to be independent of each other. Effect of Temperature Temperature effects on thermal conductivity of a number of meats and fats, as well as gelatin gel and ice, in the range of 10 to -25°C are shown in Fig. 6 (composition of sample Thermal Properties of Foods 29.13 J. 20 I I 1 I I I ~ 24 TURKEY PORK CODFISH(l) I BEEF (II) 22 I 20% GEL 15 TURKEY . -;i j; PORK(l)~ SALMON(l) SALMON 11! BEEFI1! ~ 10 TURKEY() ~ , 14 WA T E R 8 5 MEAT IAV.I -25 -20 -15 -10 -5 o 5 TEMPERATURE °C Fig. 6 Thermal Conductivity of Meats, Fats, Gelatin Gel, and Water between 100C and -25° C (II indicates heat floK' parallel to fiber structure; 1- indicates heat flow perpendicular to fiber structure). materials is in Table 8), also adapted from Ref 94. Rapid change of phase and the possibility of sub cooling and metastable states make values in the 0 to -10°C range more difficult to measure and less reliable than at other temperatures. The effect of meat fiber or structure orientation in the frozen state appears to be 10 to 20%. Thermal conductivity of fats is affected relatively little by temperature in the range studied. Thermal Conductivity and Water Content The relation between thermal conductivity and moisture content for a wide range of food materials, based on a study 97 using the aforementioned Maxwell-Eucken equation, is shown in Fig. 7. The effect of temperature is also included. The curves represent data on sugar solutions and fruit juices, 98 milk and evaporated milk, 99 butter fat and gelatin gels, 94 fats, 94.100 and meats, 94.100-102 with an accuracy of ±100J0 if an allowance of ±7OJo is made for fiber direction in frozen meats. The allowance is positive for heat flow parallel to the fiber structure; negative for flow across the structure. The study on which Fig. 7 is based differs from a number of others 94.98.99.103.104 in that water content was calculated on a volumetric rather than a gravimetric basis, and a wider range of food materials and temperatures is covered. In addition, only materials not containing appreciable air were included. For the above-freezing temperatures, the curves follow the Maxwell-Eucken equation, assuming water to be the continuous phase, and the nonaqueous part the dispersed phase. For below-freezing temperatures, the curves best fitting the experimental data (Fig. 7) represent an average of the results calculated assuming ice to be the dispersed phase in one instance, and the nonaqueous part plus unfrozen water to be the dispersed phase in the other instance. o 1 0 20 30 40 50 60 70 80 90 100 WATER CONTENT %(VOL) Fig. 7 Effect of Water Content and Temperature on Thermal Conductivity of Food Materials The Maxwell-Eucken equation is valuable in predicting thermal conductivity from water content, even though the assumptions on which it is based do not appear to be closely met, because: I. The thermal conductivity of water is high compared to that of the nonaqueous components, especially at below-freezing temperatures. 2. The thermal conductivity of the nonaqueous components falls within a relatively narrow range-most organic substances between 1.4 and 2.0 m W /(cm)(°C) with most fats in the 1.6 to 1.8 range. 