Chemistry Reference
In-Depth Information
expansion of the water (Jenness and Patton, 1959). However, the fat content
has a significant simultaneous effect, for two reasons. First, the coefficient of
cubic expansion of milk fat (0.0008 m
3
m
3
per 8C in the temperature range
0-608C) is much greater than that of water (0.00015 m
3
m
3
per 8C at 10-208C;
0.00055 m
3
m
3
per 8Cat60-708C) (Jenness and Patton, 1959). Second, as milk
fat expands by 0.045 m
3
m
3
when it melts (Jenness and Patton, 1959), the
value of density at a given temperature will depend on temperature history and
on the temperature itself.
The density of supercooled milk measured at a temperature close to
208C may be corrected to 208C using the correction factor 0.3 kg m
3
per 8C
recommended by Ruegg and Moor (1985).
There have been many attempts to develop empirical equations relating
milk density to fat content and temperature, the two most important deter-
mining variables. Bertsch et al. (1982) obtained the following such equation:
¼
0
:
2307
10
2
2
0
:
2655
þ
1040
:
51
(17)
F
ð
0
:
478
10
4
2
þ
0
:
969
10
2
þ
0
:
967
Þð
kgm
3
Þ
where
is the temperature (8C) and F is the % fat (w/w). Equation 17 is valid
for milks and creams with a fat content in the range 0-15% (w/w), at a
temperature in the range 65-1408C. The relative mean error of the equation
was
0.1 % at the 95% level of confidence (88 experimental points).
Bertsch et al. (1982) compared Equation 17 with the density data
published previously by other workers. They found that the validity of the
equation could be extended to cover the fat content range 0-50% and the
temperature range 20-408C, although with a relative mean error as high as
(but not exceeding)
0.4%. This higher error was probably due to variations
in SNF and to the effects of temperature history (within the milk fat melting
point range), as well as to experimental error (Bertsch et al., 1982).
Watson and Tittsler (1961) determined the following empirical relation-
ship for the dependence of whole milk density on fat content and SNF content
in the low-temperature range 0.95-9.858C:
¼
1003
:
073
1
:
79
3
:
68F
þ
37
:
44SNF
ð
kgm
3
Þ
(18)
The slight inverse temperature dependence of milk density was ignored
in establishing Equation 18. Fern´ ndez-Martin (1975) deliberately studied
this temperature dependence by measuring the coefficient of volumetric
thermal expansion (
V
) of milks and creams of a range of fat and total solids
contents over the temperature range 0-808C. He derived from his data the
following relationships:
