correlations of enthalpies of food systems

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Correlations of Enthalpies of Food Systems

H. D. CHANG and L. C. TAO

ABSTRACTCorrelations of enthalpies of f ood sys tems containing water fractionfrom 0.74-0.94 are presented for a temperature range 230-310°K(-50 to 95°F). with these correlations, energy requirement infreezing and thawing foods within the limits of dat a base used forthis work may be computed by providing the identity of food group(meat, juice or vegetable/fruits), wat er content, initial, and finaltemperatures.

INTRODUCTION

IN FREEZING AND THAWING FOODS, enthalpy prop-erties are necessary data for computations involved inprocess operation and equipment design. Since each speciesof food has its o wn physical structure and composition,

the sets of data for natural and synthetic foods are numer-ous. To facilitate any systematic analysis or study of oper -ation and design, it is desirable to ma ke data reduction ofavailable information so that a few sets of equations beavailable for process computation of a majority of foodsystems if not all. This article presents the findings of suchcorrelations to cover enthalpy in a temperature range ofapproximately 230-310’K (-50 to 95’F) for meats,vegetables, fruits and juices with water fraction from 0.73-0.94.

CORRELATIONSOFENTHALPYCHANGEANDTEMPERATURE

A TYPICAL ENTHALPY FUNCTION versus temperatureusually indicates a linear part representing a constant heat

Authors Chang and Tao are affiliated with the Dept. of Chemical

Engineering, Univ. of Nebraska, Lincoln, NE 68588.

Table 1 -Physical propertiesa and correlation coefficients

capacity above the freezing temperature and a curved por-tion below the freezing temperature.

Correlations below the freezing temperature are of inter-est as they involve the change of ice fraction. Reidel(195 1)correlated the enthalpies of vegetables and juices by assum-ing a correlation of ice fraction as a function of tempera-ture. Woodrich (1966) proposed the use of an integral typeof equation to fit data. In this study, a relatively sinipleenthalpy-temperature equation is developed to cover most,if not all, food systems. Ice fraction can be calculated fromthe enthalpy equation as a consequence. This approachsimplifies the use of these correlations since there will beonly two i ndependent parameters for input: water fractionand identity of food groups. Furthermore , it facilitatessimulation (Joshi and Tao, 1974) type computation.

Enthalpy is a relative quantity and the datum state is227.6’K (-50’F) as used by Joshi and Tao (1974). Fortemperature below freezing, the following empirical equa-tion of two dimensionless groups was used to correlate theenthalpy data.

H, = a T, + (1 -a)Trb (1)

where H, = H/Hf and T, = (T-227.6)/(Tf-227.6). (2)This equation assures H = Hf at the freezing temperatureTf. It ha s a steep slop dH,/dT, of a + (1 -a)b at the freez-ing temperature and changes smoothly to a small slope“a” at T, = 0.

Data of 23 food systems tabulated by Dickerson (1968)were extrapolated to -50°F from -4O’F for correlationwith Eq (1). The computed coefficients a, b are tabulated

on Table 1. Figures 1 and 2 illustrate the correlations graph-ically for beef and orange uice. Ice fraction computation isdiscussed in the latter portion of this article. Analogousfigures for other foods are available (Chang, 1977).

-Continued on nextpage

Meat/Fish Group Juice Group

Chick- Veni- Had- Rasp- Bar- Straw-

Food Beef en son Veal Cod dock Grape Cherry Apple berry Orange berry berry

Vb 0.745 0.760 0.730 0.765 0.803 0.836 0.847 0.867 0.872 0.885 0.890 0.895 0.917

Tf 272.37 272.21 272.26 272.26 272.37 272.43 271.08 271 .Jl 272.71 271.93 271.98 272.04 272.26

‘-4 312.85 312.95 302.85 317.27 332.62 345.88 350.99 360.06 361.46 369.37 369.60 372.16 381.70C 4046.1 4094.3 4046.1 4093.4 4238.8 4287.0 4383.3 4431.5 4431.5 4479.6 4479.6 4479.6 4576.0

a 0.31 0.30 0.32

b 22.0 21.4 19.1

0.31 0.30 0.28 0.32 0.31 0.31 0.29 0.29 0.28 0.26

22.97 23.1 23.3 i a.35 19.26 19.86 21.06 21.3 21.6 23.8

Vegetable/Fruit Group

Tall Straw- Aspar- Tomato AppleFood pea berry agus PUlP Carrots sauce Pear Peach Onion Spinach

b

Tf 0.75871.32 0.89372.26 0.92672.48 0.92972.43 0.87572.04 0.82871.48 0.83871.54 0.85171.59 0.85571 .Jl 0.90272.59