3. The densities of fats, proteins, and carbohydrates fall within narrow ranges which are relatively close together (values used in the stud y97 were 0.92, 1.35. and1 .55 g/cm3 for fat, protein, and carbohydrate, respectively). Tabular Data Thermal conductivity data for a wide range of foods and food materials are given in Table 8, which is based on a compilation made by the Thermal Properties Research Center at Purdue University under ASH RAE sponsorship (RP-62). Since TC 11.9 used the TPRC report as its data source without going back to the original literature, it cannot accept responsibility for correctness of the abstractions made by the TPRC, although care was used in selecting data for Table 8 to minimize typographical or other errors. While the TPRC report does not cover all literature on thermal conductivity (178 articles representing most of the world's reasonably accessible literature on the topic were reviewed), it was considered a good basis for Table 8. To reduce the volume of data in the TPRC report and facilitate use of Table 8, the data in some instances have been averaged, interpolated, extrapolated, selected, or rounded off. For example, where conductivity values were given for a range of conditions (temperature, water content, pressure), the limits of the range were usually included with a sufficient number of points in between to represent the data. Where values for similar materials were given by different authors, selection was based on completeness of information and knowledge of the author's work by the committee's reviewers, as well as other factors considered to favor one author over another. Data from different sources were not averaged. Data of doubtful accuracy or reliability were omitted. 29.14 CHAPTER 29 Table 8 Food or Food Material Temp, °C 1977 Fundamentals Handbook Thermal Conductivity" of Food and Food Materials Water Coolant, 070 (wI) k' mW/(em) (deg C) Rating A,I,U Ref' Remarks-Compositionf U 105 0.75 d 0.75 d U U U 106 107 108 O.66d A 109 Values taken from plot of series of values given by authors Grains, Cereals, and Seeds Corn, Yellow 32 Flax Seed Oats, White English Sorghum 32 27 5 Wheat, No. I Northern Hard Spring Wheat, Soft White Winter 0.9 14.7 30.2 34 12.7 13 22 2 1.40 1.59 1.72 1.15 1.30 1.31 1.50 1.35 31 7 10 14 5 1.49 1.55 1.68 1.21 10 15 1.29 1.37 0.6R d Hybrid Rs61 0 grain 110 U 105 Values taken from plot of series of values given by author U II I 0.75 d; machine sliced, scalded, Fruits, Vegetables, and By-products Beans, Runner 9 3.89 -13 -6 -16 9.20 3.R5 6.69 I I I1 I III Carrots, Puree -8 12.6 U III Potatoes, Mashed Potato Salad Apple Juice 10.9 4.79 5.59 6.31 5.04 5.64 3.89 4.35 4.18 I I A III 112 98 Apple -13 2 20 80 20 80 20 80 8 Black Currants -17 3.10 Gooseberries -15 2.76 Grapefruit .Juice Vesicle Grapefruit, Ring 30 4.64 A 30 2.37 A 79 Grapefruit, Whole 25 3.26 A 113 Grape, Green, Juice 20 80 20 80 20 80 25 30 30 25 25 20 80 20 80 20 80 -16 -14 -15 5.67 6.39 4.96 5.54 3.96 4.39 4.39 4.35 1.79 4.90 4.10 5.50 6.29 4.75 5.32 4.02 4.46 2.47 11.0 9.6 A 98 packed in slab Broccoli Carrots Lemon Orange Juice Vesicle Orange, Rind Orange, Whole Orange, Whole Pear Juice Plums Strawberries 87 70 36 89 68 37 85 60 39 0.56 d; heads cut and scalded 0.6 d; scraped, sliced and scalded 0.89 d; slab 0.97 d; tightly packed slab 1.01d Refractive index at 20°C=1.35 Refractive index al 20°C=I.38 Refractive index at 20°C= 1.45 A 74 Tasmanian French Crab, whole fruit; 140g I III I 111 O.64d 0.58 d; mixed sizes 79 Marsh, seedless; 786 p Marsh, seedless; 812p Marsh Refractive index at 20°C= 1.35 Refractive index at 20°C=1 .38 Refractive index al 20°C=I.45 A A A A I A 113 