Chemistry Reference
In-Depth Information
temperature range 5-708C. He developed from his data the following empiri-
cal equation relating specific heat capacity to composition and temperature
for the temperature range 40
<<
708C:
ð
Jkg
1
K
1
Þ
c
¼
41
:
8W
þð
13
:
71
þ
0
:
1129
Þ
TS
(56)
The equation is valid for the %TS range 8
<
TS
<
40% and the fat/SNF
ratio range 0.01
<
fat/SNF
<
0.04. Fern´ ndez-Martin (1972a) pointed out
uncertainties in the results of a similar study carried out by Rambke and
Konrad (1970).
For each of his milk preparations, Fern´ ndez-Martin (1972a) calculated
enthalpy relative to an arbitrarily assumed value of h
¼
0Jkg
1
at 58C, at each
of several temperatures in the overall range 5
<<
708C, by graphical integra-
tion of the experimentally determined specific heat capacity-temperature plot.
(This operation was equivalent to integrating the right-hand side of Equation 55
with
1
and
2
equal to 5 and 808C, respectively, and with c
app
(
) in graphical
rather than algebraic form.) Linear regression of the enthalpy-temperature
data yielded an average apparent specific heat capacity (
¼
dh/d
of Equation
53) for each preparation for the temperature range 5-708C. The results were
presented as a nomogram (stated to be valid for the temperature range 0-808C)
allowing average apparent specific heat capacity to be found for milks and
concentrated milks with fat and SNF contents in the ranges 0
<
F
<
12% and
0
<
SNF
<
43%, respectively.
Bertsch (1982) measured the specific heat capacity of skim milk and
whole milk (4% fat) over the temperature ranges 52-1348C and 53-1438C,
respectively. Specific heat was empirically related to temperature by the
following equations:
ð
Jkg
1
K
1
Þ
c
¼
2
:
814
þ
3942
Skim milk :
(57)
ð
Jkg
1
K
1
Þ
Whole milk :
c
¼
2
:
976
þ
3692
(58)
Both equations had mean relative errors of about 4% (p
¼
0.05).
Bertsch (1982) showed that his data were in good agreement with those of a
number of previous workers (including those of Fern´ ndez-Martin, 1972a) in
the temperature range 52-808C.
The ability to predict the enthalpy change between two chosen tem-
peratures is, from a technological or engineering point of view, more useful
than the ability to predict specific heat capacity at specific temperatures. An
equation for predicting enthalpy change can be derived easily by inserting an
appropriate form of c(
) into Equation 52, or of c
app
(
) into Equation 55,
and integrating. For example, taking the right-hand side of Equation 57 as
