- Email: [email protected]
Specific Heat and the Physical State of the Fat in Cream
S P E C I F I C H E A T AND T H E P H Y S I C A L S T A T E OF T H E F A T IN CREAM A. H. R I S H O I AND P A U L F. S H A R P
Department of Dairy Industry, CorneU University, Ithaca, New York INTRODUCTIOB]"
The physical state and alterations in the physical state of the fat in the globules of milk and cream offer the most reasonable explanation for the profound effect of temperature on creaming, cream viscosity, foaming, churning, lipase activity, and surface tension. Many of these effects are reversible and are probably produced or influenced by the materials adsorbed on the surface of the globules when the fat is in different physical states. In order better to understand the influence of temperature on milk products, a knowledge of the physical state and alterations in the physical state of the fat in the globules is necessary. Information obtained by a study of milkfat in mass cannot be used as indicating accurately the physical state of the fat dispersed as globules. Seeding occurring in a mass of fat will influence the crystallization of the whole mass, but in fat dispersed as globules seeding will affect only the fat in the globule in which the crystal happens to form, and will exert no direct effect on the fat in other globules. This leads to a much slower attainment of equilibrium. Furthermore the crystals are larger in fat in mass, as compared with fat in globules, and this influences the rate of solution or melting on heating. Crystallization in both fat in mass and in globules is influenced by the rate of cooling. A study was undertaken to gain information as to the physical state of the fat in globules at different temperatures and the rate of attainment of a constant physical state at the different temperatures. Determinations of specific heat were used as one method of following the alterations in the state of the fat in the fat globules. Chevreul (3) observed that the solidification of milkfat was accompanied by the evolution of heat. Fleischmann (5) (6), F j o r d (4), Landois (9), Chanoz and Vaillant (2), Schnorf (10), Hammer and Johnson (7), and Bowen (1) have reported specific heat values for milk and cream. The effect of fat has been studied more specifically by Fleischmann (6), tIammer and Johnson (7), and Bowen (1), the latter reporting values obtained by the U. S. Bureau of Standards. There is no assurance that the fat was in equilibrium at the different temperatures used. The use of an ordinary calorimeter involves difficulties when used to determine the specific heat of milk and cream at temperatures within crystallization range, because considerable time is required to attain the equilibrium state, and during this Received for publication F e b r u a r y 5, 1938, 399
400
A. H. RISHOI AND PAUL F. SHARP
time the heat exchange between the calorimeter and its surroundings makes up an ever increasing p a r t of the total heat measured. EXPERIMENTAL
Method The method of mixtures was used, since it avoids the errors due to large values f o r heat exchange with the surroundings, and has a reputation for high accuracy. Q u a r t thermos bottles were used as containers. W a r m water f r o m one bottle was poured into colder cream or milk contained in another. The thermometers used were graduated to 0.1 ° C. and were calibrated against each other over the range used f r o m 0 to 75 ° C. All readings were made with the aid of a m a g n i f y i n g glass and were estimated to 0.02 ° C. The errors and heat losses in the procedure were studied, and all equipment and procedures were thoroughly standardized. The heat " l o s s " to the container and during the manipulation was f o u n d to be given by the following equation : Loss calories = K 1 ( t f - ti) + K 2 (tw - tr) where K1 and K2 are constants representing the heat equivalent of the a p p a r a t u s and heat lost in pouring, respectively, t~ = final t e m p e r a t u r e of cream-water mixture, tl = initial t e m p e r a t u r e of the cream, tw = the t e m p e r a t u r e of the w a r m w a t e r before pouring, a n d tr----the t e m p e r a t u r e of the room. I t was found by experiment t h a t within the normal limits, the relative h u m i d i t y of the room exerted an effect so small that it could be disregarded. The constants were determined by calibration with water, the room temperatures v a r y i n g f r o m 23 to 28 ° C., cold w a t e r v a r y i n g f r o m 5 to 39 ° C., and w a r m w a t e r v a r y i n g f r o m 21 to 66 ° C. The constants were calculated by the method of least squares, and for a typical p a i r of thermos bottles gave the equation : Loss calories = 25.35 (tf - ti) + 3.38 ( t ~ - tr) About 150 grams of cream and 250 grams of w a t e r were used. The amounts were determined by weighing. The specific heat of water was taken as unity, and a f t e r correcting for the heat loss, the specific heat of the cream was calculated.