79 79 1 13 113 98 Eureka Valencia; 786p Valencia; 812p Valencia Washington navel Refractive index at 20°C-I.36 Refractive index at 20°C-l.40 Refractive index at 20°C-l.44 ! I 111 III 0.6Id; 4 cm diam., 5 em long Mixed sizes, 0.80 d slab Mixed sizes in 57°10 sucrose syrup, slab Meat' and Animal By-products Beef Brain Beef Fat 35 35 35 77.7 0.0 20 4.96 1.90 2.30 A A" 114 114 12% fat; 10.3% protein; 1.04d Melted 100% fat; 0.81 d 0.86 d Thermal Properties of Foods Table 8 29.15 Thermal Conductivity' of Food and Food Materials (Continued) Water Food or Food Materialb Beef Fat .L b Temp, content, °C % (wt) 2 -9 35 Beef Kidney Beef, Lean =b 35 3 -15 20 -15 6 Beef, Lean .L b -15 20 Beef Liver Beef, Lean =b Beef, Lean =b kC, mW/(cm) (deg C) 9 6 -15 3 -15 6 4 6 3 30 20 -15 20 -15 3 -15 4 -15 20 -13 4 -15 20 -14 25 Beef, Lean .L b Beef, Ground Horse Meat .L b Lamb b Lamb =b Pork Fat Pork, Lean =b Pork, Lean =b Pork, Lean.L b Pork, Lean .L b Sausage V eal.L b Veal = b A,I,U Remarks-Composition1 Ref" 2.17 2.87 5.24 A 94 A 114 8.3% fat, 15.3% protein; 1.02 d A A 114 94 7.2% fat; 20.6% protein; A 101 1.4% fat 76.5 4.88 5.06 14.2 4.30 14.3 4.00 A 101, 115 2.4% fat 79 13.6 4.80 A 101 Inside round; 0.8% fat A 101, 115 76A 72 75 79 -15 Beef, Lean .L b Rating d 89% fat Sirloin; 0.9% fat 13.5 76 4.10 68 11.4 4.71 11.2 4.06 4.10 3.51 3.64 4.60 4.56 11.2 3.99 12.7 2.15 2.18 4.78 14.9 4.53 14.2 4.56 12.9 5.05 13.0 4.27 25 62 3.87 A 20 -15 28 75 4.70 13.8 A 118, 119 118, 119 101 4A5 A 101 120 120 74 67 62 55 53 70 72 71 6 72 76 76 72 76 75 -15 A 94 A 116 3% fat Flank; 3 to 4% fat 12.3% fat; 0.95 d 16.8% fat; 0.98 d 18% fat; 0.93 d 22.2% fat; 0.95 d I A 117 101 Lean 8.7%fat A 101 9.6% fat A 94 93% fat A 94 6.1 % fat A JOI 6.7% fat A 94 6.1 % fat A 101 A Mixture of beef and pork; 16.1 % fat; 12.2% protein Mixture of beef and pork; 24.1% fat; 10.3% protein 2.1% fat 2.1% fat 6.7% fat 14.6 Poultry and Eggs Chicken, Breast .L b Chicken, Breast with Skin 20 20 69-75 58-74 4.12 3.66 1 I Egg White 36 88 5.58 I Egg, Whole Egg Yolk -8 31 50.6 9.60 4.20 I A Turkey, Breast.L b 3 -15 4 -15 3 -15 74 4.96 13.8 4.97 12.3 A 94 2.1% fat A 94 3.4% fat A 94 2.1% fat 3 -15 83 94 0.1% fat Turkey, Leg .L b Turkey, Breast =.L b 74 74 5.02 0-6% fat 0-30% fat 103,121 III 114 0.98d 32.7% fat; 16.7% protein; 1.02 d 15.3 Fish and Sea Products Fish, Cod .L b 5.34 A 14.6 29.16 CHAPTER 29 Table 8 1977 Fundamentals Handbook Thermal Conductivity' of Food and Food Materials (Continued) Water Temp, kC content, °C Fish, Cod Fish, Herring Fish, Salmon 1 b % (wI) 5.60 3 67 5 73 16.9 8.0 5.31 12.4 4.98 5 4.3 2.19 -15 -15 Seal Blubber 1 b -15 18 32 -9 -12 mW/(cm) (deg C) 1 -15 -19 Fish, Salmon 1 b Whale Blubber 1 b Whale Meat Rating,d , Food or Food Material 11.3 1.97 2.09 6.49 14.4 12.8 A,I,U Refe 1 122 Remarks-Composition f 123 1 A III 94 0.91d; whole and gutted 12% fat; Gaspe-Salmo Salar A 94 5.4% fat-B.C. Oncorhynchus Tehawytseha A 94 95% fat 1 1 117 106 1.04 d 1.07 d I III 0.5 It'7o fat; 1.00 d Dairy Products Butterfat Butter Buttermilk Milk, Whole Milk, Skimmed Milk, Evaporated Milk, Evaporated Milk, Evaporated Milk, Evaporated Whey 6 -15 4 20 28 2 20 50 80 2 20 50 80 2 20 50 80 2 20 50 80 23 41 60 79 26 40 59 79 2 20 50 80 0.6 89 90 83 90 72 62 67 50 90 1.73 1.79 1.97 5.69 5.80 5.22 5.50 5.86 6.14 5.38 5.66 6.06 6.35 4.86 5.04 5.42 5.65 4.56 4.72 5.10 5.31 4.72 5.04 5.16 5.27 3.24 3.40 3.57 3.64 5.40 5.67 6.30 6.40 A 94 1 A A A 124 98 99 98 0.35% fat 3% fat 3.