# Determination of Heat Capacity at High Temperatures

Differential scanning calorimetry (DSC) is an exceptional technique for measuring the specific heat capacity (Cp) of materials. In this method, very small amounts of sample are required. There are several standard DSC measurement procedures presently used for the determination of the specific heat capacity (Cp).

## Determination of Heat Flow

In DSC, the heat flow determined is directly proportional to the specific heat capacity. Hence C p is calculated directly from the DSC signal (Φmeas). In order to do this, the DSC curve is corrected by subtracting a blank curve and the crucible masses are maintained very close to each other. The isothermal baselines determined before and after the temperature increase need to be long enough for the system to stabilize and reach stationary conditions. The results are evaluated according to standards such as ISO 11357, DIN 53765, DIN 51007 or ASTM E1269.

## Determination of Specific Heat Capacity

For measuring the specific heat capacity, the following two methods are employed:

• The direct method
• The sapphire method

According to the direct method, Equation 1 is used to determine the specific heat capacity.

According to the sapphire method, Equation 2 is used to determine the specific heat capacity.

In both the methods, the impact of different crucible masses is considered.

## Determination of Specific Heat Capacity at High Temperatures Above 500°C

The experiment detailed below demonstrates the method of determining specific heat capacities at temperatures higher than 500 °C and shows suitable examples. In Table 1, different Cp reference values from the literature are summarized for the purpose of comparing the results.

Table 1. Values of specific heat capacities at different temperatures.

Material 500 550 600 1250 1300 1350 °C
platinum 0.144 0.145 0.147 0.16 0.1672 0.168 J/gK
nickel 0.529 0.534 0.54 0.62 0.616 0.629 J/gK
sapphire 1.171 1.185 1.197 1.29 1.295 1.299 J/gK
quartz 0.777 0.789 0.732 0.79 0.793 0.798 J/gK
quartz 1.24   1.14       J/gK

## Experimental Details

The conditions and methodology of the experiment are listed below:

• Experiments to determine specific heat capacity at high temperatures were carried out using several stable materials that could be subjected to measurement repeatedly and showed differences in Cp, color and thermal conductivity.
• The measurements were performed with a TGA/DSC 1 provided with a large furnace for temperatures to 1600 °C and a HSS2 sensor.
• The furnace was purged with nitrogen at 80 mL/min to prevent long-term oxidation of nickel.
• Pure metal disks of platinum and nickel were used for measurement.
• Various types of aluminum oxide such as sapphire pieces, powder and sintered alumina disks were also compared.
• The specific heat capacity of all three forms of aluminum oxide was assumed to be the same.

## Calibration

Firstly, the TGA/DSC 1 was adjusted using standard procedures using pure metals (Zn, Al, Au and Pd) in a 70-μL alumina crucible. While using the direct method, the heat flow is accurately adjusted for the required temperature range and crucibles.

As the calibration metals form alloys with platinum crucibles, a 30-μL alumina crucible was arranged inside a 150- μL Pt crucible and the reference sample weighed into the alumina crucible. For every metal a separate crucible was used. The crucibles could be repetitively for adjustment and calibration.

## Crucibles and Sample Mass

A number of measurements were initially done to determine which crucible would be ideal for determining Cp.

The sample temperature curve and the heat flow curves of platinum, sapphire and nickel samples are shown in Figure 1

Figure 1. The upper diagram (black curve) shows the sample temperature. The DSC curves of sapphire, platinum and nickel are displayed in the lower diagram (with blank curve subtraction). The dashed curves refer to alumina crucibles. The curves were not recorded during heating from 650 °C to 1200 °C and stabilized.

## Sapphire Method

In Figure 2 the curves obtained for a typical evaluation are displayed.

Figure 2. The upper diagram shows the heat flow curves of sapphire and platinum. The lower curves show the Cp curves of platinum together with three numerical values (rounded).

The diagram shown above displays the heat flow curves of platinum and sapphire. The lower diagrams display the resulting curves for the specific heat capacity of platinum separately for the lower and higher temperature ranges. Three values were automatically evaluated from the curves using the software and are presented in the table.

Table 2 shows the results of the Cp determinations of various materials determined using the sapphire method.

Table 2. Results using the sapphire method. Crucible: Pt 150-μL with lid. Here, Cp is the mean value, s is the standard deviation of the three values, and ΣCp the deviation from the literature value

°C 500 550 600 1250 1300 1350
Platinum cp J/gK 0.16 0.16 0.16 0.19 0.18 0.18
918.81 mg s % 0.0 0.0 0.0 5.3 6.0 5.6
ΔCp % 11.1 10.3 8.8 13.3 8.0 7.4
Nickel Cp J/gK 0.57 0.57 0.57 0.68 0.68 0.68
523.77 mg s % 3.0 4.1 3.0 6.0 7.4 7.4
ΔCp % 7.8 6.1 5.6 9.0 8.1 8.6
Aluminum oxide powder Cp J/gK 1.13 1.14 1.15 1.18 1.20 1.19
218.17 mg s % 2.2 2.2 2.2 2.13 1.67 1.75
ΔCp % –3.8 –4.1 –4.2 –8.3 –7.3 –8.7
Alumina lid Cp J/gK 1.16 1.17 1.18 1.29 1.25 1.20
229.63 mg s % 0.9 1.7 2.6 8.89 5.34 6.45
ΔCp % –0.9 –1.3 –1.7 0.3 –3.7 –7.4
Quartz Cp J/gK 1.23 1.28 1.24 1.30 1.30 1.31
169.83 mg s % 2.2 2.2 2.9 4.0 4.9 5.9
ΔCp % –0.8 8.8

Three separate measurements of each sample were done in the lower and higher temperature ranges. The same material measurements were done with the same single sample. The samples were placed in the furnace every time before measurement. The table shows the mean values and the standard deviation of three individual values as well as the deviation from literature values provided in Table 1.

The results are listed below:

• The reference value for aluminum oxide was assumed to be the same as that of sapphire.
• The mean values of specific heat capacities of diverse materials show a maximum deviation of about 10% from the related reference values.
• The smaller values such as platinum differ more strongly than the larger values such as aluminum oxide.
• For metals, the results deviate to larger values and for oxides to lesser values.
• The deviations also tend to be greater at higher temperatures than at lower temperatures. The standard deviation or repeatability standard deviation is better at lesser temperatures than at high temperatures.
• Comparison of the results for aluminum oxide powder and aluminum oxide lids show that the impact of packing density is not easily noticed

It is important to note that a platinum crucible used with a lid gives very good results for quantitative Cp determinations at high and low temperatures. An accuracy of ± 10% is anticipated.

## Direct Method

The measurements obtained for the sapphire method can also be used to directly determine Cp values according to Equation 3. The results are shown in Table 3. The large deviations show that this method is not suitable for Cp determination.

## Conclusions

Two standard DSC methods were used to determine Cp at temperatures up to 1600 °C. In general, results from the direct method show that repeatability and absolute accuracy are strongly dependent on the temperature. Hence this method is not recommended.

In contrast, the sapphire method has the benefit that no additional calibrations are required for special crucibles or gases. The best way to minimize the impact of the thermal conductivity of the sample and other effects is to use platinum crucibles with lids. Depending on the range of temperatures, pure substances measurements are precise to ± 5% to ± 10% when compared with literature values. To achieve high reproducibility and precision, measurements of a series must be done directly and consecutively at regular intervals. Further, one or two blank measurements should be done at the beginning of a series but not used for subtraction.

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

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