Results The specific heat of skimmilk was determined both by the method of mixtures and by means of the conventional calorimeter in which heat was produced by an electric heater immersed in the milk. Within rather narrow limits the same values were obtained by both methods. This indicates that the heat of dilution involved in the method of mixtures is negligible. The average value was f o u n d to be 0.943 with only slight deviations f o r the
401
PI::IYSICAL STATE OF TI-IE FAT IN CREAI~
various samples over the t e m p e r a t u r e range studied. The specific heat of the f a t in the cream was calculated f r o m the specific heat of the skimmilk, the specific heat and the f a t content of the cream. Cream of about 40 per cent f a t content obtained f r o m mixed milk was first w a r m e d to 45 ° C. and was then cooled r a p i d l y by immersing the container in w a t e r the t e m p e r a t u r e of which was about 5 ° C. below the final t e m p e r a t u r e desired f o r the cream. As soon as the desired t e m p e r a t u r e of the cream was reached, the t e m p e r a t u r e of the water bath was adjusted to the t e m p e r a t u r e of the cream, and an aliquot of the cream was removed at once and its specific heat determined. Determinations of specific heat were continued at intervals until it was evident that a constant value for that p a r t i c u l a r t e m p e r a t u r e had been reached. Before introducing the cream into the bottle, the t e m p e r a t u r e of the thermos bottle was adjusted to that of the cream by means of water. The t e m p e r a t u r e of the w a r m w a t e r which was poured into the cream was so adjusted that the resulting m i x t u r e would I O.S'O0
--
J
I
I
1
1
I'-O"C.
"
R
"
. . . . II
"c"
k. ~ 0.806
If
f/"
~ 0.700
~
L EGEA/O 0-40°C. • • • I0-40oc. 15-.40°C.
l°
o.~oo
O..4J:O 0
x ~ t ~ f
20-40*C. • W .~~ - 4 0 *C. -4,..,,..,. 30-40"C. ~ -
l
0.600
,
~
,eo°~.?
1 T 1
l 2
I 3 tiME
I 4 IN
I e~°C.J " ~
I
~
7
G
d~
48
~¢0U]~5
Fro. 1. T h e a p p a r e n t specific h e a t of m i l k f a t in c r e a m held a t v a r i o u s t e m p e r a t u r e s f o r v a r y i n g l e n g t h s o f time.
have a t e m p e r a t u r e of 40 ° C. or slightly above. I n this w a y values were obtained for the heat required to w a r m to 40 ° C. cream having original temp e r a t u r e s r a n g i n g f r o m 0 to 30 ° C. The specific heat values thus obtained are the average specific heats for the t e m p e r a t u r e ranges. The specific heat values attributable to the f a t alone are presented graphically in F i g u r e 1. This figure indicates t h a t if the cream is cooled r a p i d l y enough the f a t at r a t h e r low t e m p e r a t u r e s m a y for a short time still be liquid and have the specific heat of liquid fat. Crystallization soon begins, however, and continues f o r about 4 hours, since the specific heat increases f o r a period of a p p r o x i m a t e l y 4 hours. A f t e r this time the change is slight.
402
A. H. RISHOI AND PAUL F. SHARP
The effect of season a n d feed of the cow on the h a r d n e s s of the f a t has been s t u d i e d b y H u n z i k e r , S p i t z e r a n d Mills (8) a n d others. T h e f a t is gene r a l l y less h a r d on p a s t u r e t h a n on d r y feeding. F i g u r e 2 shows t h a t there k
a91
•
•
~ o.81 J"
V/~/'~'~'JUNE
°
.
, /
°
~,
C-'°GrO~E/e
~. o . ~ L ~ o..4 :
'1[ , ,
0
I
I
~
I
I
I
I
"¢ 6 8 T/ME IN /4OUR5
I
I I0
I
I IZ
l~ia. 2. The apparent specific heat of m i l k f a t in cream produced in the month of June and in October. Cream warmed from 10 ° to 40 ° C.