% fat A 98 0.1% fat A 98 4.8% fat A 98 6.4% fat A 99 10% fat A 99 15% fat A 98 No fat A 125 A 98 Sugar, Starch, Bakery Products, and Derivatives Sugar Beet Juice Sucrose Solution 25 0 20 50 80 0 20 50 80 0 20 50 80 0 20 50 80 0 20 79 82 90 80 70 60 50 5.50 5.69 5.35 5.66 6.07 6.36 5.04 5.35 5.72 6.00 4.73 5.01 5.36 5.63 4.43 4.70 5.02 5.25 4.13 4.37 Cane or beet sugar solution 29.17 Thermal Properties of Foods Table 8 Thermal Conductivity' of Food and Food Materials (Continued) Temp, Water content, kC Rating,d , Food or Food Material °C 50 80 0 20 50 80 2 20 50 80 2 20 50 80 2 20 50 80 2 20 50 80 25 Glucose Solution Corn Syrup 0-;0 (wI) 40 89 80 70 60 mW/(cm) (deg C) 4.67 4.90 3.82 4.04 4.34 4.54 5.39 5.66 6.01 6.39 5.08 5.35 5.71 5.99 4.78 5.04 5.38 5.65 4.46 4.70 5.01 5.29 5.62 4.84 4.67 3.46 Refe A,I,U A Remarks-Composition! 98 I 126 U 127 Molasses Syrup 30 23 Fats, Oils, Gums, and Extracts Gelatin Gel 5 94-80 5.22 A 94 -15 -15 -15 5 4 35 94 88 80 21.4 19.4 14.1 2.33 1.76 1.70 I U I U U U U U 124 128 103, 121 129 130 128 129 131 U I U U 128 118 132 128 Margarine Almond Oil Cod Liver Oil Lemon Oil Mustard Oil Nutmeg Oil Olive Oil Olive Oil 6 25 4 7 32 65 151 185 4 25 20 4 Peanut Oil Peanut Oil Rapeseed Oil Sesame Oil Freeze-Dried Foods App1e Peach Pears 1.56 1.70 1.56 1.75 1.68 1.66 1.60 1.56 1.68 1.69 1.60 1.76 35 Pressure, mmHg 0.020 35 0.156 1.43 21.6 0.045 35 0.156 1.16 d 1.31 d 1.34 d Conductivity did not vary with concentration in range tested (6,12,20%) 6% gelatin concentration 12% gelatin concentration 20% gelatin concentration 1.00 d O.92d 0.82d 1.02 d 0.94d 0.91 d 0.91 d O.92d 0.91 d 0.92d A 133, 134 Delicious; 88% porosity; 5.1 tortuosity factor; measured in air 0.185 0.282 0.405 0.164 A 133, 134 Clingstone; 91 % porosity; 4.1 tortuosity factor; measured in air 0.161 1.36 20.0 383 0.016 0.185 0.279 0.410 0.431 0.186 A 133, 134 97% porosity; measured in nitrogen 0.146 1.42 16.1 530 0.207 0.306 0.419 0.451 29.18 CHAPTER 29 Table 8 Food or Food Materialb Thermal Conductivity' of Food and Food Materials (Continued) Pressure, Temp, °C Beef =h mmHg 35 Egg Albumin Gel 41 Egg Albumin Gel Turkey = b 41 1977 Fundamentals Handbook 20.3 762 760 720 Turkey 1- b kC mW/(cmHdeg C) 0.0 11 0.1 71 1.7 9 0.382 Rating, d A,I,U Refc Remarks-Composition r I 133, Lean; 64070 porosity; 4.4 tortu- 134 osity factor, measured in air 2070 water content; measured in air Measured in air Cooked white meat; 68 to 72070 porosity; measured in air 0.412 0.532 0.620 0.652 0.393 U 135 0.0 33 0.0 40 0.1 1.1 13 9.8 0 3 0.0 42 0.129 0.287 U U 135 136 U 136 0.1 1.0 42 9.3 4 9 0.0 32 1.3 6 0.174 0.221 0.417 0.586 0.091 0.144 0.291 0.393 0.443 0.706 0.861 0.927 0.170 Cooked white meat; 68 10 72"70 porosity; measured in air 657 Potato Starch Gel 16.6 772 U 135 Measured in air 3To obtain W 1(Il1)(deg C) multiply by nl cal/kl)(sL)(deg C) multiply by 2.39 x 10-4; Btu/{ft)(hr)(dg F) Multiply by 0.0578; kcal/(m)(hr)(cJcg C) multiply by 0.0856. 