Determination of Heat Capacity Using Phase Changes

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 C_p Changes

The examples that follow show various application possibilities of the sapphire method for the determination of C_p 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 C_p 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 C_p 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 C_p and the magnitude of the change at the glass transition is possible only using the C_p curve.

Change in C_p 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 C_p function of cobalt at the Curie point at 1120 °C (1393 K). The C_p 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 C_p curve, literature values values: o[4], + [5], □ [6]. Cobalt measured as five disks. Heating rate 20 K/min; crucible 30-µL Pt with lid.

Change in C_p in Decomposition Reactions

While measuring C_p, 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 C_p 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 C_p 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 C_p curves of CaCO₃ and CaO calculated from the curves in Figure 3 using the sapphire method. Black dashed line: C_p without mass correction; red line with correction. Literature data: + [4], Δ [5], o [5, 6].

Observations from the example are listed below:

• There is an increase in C_p because of the overlapping decomposition enthalpy. The curve corresponds to the apparent specific heat capacity.
• After the reaction completion, the C_p 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 C_p 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 C_p 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 heating run.
• At 1100 °C, the C_p values of both measurements agree well.

Determination of the Process Enthalpy from C_p Measurements

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 C_p 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 C_p curve.

Example for Determining Process Enthalpy

The calcination of CaCO₃ is again considered as an example. In Figure 5, the C_p curve calculated with reference to the starting material is shown.

Figure 5. The C_p curve of CaCO₃ (dashed, not mass corrected). The blue curve is the enthalpy as a function of temperature.

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 C_p curve, and the starting value is set to zero.
• By integration of the C_p 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 C_p value of the sample changes proportional to the conversion.

Summary and Conclusions

The change in C_p 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 C_p. 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 C_p values of the starting and end products. The integration of the C_p curve with respect to temperature yields the enthalpy of a process. This was shown using the calcination of CaCO₃ as an example.

This information has been sourced, reviewed and adapted from materials provided by Mettler Toledo - Thermal Analysis.

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