is also a difference i n specific h e a t of the f a t i n the t e m p e r a t u r e r a n g e i n which c r y s t a l l i z a t i o n of f a t occurs. A l i q u o t s of cream, one a t e q u i l i b r i u m at 15 ° C., the other a t e q u i l i b r i u m at 20 ° C., differ i n the n u m b e r of calories r e q u i r e d to w a r m the cream f r o m e q u i l i b r i u m at 15 t o e q u i l i b r i u m at 20 ° C. b y the difference i n the a m o u n t of heat r e q u i r e d to raise each to 40 ° C., a t e m p e r a t u r e at which the f a t is liquid. U s i n g this p r o c e d u r e , the h e a t r e q u i r e d to raise m i l k f a t f r o m successive e q u i l i b r i u m states a t 5 ° C. i n t e r v a l s i n t e m p e r a t u r e was calculated. I n Table I are recorded the average e q u i l i b r i u m specific h e a t values of the f a t calculated TABLE
I
A p p a r e n t specific heat o f / a t in cream f o r each 5 ° C. interval r a n g i n g f r o m 0 to 40 ° C. Mil~ produced in October and N o v e m b e r
Temp. range
Apparent" sp. heat
°C.
°C. 30-40 25-40 20-40 15-40 10-40 5-40 0-40
Temperature difference
...... ...... ...... ...... ...... ...... .....
10 15 20 25 30 35 40
Heat required calories
0.475 0.475 0.50 0.77 0.88
0.89 0.89
4.75 7.13 10.00 19.25 26.40 31.15 35.60
Heat required 5° C. interval
Average sp. heat for interval
Temperature interval
0.475
°C. 30-40
0.475 0.575 1.85 1.43 0.95 0.89
25-30 20-25 15-20 10-15 5-10 0-5
calories
2.38 2.87 9.25 7.15 4.75 4.45
P H Y S I C A L S T A T E OF T H E F A T I N CREAlV[
403
from the calories required to warm to 40 ° C. cream held at a series of temperatures. The total number of calories required to warm the fat through the given temperature range was then calculated, and by difference the increments in calories for each 5 degrees. I n the next to the last column the average specific heat of the fat in each 5 degree range is given. This table indicates that the apparent specific heat of the fat varies from 0.475 for liquid f a t to 1.85 for the temperature range between 15 and 20 ° C., the range in which the greatest change in physical state occurs. I f smaller increments in the region of 15 ° C. had been taken, still higher values might be obtained. The data in this table are in general agreement with those of Fleischmann (6), H a m m e r and Johnson (7), and Bowen (1). The data from Table I were used to calculate the specific heat increments over the temperature range of from 0 to 2.00
~ l.~O -
1.00-
"~.'j---~ ....... k- ~ 0
1
I o.so-
I ol
I
I
I
0
!0 20 30 40 TEl~IPCl2RTUl-t't't't't't't't't~C OF- 5TO/'~G~5~ FzG 3. The calculated apparent specific beat of milkfat and of milk and cream, within each 5° C. interval in the 0-30 ° C. and in the 30-40 ° C. range. The calculations are based on values obtained on samples which had been stored at the various temperatures for 4 hours.
40 ° C. of milk and cream containing various percentages of fat, and the results are given in Table 2. The relationships are more readily visualized in Figure 3.
404
RISHOI A N D
A.H.
PAUL F. SHARP 2
TABLE
Specific heat o f Skimmil~, cream, and m i l k f a t globules f o r 5 ° intervals r a n g i n g f r o m 0 to dO ° C. mil~ produced in October and N o v e m b e r Temperature interval oC. 0~
5
5 -1 0 10-15 15-20 20-25 25-3 0 30-4 0
...............
...............
............... ............... ............... ............... ...............