0The symbol .1 indicates heal flow perpendicular 10 the grain or structure; the symbol = indicates heal flow parallel 10 the grain or structure. "The symbol k is used for thermal conductivity. The ring "A" indicates data considered reliable by reviewers from TC 11.9, within practical limits. The rating •• ," indicates data that appears to be reliable within practical limits, but for which background information supplied (e.g. composition factors or conditions of measurement) was insufficient for a firm assessment. "U" indicates data un-ruled because it did not fall within the area of competence of any reviewer of the TC J 1.9. c References Quoted are those on which given data are based, although actual values in this whole may have been averaged. interpolated, extrapolated, selected, or rounded off. This column includes density (d, in g/cm3), pressure (P. in mm Hg), fat content (D), and other details. REFERENCES t J. E. Siebel: Specific heat of various products (Ice and Refrigeration, April1 892, p. 256). 2Chapter 35, Table 3 (1977 ASH RAE HANDBOOK & Product Director,' New York, NY). - R. W. Dickerson, Jr.: Thermal Properties of Food (Chapter 2 in The Freezing Preservation of Foods, 4th cd., Vo\. 2, Avi Publishing Co., Westport, CT, 1968). 4 L. Riedel: Calorimetric investigations of the meat freezing process (Kaltetechnik, Vo\. 9, No.2, 1957, p. 38). 5A. L. Ryall and W . .1_ Lipton: -Vegetables as Living Products. Respiration and Heat Production. (Chapter 1, Table I, in Transportation and Storage of Fruits and Vegetables, vo\. I, Avi Publishing Co., Westport, CT, 1972, p. 5). ° J. M. Lutz and R. E. Hardenburg: The Commercial Storage of Fruits, Vegetables, and Florists and Nursery Stocks (USDA Handbook 66, 1968). 7 il. K. Watt and A. L. Merrill: Composition of Foods (USDA Handbook 8, 1963). 8Chapter 40, Table 5 (1974 ASH RAE HANDBOOK& Product Director?;, New York, p. 40.5). Chapter 29, Table 3 (1974 ASH RAE HANDBOOK & Product Directory, New York, NY, p. 29.10). IO Chapter 30, Table 4 (1972 ASH RAE HANDBOOK OF FUNDAMEN· TALS, New York, NY, p. 572). lit M. Whiteman: Freezing Points of Fruits, Vegetables and Florists Stocks (USDA Marketing Research Report 196, 1957). 12Chapter 42, Table 2 (1974 ASH RAE HANDBOOK & Product Directory, New York, NY, p. 42.3). I JR. C. Wright, D. H. Rose, and T. H. Whiteman: The Commercial Storage of Fruits, Vegetables, and Florists and Nursery Stocks (USDA Handbook 66, 1954). 14Recommended Conditions for the Cold Storage of Perishable Produce, 2nd cd. (International Institute of Refrigeration, Paris, France, 1 967). t5L. Rappaport and A. E. Watada: Effect of temperature on artichoke quality (Proceedings of the Conference on Transportation of Perishables. University of California at Davis, 1 958, p. 142). low. J. Lipton: Physiological Changes in Han'ested Asparagus (Aspargus officinales) as Related to Temperature. (Ph.D. Thesis, University of California at Davis, 1957). 17.1. B. iliale: Respiration of fruits (Encyclopedia of Plant Physiology, Vo\.12, 1960,p.536). 18S. Tewfik and L. E. Scott: Respiration of vegetables as affected by post-harvest treatment (Journal of Agricultural and Food Chemistry, Vol. 2,1954, p. 415). t9 A. E. Watada and L. L. Morris: Effect of chilling and nonchilling temperatures on snap bean fruits (Proceedings of the American Society. for Horticultural Science, Vol. 89, 1966, p. 368). oW. H. Smith: The production of carbon dioxide and metabolic heal by horticultural produce (Modern Refrigeration, V o\. 60, 1957, p.493). 21 R. E. Anderson, R. E. Hardenburg, and H. C. Vaught: Controlled atmosphere storage studies with cranberries (Proceedings of the American Society for Horticultural Science, Vol. 83, 1963, p. 416J. 2 W. H. Smith: The storage of gooseberries (Great Britain Agricultural Research Council, Dillon and Covent Garden Laboratories Annual Report, 1965-66, p. 13). 