‘-4 327.97 374.72 383.32 387.74 365.18 347.74 349.37 354.25 356.81 374.25C 4094.3 4527.8 4576.0 4624.1 4479.6 4287.0 4287.0 4335.1 4383.3 4479.6

a 0.36 0.27 0.23 0.25 0.30 0.34 0.33 0.31 0.31 0.24

b 19.2 24.2 25.9 25.1 21.52 18.84 19.16 19.64 19.6 26.6

a Dickerson, 1968

by = Water Fraction; Tf In OK; Hf in kJ/kg; C In J/kg.K

Volume 46 (1981kJ OURNAL OF FOOD SCIENCE- 1493



A further study of these coefficients indicates that theyare related to water content and the food type. The lattercharacterizes the structure and composition of a foodsystem. Figures 3 and 4 show the plots between the coef-ficients and water content for mea t and nonmeat groups.The meat group includes fish. Equations to correlate thesecoefficients are as follows:

Meatgroup

a = 0.316 - 0.247 y-0.73) - 0.688 y-0.73)* (3)

b = 22.95 + 54.68 (a-0.28) - 5589.03 (a-0.28)2 (4)

Vegetables,ruits, uices roup

a = 0.362 + 0.0498 (y-0.73) - 3.465 (y-0.73)* (5)b = 27.2 -129.04 (a-0.23) - 481.46 (a-0.23)* (6)

For enthalpy values above freezing, dH/dT = C whichcan be assumed to be independent of temperature. Dicker-son (1968) correlated the data of juices as a function of

.8.* A data-eq 1 and Table

0 ,0 .2 .4 Tr .6 .8 I.0

Fig. 1 Correcred enrhalpy and ice fraction of beef.

- eq.1 and Table 1

0 .2 .4 T .6 .8 1.0r

contents of foods. With the least square method, coeffi-cients of a linear equation were calculated to includejuices, vegetables, fruits, and meat. Eq (7) shows the corre-lation of data on Figure 5. Since the objective is to corre-late food systems, no attempt was made to make C converg-ing to that of water for y = 1 O.

C = 1597.3 + 2583.3 y (7)

CORRELATIONS F H, andT,

IN ORDER TO USE the equations developed above to

compute enthalpy, it is necessary to find Hr and Tf of vari-ous foods systems. These variables are plotted versus watercontent on Figures 6 and 7 to compare with Eq (8) to (11).

Hf = 9792.46 + 405,096 y (8)

MeatgroupTf = 271.18 + 1.47~ (9)

*” h .

Y

.a-

.2*.A data

- eq 12

O0.i .i3r b6

4

.4 T -6 -8 l.(r

Fig. Z-Corrected enthalpy and ice fraction of orange juice.

1494-JOURNAL OF FOOD SCIENCE-V olume 46 (1981)



CORRELATION OF ENTHALPIES OF FOOD SYSTEMS.

Vegetable and fruit group

Tf = 287.56 - 49.19 y + 37.07 y*

Juice group

(IO)

Tf = 120.47 + 327.35 y - 176.49 y* (11)

COMPUTATION F ENTHALPY

WITH THESE CORRELATIONS, one may thus computethe enthalpies of food by identifying the food system andwater content y as nput parameters. From these, computa-

tions can be made to obtain an enthalpy value at any giventemperature o r to plot the enthalpy curve. The followingprovide the sequential use of equations described above.

ObjectivesVegetables

Meat & Fruits Juices

General characterization:

Hf Eq. (8) Eq. (8) Eq. (8)Tf Eq. (9) Eq. (10) Eq. (11)

Enthalpy above Tf:

H = H, + C(T-T,) Eq. (7) Eq. (7) Eq. (7)

Enthalpy below Tf:

Coefficient a Eq. (3) Eq. (5) Eq. (5)Coefficient b h.(4) Eq. (6) Eq. (6)Enthalpy Eq. (1) Eq. (1) Eq. (1)

These equations can be conveniently programmed intoa TI-59 calculator with two magnetic record ca rds, one forprogram and the other for constants in equations. Withthese portable facilities, one can conveniently compute theenthalpy difference between two tempera ture levels for anyone of three food groups described here. Figures 8 and 9show comparison between the literature values and thosecomputed from these equations.

