Effective Heat Capacities for the Freezing and Thawing of Food

Abstract

Based on a modified form of the freezing point depression equation we have derived a set of rigorous, broadly applicable equations for effective heat capacity during the freezing and thawing of foods and biological materials. The equations have been integrated with respect to temperature, thereby providing a set of useful equations for enthalpy during freezing and thawing. The validity and utility of the equations are demonstrated using data from the literature. Methods for adjusting the equations to account for changes in water content and fat content are presented. The enthalpy equations are useful for calculating heattransfer loads during freezing and thawing, and the heat capacity equations can be advantageously used in differential equations for calculating freezing and thawing heat-tra,nsfer rates. THE CALCULATIONof cooling and heating loads and rates are central problems in designing food freezing and thawing systems. To facilitate such calculations we have developed a generalized equation for effective heat capacity during freezing and thawing. It provides much of the same information as the enthalpy -moisture content -temperature diagrams developed by Riedel (1956; 1957a, b), but it is more compact and convenient, and is directly usable in a broader range of problem situations.Foods start to freeze at lower temperatures than pure water. Their freezable water content changes to ice over a range of temperatures rather than at a single temperature. Since the ice forms over a range of temperatures, the associated latent heat effect per degree can be added to the normal heat capacity, yielding an effective heat capacity Ce which is a function of temperature. Values of Ce vs temperature have been calorimetrically determined for meat and fish by Jason and Long (195 5), Fleming (1969) and by Rolfe (1968) using the calorimetric data of Riedel (1956; 1957a, b). Heldman (1974a, b) has used the freezing point depression equation to calculate ice content and enthalpy changes for small temperature changes during freezing, and from these values he calculated values for C,. We utilize the same equation in a somewhat different fashion in this paper. Freezing point depression Foods, during freezing, obey the freezing point depression equation. The differential and integral forms of this equation are : 3 Ina,-1 aa, _ I~AHT --__--aT a, aT RT2 Ina,= 18&T -To) RToT(2) where a, is the water activity, To the freezing point of pure water, T the freezing point of the solution (T and To are absolute temperatures), R the gas law constant (1.987 BTU/lb mole OR or 1.987 Cal/g mole OK), AHT the heat of fusion per unit weight at T and AH the average heat of fusion over the range between To and T. Since AH = H, -HI, where H, and HI are the specific enthalpy of water and ice respectively; dAH/dT the temperature coefficient of latent heat = dH,/dT -dHI/dT = C, -CI = ACp, where ACp is the difference between Cw the heat capacity of water and CI the heat capacity of ice. By integrating the temperature coefficient of latent heat between To a...

Extension of soil thermal conductivity models to frozen meats with low and high fat content

“…In the frozen range, the mass fraction of ice content was estimated from the widely used empirical relationship, developed by Schwartzberg [19], which is based on Raoult's law of dilute solutions and the Claussius-Clapeyron relationship:…”

ESTUDIO DE LAS PROPIEDADES TERMO FISICAS DE CONGELACION DE MUSCULO DE CAMARON GIGANTE (Macrobrachium rosembergii): punto inicial de congelación y entalpia

“…Los valores experimentales se los comparó con los obtenidos mediante fórmulas de correlación de Schwartzberg (1976) Schwartzberg H.G. (1976).…”

“…El error medio relativo (EMR) estimado es de 6.38% lo que indica una buena concordancia de los valores experimentales con los predichos mediante la ecuación propuesta por Schwartzberg (1976). En el gráfico 4 se presenta los valores experimentales y calculados para el punto inicial de congelación del músculo de camarón gigante.…”

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“…At the freezing temperature range (approx. -1 o to -5 o C) some values, such as k, were taken from an extrapolation procedure, C p was from the equation reported by Schwartzberg, 24 and ρ was assumed to be constant of 985.5 kg/m 3 . Table 7 shows the values used for the freezing time prediction.…”