23M. H. Haller, D. H. Rose, and P. L. Harding: Studies on the Respiration of Strawberry and Raspberry Fruits. USDA Circular, Vol. 613,1941). 24E. C. Maxie, F. G. Mitchell, and A. Greathead: Studies on strawberry quality (California Agriculture, Vol. 13, No.2, 1959, p. II and 16.) 25L. L. Morris: A study of broccoli deterioration (Ice and Refrigeration, Vol. 1 13, No.5, 1947, p. 41). °E. W. Scholz, H. B. Johnson, and W. R. iluford: Heat evolution rates of some Texas-grown fruits and vegetables (Rio Grande Valley Horticultural Society Journal, Vol. 17, 1963, p. 170). 27 L. van den Berg and C. P. Lentz: Respiratory heat production of vegetables during refrigerated storage (Journal of the American Society or Horticultural Science, Vo\. 97, 1972, p. 431) . • 8L. A. Hawkins: Governing factors in transportation ofperishabJe commodities (Refrigerating Engineering, Vol. 18, 1929, p. 130). 29W. C. Micke, F. G. Mitchell, and E. C. Maxie: Handling sweet cherries for fresh shipment (California Agriculture, Vol. 19, No.4, 1965, p. 12). Thermal Properties of Foods 3°F. Gerhardt, H. English, and E. Smith: Respiration, internal atmosphere, and moisture studies of sweet cherries during storage (Proceedings of the American Society for Horricultural Science, Vol. 41, 1942, p. 119). 31 J. L. Eaks and L. L. Morris: Respiration of cucumber fruits associated with physiological injury at chilling temperatures (Plant Physiology, Vol. 31,1956, p. 308). 32 L. L. Claypool and S. Ozbek: Some influences of temperature and carbon dioxide on the respiration and storage life of the Mission Fig (Proceedings of the American Society for Horticultural Science, Vol. 60,1952, p. 226). 33 L. K. Mann and D. A. Lewis: Rest and dormancy in garlic (Hi1j;,ardia, Vol. 26,1956, p. 161). 3 .1. M. Lutz: Factors Influencing the Quality of American Grapes in Storage (USDA Technical Bulletin, Vol. 606, 1938). 35W. T. Pentzer, C. E. Asbury, and K. C. Hamner: The effect of sulfur dioxide fumigation on the respiration of Emperor grapes (Proceedings of the American Society for Horticultural Science, Vol. 30) 1933, p. 258). 6Chapter 32, Table I, (1974 ASH RAE HANDBOOK & Product Directory, New York, NY, p. 32.4). 37 H. C. Gore: Studies on Fruit Respiration (USDA Bur. Chern Bulletin, Vol. 142, 1911). J~D. V. Karmarkar and B. M. Joshe: Respiration studies on the Alphonse mango (Indian Journal of Agricultural Science, Vol. 11, 1941, p. 993). 39H. K. Pratt and L. L. Morris: Some physiological aspects of vegetable and fruit handling (Food Technology in Australia, Vol. 10, 1958, p. 407). 40W. H. Smith: The storage of mushrooms (Great Britain Agricultural Research Council, Ditton and Covent Garden Laboratories Annual Report, 1963-64, p. 18). 41 E. B. Pantastico: Table 16.2, Postharvest Physiology (Handling and Utilization of Tropical and Subtropical Fruits and Vegetables, Avi Publishing Co., Inc., Westport, CT, 1974, p. 323). 42 W. W. Jones: Respiration and chemical changes of papaya fruit in relation to temperature (Plant Physiology, Vol. 17, 1942, p. 481). 43M. H. Haller, P. L. Harding, J. M. Lutz, and D. H. Rose: The respiration of some fruits in relation to temperature (Proceedings of the American Society for Horticultural Science, Vol. 28, 1932, p. 583). 44H. Thompson, S. R. Cecil, and J. G. Woodroof: Storage of Edible Peanuts, Georgia Agricultural Experiment Station Bulletin, Vol. 268,1951). 