ICE FRACTIONSN FROZENFOODS

ICE FRACTION is important in simulation computationsof freezing as it affects the thermal conductivity of the

frozen phase. The enthalpy balance equation of thawing afrozen specimen at T to Tf can be written as Eq (12). Sincethe freezing temperatures ranges 2 or less OK below thefreezing temperature of water, h, latent heat of fusion ofwater, at 273.15’K was used. -Continued on next page

A meat

Fig. 3-Correlarion paramerer ‘a” vs water fraction.

3c

27

24

b

21

1e

15I 1

12 .25 .28 .31 .34 .37a

A meat

l non-meat

Fig. 4-Correlarion parameters ‘a” vs “b’:

3%.

160 -

f

A meats

l vegetables,fruitsa juices

3c&~ r.75 .80

Y.85 .90 .q

Fig. 5-Enthalpy at freezing point vs water fracrion.

Volume 46 (1981/-JOURNAL OF FOOD SCIENCE-1495



Hf-H = w C,(Tf-T) + (l-w) DISCUSSION

(X[ X+C, (Tf-T)] + (1 -X) (Tf-T)} (12)

By using X = 3.334 x lo5 and Ci = 2.01 (Keenan and Keyes,1936) in the above equation, the ice fraction may thus becalculated. Figures 1 and 2 show the comparison betweenliterature values (Dickerson, 1968) and those from Eq (12).

EVEN THOUGH the varieties of foods are large, theirgeneral structures have many similarities. The meat groupconsists of beef, chicken and fish which exhibit moreoriented fiber cells structure with a relatively smal l amount

4.2 W-A meatsl vegetables, fruits

0 juices

.95.

273

32- ----_

A meats

l vegetables, fruits031.

juices

Y

272

271 28, P

.70 .75 .80 y .85

Fig. d-freezing temperatur vs water fraction.

3

2

0)

sv)

0

1

0 Data

- Calculated

0 I I I I 1 I I I-40 -20 0 OF 20 4c

BO-

y3.8-

B

>t-9 3-b0

3-4J .8$___,

.70 .75 .80Y

35 -90 .!

Fig. 7-Heat capacity of nonfrozen food KS water fraction.

I I I I I .

240I ’ I

250 260K

270 280

Fig. B-Calculated enthalpy of beef.

1496-JOURNAL OF FOOD SCIENCE-Volume 46 (79811

3,

2

cn

rVI

0

-1.

O-

0 Data

-Calculated

0

1 I I I I 1 I

I -20 0 OF 20 40

I I I I I I I I I I

240 250 260K

270 280

Fig. 9-Calculated en thalp y of onion vs data.



CORRELATION OF ENTHALPIES OF FOOD SYSTEMS.. .

of fluid between. The vegetable and fruit group has a non-oriented matrix of cells having a large moisture fraction.The juice group consists of crushed cells mixed with thefluid. These differences in structure and chemical composi-tion would affect the mobility of water in freezing. Thismay result in the grouping effect as shown in Figures 3,4, and 7.

As common to all correlations, equations are reliableonly within the limits of data base used. Since the presentcorrelations are based on the data (Dickerson, 1968)with the water fraction 0.70-0.95, partially dehydrated orconcentrated foods with a water fraction below 0.70 arenot included. However, within this range, any syntheticfoods or mixtures may use this correlation. For example,the freezing of a pre-packaged convenience food may beestimated by calculating the enthalpy change of each con-stituent group and s um up these groups according tomass raction ccntribution.

A comparison of 17 correlated enthalpy values anddata over a temperature range233.2’K (-40’F) to 277.6’K(40’F) for each species indicates that the averages of ab-solute errors of meat, fruits/vegetables, and juices groupsare respectivel y 3954, 10467, 7489 (or 1.7, 4.5,3.2 Btu/lb).These correspond to l-2% of enthalpies at 277.6’K.

Probably the most interesting aspect of this study isthat these correlations indicate that one needs only two

input paramete rs to estimate the refrigeration load offoods, i.e. the water fraction and identity of one of threefood groups. Identity of food group is a visual observationand the measurement of water fraction is often simple.Therefore, these correlations especially with the aid of aprogrammable calculator can provide the freezing heatload information readily.

CONCLUSION

A SET of simple correlation equation was developed tofacilitate the computation of enthalpy changes of food

systems with a water fraction larger than 0.70. The re-quired input information is water fraction and the identityof food as one of three groups: meat, vegetable/fruit, orjuice.

SYMBOLS

a,b - Correlation parameters in Eq (1)- Heat capacity, J/kg.K

g - Enthalpy, J/k%

T - Temperature, KW - Fraction of solidsX - Ice fraction

Y - Fraction of total water in foodX - Latent heat of fusion at 273.15’K, J/kg

Subscripts

f - At freezing temperatu rei - Of icer - Reduced or dimensionless parameterS - Of solid

REFERENCES

Chang. H.D. 1977. MS. thesis, Dept. of Chemical Engineering.Univ. of Nebraska, Lincoln.