F a t c o n t e n t ~er c e n t 0
5
10
20
30
40
5O
60
100
.943 .943 .943 .943 .943 .943 .943
.940 .943 .967 .988 .924 .919 .919
.937 .943 .991 1.033 .905 .895 .895
.932 .944 1.040 1.124 .869 .849 .849
.927 .945 1.089 1.215 .832 .802 .802
.921 .945 1.138 1.305 .795 .755 .755
.916 .946 1.186 1.396 .758 .708 .708
.911 .947 1.235 1.487 .722 .662 .662
.890 .950 1.43 1.85 .575 .475 .475
DISCUSSION
The following melting point temperatures are typical of those given in the literature: tristearin 71 ° C., tripalmitin 65 ° C., trimyristin 55 ° C., and triolein -5 ° C. Stearic, palmitic, myristic and oleic are the principal acid components of milkfat. IV[ilkfat may be considered as a solution which on cooling becomes supersaturated with respect to one or more of the mixed glycerides of which it is composed. The uncertainty and indistinctness of the so-called solidifying point would be expected, since a true solidifying point is not involved. The temperature at which a supersaturated solution begins to crystallize varies with the conditions, such as degree of supersaturation, agitation, seeding, etc. Furthermore, after crystallization starts the rate of crystallization of a solute from its supersaturated solution may v a r y greatly and crystallization may extend over a considerable period of time. The crystallization of milkfat is still f u r t h e r complicated because on cooling it probably becomes supersaturated with respect to more than one solute. Milkfat can readily be fractionated into one component which will not melt unless heated above 45 ° C., and into another which will not solidify when cooled to 5 ° C. The so-called melting point of milkfat is not definite because we are really dealing with a temperature-solubility relationship. As the milkfat is warmed, the solid glycerides become more soluble in the liquid fractions, and an appreciable increase in solubility is noticed in the region of 15 ° C., but complete solution is usually not obtained until the fat is heated above 30 ° C. The rate at which the crystals dissolve is dependent upon their size, which in t u r n is dependent upon the rate and conditions of the previous cooling. These phenomena are all demonstrable with milkfat in mass. On cooling, the lag in the formation of the solid phase in milkfat in the globule state is much greater than for fat in mass. The alteration of the specific heat of cream with time was used as a method
PHYSICAL STATE OF THE FAT IN CREA1V[
405
for following the rate of formation of solid milkfat at the various temperatures. Below 20 ° C., the greater part of the crystallization is complete in about four hours. This is in agreement with some experiments carried out by Troy and Sharp (11), who showed that solidification of the fat globules, as indicated by resistance to pressure in the centrifuge, was not complete in two hours, but was complete in five hours, at 3 ° C. CONCLUSIONS
1" The method of mixtures is a reliable method for the determination of specific heat of cream within the range in which a change in the relative amounts of crystalline and liquid fat occurs. 2. W h e n cream is cooled to temperatures within the range of 0 to 20 .0 C., the phase adjustment is nearly complete in about 4 hours, so far as this is indicated by the specific heat. 3. The average equilibrium specific heat for milk-fat in the globules for 5 ° C. temperature intervals is as follows • 0-5 ° C., 0.89 ; 5-10 ° C., 0.95 ; 10-15 ° C., 1.43; 15-20 ° C., 1.85; 20-2.5 ° C., 0.575; 25-40 ° C., 0.475; for fat in milk produced in October and November. 4. A variation in the specific heat of the milkfat with feed or season was shown. REFERENCES
(1) ]3OWEN,J . T . (2) (3) (4)
(5) (6) (7) (8)
(9) (10) (11)
The application of refrigeration to the handling of milk. U . S . D . A . Dept. Bul. 98. 1914. CHANOZ, M., ANt) VA~LLANT, P. Chaleur spdcifique de quelques liquides de l'organisme. Jour. de physiologie et de pathologie gdn~rale 8: 413--416. 1906. CHEVREUL, M. Faits pour servir ~ l'histoire du buerre de vache. Annales de chemie et de physique, Ser. 1, 22". 366-374. 1823. FJORD, N. 5. Beretning om Fors0g paa Ismejeriets Omraade. Tidsskrift for Land~k~nomi. 4 de Raekke 11: 16. 1877. (Courtesy of Prof. N. K j a e r g a a r d Jensen, Kgl. Veterinaer og Landboh~jskole, Copenhagen, Denmark.) Fr.EISCH~AN~, W. Die specifische W~rme der Milch, etc. Sitzungsberichte der kSnigliche bayerisch Akademie der Wissensehaften zu Mfinehen 4 • 97-108. 1874. FLEISC~MA~, W. i~ber de specifische W~rme der Milch. Jour. f. Landwirtschaft 50: 533-576. 1902: HA]YI~IER, B. W., AND JOHNSON, _A_.R. The specific heat of milk and milk derivatives. Iowa Agr. Exp. Sta. Res. ]~ul. No. 14. 1913. HUNZIKER, 0. F., MILLS, n . C., AND SPITZEI~, G. Moisture control of butter. I. Factors not under control of the buttermaker. I n d i a n a Agr. Exp. Sta. Bul. 159. 1912. LANDOIS, ]~. A textbook of human physiology. Translated from the 6th German Ed. p. 389. 1905. SCHN0~tF, C. La ehaleur sp~cifique du lait. Revue gdndrale du lair 4: 313-315. 1905. TROY, It. C., AND SHARp, P . F . Physical factors influencing the formation and f a t content of gravity cream. JORVRNALOF DAmY Scm~c~ 11 : 189-226.
