By AZoM Editors
Table of ContentsIntroductionDetermination of Cp ChangesChange in
Cp at the Glass TransitionChange in
Cp in Second Order Phase TransitionsChange in
Cp in Decomposition Reactions
Example to Study
Cp in Decomposition Reactions Determination of
the Process Enthalpy from Cp Measurements
Example for Determining
Process EnthalpySummary and ConclusionsAbout Mettler Toledo
Using differential scanning calorimetry (DSC) it is possible to
measure the specific heat capacity using different methods. The direct method
and the sapphire method are commonly used and it should be noted that the
sapphire method provides reliable results especially for temperatures above
1600°C. Applications of the sapphire method are discussed in this paper.
Determination of Cp Changes
The examples that follow show various application possibilities of the
sapphire method for the determination of Cp at high temperatures. The
measurements were done with the use of a METTLER TOLEDO TGA/DSC 1
equipped with an HSS2 sensor. For all the experiments a platinum crucible with
lid was used. The curves are blank corrected.
Change in Cp at the Glass Transition
There is a marked change in the specific heat capacity during glass
transition. With the help of the sapphire method, it is possible to measure this
change with a glass sample as shown in Figure 1.
Figure 1. DSC curves of a glass sample and sapphire to
determine the glass transition and the change in Cp of the glass.
Heating rate 10 K/min; crucible 30-μL Pt.
It is possible to read the characteristic glass transition temperature from
the DSC curve, whereas the overall course of the Cp and the magnitude
of the change at the glass transition is possible only using the Cp
Change in Cp in Second Order Phase Transitions
Second order phase transitions show a distinctive change in the specific heat
capacity without any involvement of latent heat or additional energy. The change
is noted as an apparent endothermic effect on the DSC heating curve of a
suitable sample. The dependence of the specific heat capacity is measured using
the sapphire method. The example shown in Figure 2 displays the Cp
function of cobalt at the Curie point at 1120 °C (1393 K). The Cp
curve shows a typical l-shape. The measurement values lie in the range of
literature values for cobalt and the standard deviation is about ± 10%.
Figure 2. Upper diagram: DSC curves of cobalt and
sapphire using the sapphire method.
Lower diagram: the Cp curve,
literature values values: o, + , □ . Cobalt measured as five disks.
Heating rate 20 K/min; crucible 30-µL Pt with lid.
Change in Cp in Decomposition Reactions
While measuring Cp, it is assumed that the sample does not change,
but since this does not happen in a decomposition reaction the sapphire method
would measure an apparent specific heat capacity. It is important to consider
the change in mass to measure Cp of the start and end product.
By using TGA and DSC techniques in the TGA/DSC 1 mass
and enthalpy changes are simultaneously measured using the same test specimen.
Example to Study Cp in Decomposition Reactions
The thermal decomposition of calcium carbonate to calcium oxide is studied as
an example. The heat flow determined during the decomposition of calcium
carbonate includes a latent heat component that is measured by the reaction
enthalpy. The TGA and DSC curves are shown in Figure 3.
Figure 3. TGA and DSC curves of sapphire,
CaCO3 and CaO measured according to the sapphire method. Heating rate
20 K/min; crucible: 150-μL Pt with lid.
Pure calcium carbonate in a nitrogen atmosphere decomposes to calcium oxide
that is left behind as a residue. There is a mass loss of 43.97%. The specific
heat capacity of CaCO3 measured before decomposition that starts at
about 600 °C agrees well with the literature value as shown in Figure 4.
Figure 4. The Cp curves of CaCO3
and CaO calculated from the curves in Figure 3 using the sapphire method. Black
dashed line: Cp without mass correction; red line with correction.
Literature data: + , Δ , o [5, 6].
Observations from the example are listed below:
- There is an increase in Cp because of the overlapping
decomposition enthalpy. The curve corresponds to the apparent specific heat
- After the reaction completion, the Cp value measured is too low
if normalization is performed as usual with respect to the original starting
mass (dashed curve).
- The STARe software enables the Cp calculation to be performed
with respect to the changing mass. The result of this calculation is shown in
Figure 4 as the red curve that is mass corrected. It shows that correct values
are obtained for the calcium oxide.
- Another heating run of the same test specimen as shown in Figure 3 produced
the Cp curve of CaO for the complete temperature range as shown by
the blue curve in Figure 4.
- There is no mass change hence calculation is made with constant starting
mass. In the example shown, this corresponds to the residue from the first
- At 1100 °C, the Cp values of both measurements agree well.
Determination of the Process Enthalpy from Cp
The process enthalpy is the sum of the heat needed to heat the material
called the sensible heat and the latent heat or the reaction enthalpy. It is
possible to calculate both these values from the Cp curve but the
process enthalpy is studied with respect to initial mass.
The enthalpy and its change as a function of temperature are determined by
integrating the Cp curve.
Example for Determining Process Enthalpy
The calcination of CaCO3 is again considered as an example. In
Figure 5, the Cp curve calculated with reference to the starting
material is shown.
Figure 5. The Cp curve of CaCO3
(dashed, not mass corrected). The blue curve is the enthalpy as a function of
Observation from the example is listed below:
- Integration with reference to temperature gives a process enthalpy of
approx. 2217 J/g for the calcinations between 450 and 1000°C.
- The enthalpy is calculated as a function of the temperature shown by the
blue curve by partial integration of the Cp curve, and the starting
value is set to zero.
- By integration of the Cp curve above the red baseline, the
reaction enthalpy is obtained
- This gives a value of approx. 1692 J/g. The baseline is constructed assuming
that the Cp value of the sample changes proportional to the
Summary and Conclusions
The change in Cp occurring during different thermal events are
studied. The glass transition of an inorganic glass and the second order phase
transition of cobalt are shown as examples. The sample mass normally remains
constant during determination of Cp. If a chemical or physical change
involving latent heat takes place, an apparent heat capacity is determined. In a
decomposition reaction, there is a change in the mass of the sample. This mass
change must be considered in order to determine correct Cp values of
the starting and end products. The integration of the Cp curve with
respect to temperature yields the enthalpy of a process. This was shown using
the calcination of CaCO3 as an example.
About Mettler Toledo
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sample materials over a very wide temperature range. Control all the instruments
from a single, powerful, easy-to-use software platform. Each instrument
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confidence in your results.
This information has been sourced, reviewed and adapted from
materials provided by METTLER TOLEDO.
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