Dickerson, R.W. Jr. 1969. Thermal properties of foods. In “Freez-ing Preservation of Foods, 4th ed. Avi Pub. Company, Westport,CT.

Joshi, C. and Tao, L.C. 1974. A numerical method of simulati ng theaxisymmetri cal freezing of food systems. J. Food Sci. 39: 623.

Keenan, J.H. and Keyes, F.G.. 1936. “Thermodynami c Propertiesof Steam.” John Wiley, New York, NY.

Riedel, L. 1951. The refrigerating effect required to freeze fruitsand vegetables. Refrig. Eng. 59: 670.

Woodrich, W.R. 1966. Specific and latent heat of foods in the freez-ing zone, ASHRAE J. 8: 43.

Ms received 7/26/80: revised 11/12/80: accepted 3/12/81.

YEAST CELL WALL GLLJCAN IN FOODS. . . From page 1492

8%, respectively) over that found with the control sample(glycan in buffer with no other compou nd added) in a 1day digest. The inhibition was more apparent after a 7day digestion with the first lot and very evident after a 14day digestion with the second lot (where “Pioneer” blend/glycan showed 6% inhibition and GMS/gJycan showed 12%inhibition). These latter results indicate that lipid-likecompounds may mask the yeast cell wall surface throughhydrophobic interaction and thus prevent a full interactionof the enzyme with substrate. In a Zymolyase digestion ofa normal glycan substrate, the reaction will proceed to-wards an end point, whereas in an inhibited reaction, somesubstrate will remain unavailable for hydrolysis. The longer

the reactions proceed, the greater the discrepancy will bewhere all conditions are the same, except for the substrateinhibition factor. This hypothes is is also consistent withthe results obtained in frozen dessert B-4 or 17-7 wherelower glycan values were obtained with a 7 day digestionthan with a l-day digestion of the same sample. Saponifi-cation of these lipid-like compounds by methanolic KOHallows solubilization of fatty acids to occur and their re-moval during washing. Experimentally determined glycancontents in frozen desserts pretreated in this manner gavevalues close to the levels reported present in these products.

REFERENCES

Anon. 1974. Federal Register 39: 34186.Ast. H.J. 1963. Inadvertent isomerlzati on of polyunsaturated acids

during ester preparation. Anal. Chem. 35: 1539.Kitamura. K.. Kaneko, T.. and Yamamoto. Y. 1972. Lysis of viable

yeast cells by enzymes of Arthrobacter luteus. 1. Isolation of lyticstrain and studies on its lytic activity. J. Gen. Appl. Microbial.18: 57.

Kitamura, K.. Kaneko, T.. and Yamamoto. Y. 1974. Lysis of viableyeast cells by enzymes of Arthrobacter luteus. 2. Purification andproperties of an enzyme. Zymolyase. which lyses viable yeastcells. J. Gen. Appl. Microbial. 20: 323.

Robbins. E.A. and Seeley, R.D. 1978. Process for Manufacture ofYeast Glycan. U.S. Patent 4.122.196.

Seeley, R.D. 1977. Fractionation and utilization of baker’s yeast.Master Brewers Assoc. of Amer. Technical Quarterly 14(l): 35.

Seeley, R.D., Robblns. E.A.. Sucher, R.W.. Schuldt. E.H., Newell,

J.A., Sidoti. D.R.. and Clayton, R.A. 1974. Protein is olatesfrom bakers yeast. Proc. 4th Int. Congr. Food Sc i. & Technol.5: 135.

Sidoti. D.R.. Landgraf. G.M.. and Khalifa. R.A. 1973. The function-al properties of baker’s yeast glycan. Presented at the 33rd AnnualMeeting of the Institute of Food Technologists, Miami , FL, June10-14.

Spiro, R.G. 1966. Analysis of sugars found in glycoproteins. In“Methods in Enzymology ,” Ed. E.F. Neufeld and V. Ginsberg,Vol. 8, p. 3. Academi c Press, New York.

Sucher, R.W., Robbins, E.A.. Sidoti. D.R.. Schuldt. E.H.. andSeeley, R.D. 1975. Yeas t glycan and process of making same.U.S. Patent 3.867.554.

MS received 9/29/80:revlsed 4/12/81. accepted 4115181.

Volume 46 (1981)-JOURNAL OF FOOD SCIENCE- 1497

correlations of enthalpies of food systems

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