Department of Dairy Industry, CorneU University, Ithaca, New York INTRODUCTIOB]"
The physical state and alterations in the physical state of the fat in the globules of milk and cream offer the most reasonable explanation for the profound effect of temperature on creaming, cream viscosity, foaming, churning, lipase activity, and surface tension. Many of these effects are reversible and are probably produced or influenced by the materials adsorbed on the surface of the globules when the fat is in different physical states. In order better to understand the influence of temperature on milk products, a knowledge of the physical state and alterations in the physical state of the fat in the globules is necessary. Information obtained by a study of milkfat in mass cannot be used as indicating accurately the physical state of the fat dispersed as globules. Seeding occurring in a mass of fat will influence the crystallization of the whole mass, but in fat dispersed as globules seeding will affect only the fat in the globule in which the crystal happens to form, and will exert no direct effect on the fat in other globules. This leads to a much slower attainment of equilibrium. Furthermore the crystals are larger in fat in mass, as compared with fat in globules, and this influences the rate of solution or melting on heating. Crystallization in both fat in mass and in globules is influenced by the rate of cooling. A study was undertaken to gain information as to the physical state of the fat in globules at different temperatures and the rate of attainment of a constant physical state at the different temperatures. Determinations of specific heat were used as one method of following the alterations in the state of the fat in the fat globules. Chevreul (3) observed that the solidification of milkfat was accompanied by the evolution of heat. Fleischmann (5) (6), F j o r d (4), Landois (9), Chanoz and Vaillant (2), Schnorf (10), Hammer and Johnson (7), and Bowen (1) have reported specific heat values for milk and cream. The effect of fat has been studied more specifically by Fleischmann (6), tIammer and Johnson (7), and Bowen (1), the latter reporting values obtained by the U. S. Bureau of Standards. There is no assurance that the fat was in equilibrium at the different temperatures used. The use of an ordinary calorimeter involves difficulties when used to determine the specific heat of milk and cream at temperatures within crystallization range, because considerable time is required to attain the equilibrium state, and during this Received for publication F e b r u a r y 5, 1938, 399
400
A. H. RISHOI AND PAUL F. SHARP
time the heat exchange between the calorimeter and its surroundings makes up an ever increasing p a r t of the total heat measured. EXPERIMENTAL
Method The method of mixtures was used, since it avoids the errors due to large values f o r heat exchange with the surroundings, and has a reputation for high accuracy. Q u a r t thermos bottles were used as containers. W a r m water f r o m one bottle was poured into colder cream or milk contained in another. The thermometers used were graduated to 0.1 ° C. and were calibrated against each other over the range used f r o m 0 to 75 ° C. All readings were made with the aid of a m a g n i f y i n g glass and were estimated to 0.02 ° C. The errors and heat losses in the procedure were studied, and all equipment and procedures were thoroughly standardized. The heat " l o s s " to the container and during the manipulation was f o u n d to be given by the following equation : Loss calories = K 1 ( t f - ti) + K 2 (tw - tr) where K1 and K2 are constants representing the heat equivalent of the a p p a r a t u s and heat lost in pouring, respectively, t~ = final t e m p e r a t u r e of cream-water mixture, tl = initial t e m p e r a t u r e of the cream, tw = the t e m p e r a t u r e of the w a r m w a t e r before pouring, a n d tr----the t e m p e r a t u r e of the room. I t was found by experiment t h a t within the normal limits, the relative h u m i d i t y of the room exerted an effect so small that it could be disregarded. The constants were determined by calibration with water, the room temperatures v a r y i n g f r o m 23 to 28 ° C., cold w a t e r v a r y i n g f r o m 5 to 39 ° C., and w a r m w a t e r v a r y i n g f r o m 21 to 66 ° C. The constants were calculated by the method of least squares, and for a typical p a i r of thermos bottles gave the equation : Loss calories = 25.35 (tf - ti) + 3.38 ( t ~ - tr) About 150 grams of cream and 250 grams of w a t e r were used. The amounts were determined by weighing. The specific heat of water was taken as unity, and a f t e r correcting for the heat loss, the specific heat of the cream was calculated.