45R. U. Schenk: Respiration of peanut fruit during curing (Proceedings of the Association of Southern Agricultural Workers, Vo1.56, 1959, p. 228). 46R. U. Schenk: Development of the Peanut Fruit (Georgia Agricultural Experiment Station Bulletin N .S., Vol. 22, 1961). 47L. L. Claypool and F. W. Allen: The influence of temperature and oxygen level on the respiration and ripening of Wickson plums (Hillardea, Vol. 21, 1951, p. 129). 4 H. W. Hruschka: Storage and Shelf Life of Packaged Rhubarb (USDA Marketing Research Report, Vol. 771,1966). 49D. A. Lewis and L. L. Morris: Effects of chilling storage on respiration and deterioration of several sweet potato varieties (Proceedings of the American Society for Horticultural Science, Vol. 68, 1956, p. 421). 50M. Workman and H. K. Pratt: Studies on the physiology of tomato fruits; II, Ethylene production at 20°C as related to respiration, ripening and date of harvest (Plant Physiology, Vol. 32,1957, p. 33°1·5 L. L. Morris: Unpublished data, 1952. 52 P. L. Harding: Respiration studies of Grimes apples under various controlled temperatures (Proceedings of the American Society for Horticultural Science, Vol. 26, 1929, p. 319). 53R. E. Hardenburg: Unpublished data, 1966. 54L. Rappaport and A. E. Watada: Unpublished data, 1953. 55H. K. Pratt, L. L. Morris, and C. L. Tucker: Temperature and lettuce deterioration (Proceedings of the Conference on Transportation of Perishables, University of California at Davis, 1954, p. 77). 56E. C. Maxie, P. B. Catlin, and H. T. Hartmann: Respiration and ripening of olive fruits (Proceedings of the American Society for Horticultural Science, Vol. 75,1960, p. 275). 57D. V. Karmarkar and B. M. Joshe: Respiration of onions (Indian Journal of Agricultural Science, Vol. 11, 1941, p. 82). 58S. E. Charm and P. Moody: Bound water in haddock muscle (ASH RAE JOURNAL, Vol. 8, No.4, 1966, p. 39). 59W. R. Woolrich: Specific and latent heat of foods in the freezing zone (ASH RAE JOURNAL, Vol. 8, No.4, 1966, p. 43). 6oH. E. Staph and W. R. Woolrich: Specific and latent heats of foods in the freezing zone (Refrigerating Engineering, Vol. 59, 1951, p.1086). 29.19 61H. C. Mannheim, M. P. Steinberg, and A.!. Nelson: Determinations of enthalpies involved in food freezing (Food Technology, Vol. 9,1955, p. 556). 62B. F. Short and H. E. Staph: The energy content of foods (Ice and Refrigeration, Vol. 121, No. 11, 1951, p. 23). 63L. H. Bartlett: A thermodynamic examination of the "latent heat" of food (Refrigerating Engineering, Vol. 47, 1944, p. 377). 64S. W. Moline, J. A. Sawdye, J. A. Short and A. P. Rinfret: Thermal properties of foods at low temperatures (Food Technology, Vol. 15,1961,p.228). 65 L. Riedel: The refrigerating effect required to freeze fruits and vegetables (Refrigerating Engineering, Vol. 59, 1951, p. 670). 6L. Riedel: Calorimetric investigations of freezing of egg white and yolk (Kaltetechnik, Vol. 9, No. 11, 1957, p.342). 67L. Riedel: Calorimetric investigations of the melting of fats and oils (Fette, Seifen, Anstrichmittel, Vol. 57, No. 10, 1955, p. 771). 68Chapter 37, (1964 ASH RAE HANDBOOK & Product Directory, New York, NY, p. 437). 69M. P. Heisler: Temperature charts for induction and constant temf,erature heating (ASME Transactions, Vol. 69, 1947, p. 227). 7 P. J. Schneider: Temperature Response Charts (John Wiley and Sons, New York, NY, 1963). 