4. DESARROLLO DE LA INVESTIGACIÓN
4.2. Extracción de Características
4.2.3. Codificación predictiva lineal (LPC)
The specific heat capacity measurement methods can be grouped as: (A) Method of mi xture, (B) Comparison method, (C) Adiabatic method, and (D) Di fferential scanning calorimetry (DSC) (Rahman, 1 995).
The method of mixtures is the most widely used method to measure specific heat due to its simplicity (Rahman, 1 995). Mohsenin ( 1 980) explai ned that in this method the speci men of known mass and temperature is added in a calorimeter of known specific heat capacity containing water or liquid of known temperature and mass. The unknown specific heat then can be computed from a
heat balance between the heat gained or lost by the water or liquid and the calorimeter and that gained by the specimen. The advantage of this method is that it is easy to apply and the apparatus is easy to assemble but there are many sources of error in it i ncluding thermal leakage, direct contact with the specimen and the heat exchange medium and problems in mixing due to density
differences. Although a number of researchers have made changes in the method to avoid these errors, the system relies on having the fluid in the calorimeter available at the temperature range of interest and to get useful results many experimental trials are required.
The comparison method is usually used to determine the specific heat of liquids. Figure 3.8(a)
shows a schematic diagram of comparison calorimeter. While conducting the experiment cup A is fi l led with water or any other liquid of known specific heat capacity and cup B is fil led with the l iquid whose specific heat capacity has to be determined. Both cups are heated to same temperature and then placed in the calorimeter to cool. The unknown specific heat capacity is calculated from the cooling curves of both the liquids in cups A and B . If both the cups are of same material, same size, same exterior finish and of identical masses then they can be considered as identical emitters (Mohsenin, 1 980). If the two cups have the same initial temperature and the surrounding medium (air or fluid) have nearly constant temperature than the net rate of heat 10 s through both the cups wi ll be same. The heat balance equation for the cups can be written as (Mohsenin, 1 980):
�QA
_�QIJ
�tA
�t/3
(3- 1 0)If the temperature changes in the cooli ng body are small, the specific heats are constants and the rate of heat loss is equal to rate of temperature change as (Mohsenin, 1 980):
both of the above equation can be equated by using equation (3- 1 0) and can be rewritten after simplification as:
where
Q = heat rate
1'1. T = temperature drop for c ups A and B
W = weight of the reference liquid (water) or the sample
I'1.tA= time for cup A and contents to drop to I'1.T I'1.tlF time for cup B and contents to drop to I'1.T
(3- 1 2)
The subscripts A, B, W, and Sa denote cup A, cup B, water and the sample respectively. Typical cooling curves to determine I'1.tA and I'1.tn are given in Figure 3. 8(b) . The specific heat capacity of the sample can be calculated from equation (3- 1 2) (Mohsenin, 1 980)
(a) (b)
",
Water Tin-c ( .:; )
Figure 3.8: (a) Comparison calorimeter, (b) Example of cooling curve for use in method of comparison calorimeter ( adaptedfrom Mohsenin, 1980)
Moline et at. ( 1 96 1 ) proposed a simple and rapid adiabatic method to measure the specific heat capacity of frozen food materials (Figure 3.9). The apparatus consists of rectangular polystyrene foam with a cylindrical hole in the center to place the aluminum sample container. A polystyrene plug is inserted on the top to minimise the heat transfer to the sample. The sample container is fil led with the sample, frozen in liquid nitrogen rapidly till it reaches the equili brium temperature and then it is transferred quickly to the foam block maintained at room temperature. Moline et at. ( 1 96 1 )
measured the heat leakage Q (1s-l ) of the calorimeter by using a sample of standard copper material with the known weight and specific heat capacity as:
Q
-- Ccopper copper w!1T:: !1t
(3- 1 3)Where ccopper and Wcopper is the specific heat capacity (1 kg-lOCi ) and weight (kg) of the copper probe, and (!1Tc/flt) is the rate of the core temperature change. Once the rate of heat leakage is determined over the temperature range of interest, the specific heat of any material of identical geometry may be determjned, assuming that the rate of heat transfer into the cel l will be the same at any given temperature. The specific heat capacity of food sample is then calculated as:
Q
( ¥:-) -( c,'"mm"m W,'"mm"m )
c,ample =
WsamPle
(3- 1 4)Where
Csample
andWsample
are the specific heat (J kg-lOC i ) and weight (kg) of the sample under study.By carrying out these measurements for several temperatures, the change in specific heat with
temperature can be determined. This method was used by Moline et al. ( 1 96 1 ) to measure the
specific heat of meat. The main disadvantage of this method is the needed to do measurements at each temperature point.
ThernuroupJe 10 R."Cortkr
:
,:,:
, '-ruNn �anvlcFigure 3.9: Specific heat capacity measurement apparatus for frozen specimen (Moline et al. 1961)
Mohsenin ( 1 980) presented the guarded hot plate method to measure the specific heat capacity of food and agricultural materials. In this method the specimen is surrounded by electrically heated thennal guards as shown in Figure 3. 1 0. The specimen and the thennal guards are maintained at the same temperature so there is no heat loss from the speci men and the specimen is electrically heated. The specific heat can be calculated by the heat balance as:
Heat gain by the sample = Heat supplied by the e lectrical heater
(3- 1 5 )
Vlt
(3- 1 6)
Csample =