Results The specific heat of skimmilk was determined both by the method of mixtures and by means of the conventional calorimeter in which heat was produced by an electric heater immersed in the milk. Within rather narrow limits the same values were obtained by both methods. This indicates that the heat of dilution involved in the method of mixtures is negligible. The average value was f o u n d to be 0.943 with only slight deviations f o r the
401
PI::IYSICAL STATE OF TI-IE FAT IN CREAI~
various samples over the t e m p e r a t u r e range studied. The specific heat of the f a t in the cream was calculated f r o m the specific heat of the skimmilk, the specific heat and the f a t content of the cream. Cream of about 40 per cent f a t content obtained f r o m mixed milk was first w a r m e d to 45 ° C. and was then cooled r a p i d l y by immersing the container in w a t e r the t e m p e r a t u r e of which was about 5 ° C. below the final t e m p e r a t u r e desired f o r the cream. As soon as the desired t e m p e r a t u r e of the cream was reached, the t e m p e r a t u r e of the water bath was adjusted to the t e m p e r a t u r e of the cream, and an aliquot of the cream was removed at once and its specific heat determined. Determinations of specific heat were continued at intervals until it was evident that a constant value for that p a r t i c u l a r t e m p e r a t u r e had been reached. Before introducing the cream into the bottle, the t e m p e r a t u r e of the thermos bottle was adjusted to that of the cream by means of water. The t e m p e r a t u r e of the w a r m w a t e r which was poured into the cream was so adjusted that the resulting m i x t u r e would I O.S'O0
--
J
I
I
1
1
I'-O"C.
"
R
"
. . . . II
"c"
k. ~ 0.806
If
f/"
~ 0.700
~
L EGEA/O 0-40°C. • • • I0-40oc. 15-.40°C.
l°
o.~oo
O..4J:O 0
x ~ t ~ f
20-40*C. • W .~~ - 4 0 *C. -4,..,,..,. 30-40"C. ~ -
l
0.600
,
~
,eo°~.?
1 T 1
l 2
I 3 tiME
I 4 IN
I e~°C.J " ~
I
~
7
G
d~
48
~¢0U]~5
Fro. 1. T h e a p p a r e n t specific h e a t of m i l k f a t in c r e a m held a t v a r i o u s t e m p e r a t u r e s f o r v a r y i n g l e n g t h s o f time.
have a t e m p e r a t u r e of 40 ° C. or slightly above. I n this w a y values were obtained for the heat required to w a r m to 40 ° C. cream having original temp e r a t u r e s r a n g i n g f r o m 0 to 30 ° C. The specific heat values thus obtained are the average specific heats for the t e m p e r a t u r e ranges. The specific heat values attributable to the f a t alone are presented graphically in F i g u r e 1. This figure indicates t h a t if the cream is cooled r a p i d l y enough the f a t at r a t h e r low t e m p e r a t u r e s m a y for a short time still be liquid and have the specific heat of liquid fat. Crystallization soon begins, however, and continues f o r about 4 hours, since the specific heat increases f o r a period of a p p r o x i m a t e l y 4 hours. A f t e r this time the change is slight.
402
A. H. RISHOI AND PAUL F. SHARP
The effect of season a n d feed of the cow on the h a r d n e s s of the f a t has been s t u d i e d b y H u n z i k e r , S p i t z e r a n d Mills (8) a n d others. T h e f a t is gene r a l l y less h a r d on p a s t u r e t h a n on d r y feeding. F i g u r e 2 shows t h a t there k
a91
•
•
~ o.81 J"
V/~/'~'~'JUNE
°
.
, /
°
~,
C-'°GrO~E/e
~. o . ~ L ~ o..4 :
'1[ , ,
0
I
I
~
I
I
I
I
"¢ 6 8 T/ME IN /4OUR5
I
I I0
I
I IZ
l~ia. 2. The apparent specific heat of m i l k f a t in cream produced in the month of June and in October. Cream warmed from 10 ° to 40 ° C.
is also a difference i n specific h e a t of the f a t i n the t e m p e r a t u r e r a n g e i n which c r y s t a l l i z a t i o n of f a t occurs. A l i q u o t s of cream, one a t e q u i l i b r i u m at 15 ° C., the other a t e q u i l i b r i u m at 20 ° C., differ i n the n u m b e r of calories r e q u i r e d to w a r m the cream f r o m e q u i l i b r i u m at 15 t o e q u i l i b r i u m at 20 ° C. b y the difference i n the a m o u n t of heat r e q u i r e d to raise each to 40 ° C., a t e m p e r a t u r e at which the f a t is liquid. U s i n g this p r o c e d u r e , the h e a t r e q u i r e d to raise m i l k f a t f r o m successive e q u i l i b r i u m states a t 5 ° C. i n t e r v a l s i n t e m p e r a t u r e was calculated. I n Table I are recorded the average e q u i l i b r i u m specific h e a t values of the f a t calculated TABLE
I
A p p a r e n t specific heat o f / a t in cream f o r each 5 ° C. interval r a n g i n g f r o m 0 to 40 ° C. Mil~ produced in October and N o v e m b e r
Temp. range
Apparent" sp. heat
°C.