71 R. E. Smith, G. L. Nelson, and R. L. Hendrickson: Analyses on transient heat transfer from anomalous shapes (ASAE Transactions, Vol. 10, No.2, 1967, p. 236). 72R. E. Smith, G. L. Nelson, and R. L. Hendrickson: Applications of geometry analysis of anomalous shapes to problems in transient heat transfer. ASAE Transactions, Vol. 11, No.2, 1968, p. 296. 73R. W. Dickerson: Computing heating and cooling rates of foods (Symposium on Prediction of Cooling/Freezing Times for Food Products, ASH RAE Bulletin NO-72-3, 1972, p. 5). 74R. Gane: The thermal conductivity of the tissue of fruits (Annual Ref:0rt, Food Investigation Board, Great Britain, 1936, p. 21 I). 5E. Slavicek, K. Handa, and M. Kminek: Measurements of the thermal diffusivity of sugar beets (Cukrovarnicke Listy, Vol. 78, Czechoslovakia, 1962, p. 116). 76p. J. Schneider: Conduction Heat Transfer (Addison-Wesley Publishing Co., Reading, MA, 1955, p. 15). 77 L. Riedel: Measurements of thermal diffusivity on foodstuffs rich in water (Kaltetechnik-Klimatisierung, Vol. 21, No. 11,1969, p. 315). 78A. H. Bennett, W. G. Chace, Jr., and R. H. Cubbedge: Thermal Properties and Heat Transfer Characteristics of Marsh Grapefruit (USDA Agricultural Research Service, Technical Bulletin No. 1413, U.S. Government Printing Office, Washington, DC, 1970). 79A. H. Bennett, W. G. Chace, Jr., and R. H. Cubbedge: Thermal conductivity of Valencia orange and Marsh grapefruit rind and juice vesicles (ASH RAE TRANSACTIONS, Vol. 70, 1964, p. 256). 8oR. L. Perry, F. M. Turrell, and S. W. Austin: Thermal Diffusivity of Citrus Fruits (Heat Transfer, Thermodynamics, and Education, ed., H. A. Johnson, McGraw-Hill, New York, NY, 1964, p. 242). 81 L. Riedel: Calorimetric investigations of the freezing of fish meat (Kaltetechnik, Vol. 8, No. 12, 1956, p. 374). 82L. Riedel: Calorimetric investigations of the freezing of white bread and other flour products (Kaltelechnik, Vol. II, No.2, 1959, p. 41~. 3 A. H. Bennett, W. G. Chace, Jr., and R. H. Cubbedge: Heat transfer properties and characteristics of Appalachian area 'Red Delicious' apples (ASH RAE TRANSACTIONS, Vol. 75, Part II, 1969, p. 133). 84R. E. Parker and B. A. Stout: Thermal properties of tart cherries (ASAETransactions, VoI.I0,No.4, 1967,p.489). 85 A. H. Bennett: Thermal Characteristics of Peaches as Related to Hydrocooling (USDA Agricultural Marketing Service, Technical Bulletin No. 1292, U.S. Government Printing Office, Washington, DC, 1963). 86T. V. Minh, J. S. Perry, and A. H. Bennett: Forced-air precooling of white potatoes in bulk (ASH RAE TRANSACTIONS, Vol. 75, Part 2,1969, p. 143). 87F. V. Mathews, Jr. and C. W. Hall: Method of finite differences used to relate changes in thermal and physical properties of potatoes (ASAE Transactions, Vol. 11, No.4, 1968, p. 558). 88R. W. Dickerson, Jr. and R. B. Read, Jr.: Thermal diffusivity of meats (ASH RAE TRANSACTIONS, Vol. 81, Part I, 1975, p. 356). 89 Metals Handbook (The American Society for Metals, 1948, p. 555J. 9 N. A. Lange: Handbook of Chemistry, 10th ed. (McGraw-Hill, New York, NY, 1961, p. 834). 91 Modern Plastics Encyclopedia: Plastics Properties Chart, Part I, (Breskin Publications, New York, NY, 1963). 92Chapter 23, Table 4 (1963 ASHRAE GUIDE AND DATA BOOK, Fundamentals and Equipment, New York, NY, p. 398). 93Chapter 37, Fig. 13, (1964 ASHRAE GUIDE AND DATA BOOK, Applications Volume, New York, NY, p. 446). 94C. P. Lentz: Thermal conductivity of meats, fats, gelatin gels,