Chemistry Reference
In-Depth Information
c(
) in Equation 52 gives the following expression for enthalpy change in
skim milk (valid for the temperature range 52-1348C):
h
1
$
2
¼
1
:
407
2
1
:
407
1
þ
3824
ð
2
1
Þð
Jkg
1
Þ
(59)
Similar expressions (valid for temperatures
>
408C) could be obtained
by taking the right-hand sides of Equations 56 and 58 as c(
).
For whole milk and cream (unconcentrated or concentrated, and at
temperatures above or below 408C, but above the product's freezing point),
enthalpy change can be predicted using the following general expression
(Miles et al., 1983):
h
1
$
2
¼
h
fat
x
fat
þ
h
non
fat
x
non
fat
(60)
where h
fat
is the enthalpy change (J kg
1
) in milk fat between
1
and
2
,
h
non-fat
is the enthalpy change in the non-fat portion of the product between
1
and
2
,x
fat
is the fraction of milk fat in the product and x
non-fat
is the mass
fraction of the non-fat portion. h
fat
must be found from empirical data;
Riedel (1955), for example, tabulated the enthalpies of summer and winter
milk fat at temperatures in the range
50 (h
¼
0) to 558C.
h
non-fat
can be predicted from
h
milk plasma
¼
Z
2
ð
c
i
x
i
Þ
d
¼
ð
c
i
x
i
Þð
1
2
Þ
(61)
1
where c
i
is the specific heat of the ith component, x
i
is the mass fraction of the
ith component and (c
i
x
i
) is the specific heat of milk plasma. Suitable values
of c
i
for water, lactose, protein and ash are 4200, 1400, 1600 and 800 J kg
1
K
1
, respectively (Kessler, 1981). The slight temperature dependence of the
specific heat capacities of the non-fat components may, for practical pur-
poses, usually be ignored.
The calculation of specific heat as (c
i
x
i
), which embodies the
principle of additivity of specific heats, can be applied to whole milk and
cream at temperatures
>
408C (milk fat completely liquid; no latent heat
effects) by including the term c
fat
x
fat
in (c
i
x
i
). A suitable value of c
fat
is
2174 J kg
1
K
1
(Sherbon, 1988). In applying the principle of additivity it
is assumed implicitly that there are no interactions between the different
components of the mixture that affect the components' individual specific
heat capacities; this assumption is considered valid for the non-fat part of
milk or cream (Phipps, 1957) and is thus almost certainly valid for the
whole product.