°C. 30-40 25-40 20-40 15-40 10-40 5-40 0-40
Temperature difference
...... ...... ...... ...... ...... ...... .....
10 15 20 25 30 35 40
Heat required calories
0.475 0.475 0.50 0.77 0.88
0.89 0.89
4.75 7.13 10.00 19.25 26.40 31.15 35.60
Heat required 5° C. interval
Average sp. heat for interval
Temperature interval
0.475
°C. 30-40
0.475 0.575 1.85 1.43 0.95 0.89
25-30 20-25 15-20 10-15 5-10 0-5
calories
2.38 2.87 9.25 7.15 4.75 4.45
P H Y S I C A L S T A T E OF T H E F A T I N CREAlV[
403
from the calories required to warm to 40 ° C. cream held at a series of temperatures. The total number of calories required to warm the fat through the given temperature range was then calculated, and by difference the increments in calories for each 5 degrees. I n the next to the last column the average specific heat of the fat in each 5 degree range is given. This table indicates that the apparent specific heat of the fat varies from 0.475 for liquid f a t to 1.85 for the temperature range between 15 and 20 ° C., the range in which the greatest change in physical state occurs. I f smaller increments in the region of 15 ° C. had been taken, still higher values might be obtained. The data in this table are in general agreement with those of Fleischmann (6), H a m m e r and Johnson (7), and Bowen (1). The data from Table I were used to calculate the specific heat increments over the temperature range of from 0 to 2.00
~ l.~O -
1.00-
"~.'j---~ ....... k- ~ 0
1
I o.so-
I ol
I
I
I
0
!0 20 30 40 TEl~IPCl2RTUl-t't't't't't't't't~C OF- 5TO/'~G~5~ FzG 3. The calculated apparent specific beat of milkfat and of milk and cream, within each 5° C. interval in the 0-30 ° C. and in the 30-40 ° C. range. The calculations are based on values obtained on samples which had been stored at the various temperatures for 4 hours.
40 ° C. of milk and cream containing various percentages of fat, and the results are given in Table 2. The relationships are more readily visualized in Figure 3.
404
RISHOI A N D
A.H.
PAUL F. SHARP 2
TABLE
Specific heat o f Skimmil~, cream, and m i l k f a t globules f o r 5 ° intervals r a n g i n g f r o m 0 to dO ° C. mil~ produced in October and N o v e m b e r Temperature interval oC. 0~
5
5 -1 0 10-15 15-20 20-25 25-3 0 30-4 0
...............
...............
............... ............... ............... ............... ...............
F a t c o n t e n t ~er c e n t 0
5
10
20
30
40
5O
60
100
.943 .943 .943 .943 .943 .943 .943
.940 .943 .967 .988 .924 .919 .919
.937 .943 .991 1.033 .905 .895 .895
.932 .944 1.040 1.124 .869 .849 .849
.927 .945 1.089 1.215 .832 .802 .802
.921 .945 1.138 1.305 .795 .755 .755
.916 .946 1.186 1.396 .758 .708 .708
.911 .947 1.235 1.487 .722 .662 .662
.890 .950 1.43 1.85 .575 .475 .475
DISCUSSION
The following melting point temperatures are typical of those given in the literature: tristearin 71 ° C., tripalmitin 65 ° C., trimyristin 55 ° C., and triolein -5 ° C. Stearic, palmitic, myristic and oleic are the principal acid components of milkfat. IV[ilkfat may be considered as a solution which on cooling becomes supersaturated with respect to one or more of the mixed glycerides of which it is composed. The uncertainty and indistinctness of the so-called solidifying point would be expected, since a true solidifying point is not involved. The temperature at which a supersaturated solution begins to crystallize varies with the conditions, such as degree of supersaturation, agitation, seeding, etc. Furthermore, after crystallization starts the rate of crystallization of a solute from its supersaturated solution may v a r y greatly and crystallization may extend over a considerable period of time. The crystallization of milkfat is still f u r t h e r complicated because on cooling it probably becomes supersaturated with respect to more than one solute. Milkfat can readily be fractionated into one component which will not melt unless heated above 45 ° C., and into another which will not solidify when cooled to 5 ° C. The so-called melting point of milkfat is not definite because we are really dealing with a temperature-solubility relationship. As the milkfat is warmed, the solid glycerides become more soluble in the liquid fractions, and an appreciable increase in solubility is noticed in the region of 15 ° C., but complete solution is usually not obtained until the fat is heated above 30 ° C. The rate at which the crystals dissolve is dependent upon their size, which in t u r n is dependent upon the rate and conditions of the previous cooling. These phenomena are all demonstrable with milkfat in mass. On cooling, the lag in the formation of the solid phase in milkfat in the globule state is much greater than for fat in mass. The alteration of the specific heat of cream with time was used as a method
PHYSICAL STATE OF THE FAT IN CREA1V[
405
for following the rate of formation of solid milkfat at the various temperatures. Below 20 ° C., the greater part of the crystallization is complete in about four hours. This is in agreement with some experiments carried out by Troy and Sharp (11), who showed that solidification of the fat globules, as indicated by resistance to pressure in the centrifuge, was not complete in two hours, but was complete in five hours, at 3 ° C. CONCLUSIONS
1" The method of mixtures is a reliable method for the determination of specific heat of cream within the range in which a change in the relative amounts of crystalline and liquid fat occurs. 2. W h e n cream is cooled to temperatures within the range of 0 to 20 .0 C., the phase adjustment is nearly complete in about 4 hours, so far as this is indicated by the specific heat. 3. The average equilibrium specific heat for milk-fat in the globules for 5 ° C. temperature intervals is as follows • 0-5 ° C., 0.89 ; 5-10 ° C., 0.95 ; 10-15 ° C., 1.43; 15-20 ° C., 1.85; 20-2.5 ° C., 0.575; 25-40 ° C., 0.475; for fat in milk produced in October and November. 4. A variation in the specific heat of the milkfat with feed or season was shown. REFERENCES
(1) ]3OWEN,J . T . (2) (3) (4)
(5) (6) (7) (8)
(9) (10) (11)
The application of refrigeration to the handling of milk. U . S . D . A . Dept. Bul. 98. 1914. CHANOZ, M., ANt) VA~LLANT, P. Chaleur spdcifique de quelques liquides de l'organisme. Jour. de physiologie et de pathologie gdn~rale 8: 413--416. 1906. CHEVREUL, M. Faits pour servir ~ l'histoire du buerre de vache. Annales de chemie et de physique, Ser. 1, 22". 366-374. 1823. FJORD, N. 5. Beretning om Fors0g paa Ismejeriets Omraade. Tidsskrift for Land~k~nomi. 4 de Raekke 11: 16. 1877. (Courtesy of Prof. N. K j a e r g a a r d Jensen, Kgl. Veterinaer og Landboh~jskole, Copenhagen, Denmark.) Fr.EISCH~AN~, W. Die specifische W~rme der Milch, etc. Sitzungsberichte der kSnigliche bayerisch Akademie der Wissensehaften zu Mfinehen 4 • 97-108. 1874. FLEISC~MA~, W. i~ber de specifische W~rme der Milch. Jour. f. Landwirtschaft 50: 533-576. 1902: HA]YI~IER, B. W., AND JOHNSON, _A_.R. The specific heat of milk and milk derivatives. Iowa Agr. Exp. Sta. Res. ]~ul. No. 14. 1913. HUNZIKER, 0. F., MILLS, n . C., AND SPITZEI~, G. Moisture control of butter. I. Factors not under control of the buttermaker. I n d i a n a Agr. Exp. Sta. Bul. 159. 1912. LANDOIS, ]~. A textbook of human physiology. Translated from the 6th German Ed. p. 389. 1905. SCHN0~tF, C. La ehaleur sp~cifique du lait. Revue gdndrale du lair 4: 313-315. 1905. TROY, It. C., AND SHARp, P . F . Physical factors influencing the formation and f a t content of gravity cream. JORVRNALOF DAmY Scm~c~ 11 : 189-226.