Measuring the heat capacity of liquids at high temperatures – applications to molten salts

Figure 1. Liquids vessel for SETARAM C80.

Accurate measurement of specific heat capacity by traditional pan-style DSC is a technically demanding operation: sample size, sample loading, stability of the heat flow sensor mounting in the furnace, contact agents, thermal history of the sample and, at times, temperature stability of the ambient environment when conducting a test can all affect the quality of the data. Much has been written on technical considerations for valid specific heat capacity measurements in the context of solids thermal conductivity measurement. Liquids have traditionally added another layer of complexity to the problem of accurate specific heat capacity measurement.

Liquids generally have non-zero vapor pressures. This means that in a typical Cp test configuration, where the sample is open to a constant flow of a dry purge gas, a liquid is constantly evaporating to achieve the equilibrium vapor pressure. However, because the vapor is constantly being pulled away by the purge gas flow, the equilibrium pressure cannot be released, so the liquid continually evaporates – an illustration of the phenomenon known as Le Chatelier’s Principle. This evaporation is associated with a heat flow signal, which is related to the enthalpy of vaporization and the rate of vaporization of the liquid. Therefore, traditional heat capacity measurement techniques are inappropriate for measuring liquids, as the signal will be affected by the heat of vaporization.

Figure 2. Heat capacity testing of steel through melting.

How, then, do you measure the heat capacity of liquids? There are generally two methods: Firstly, you can machine a vessel with a long, thin tube to allow free expansion of the fluid and thus keep pressure constant but minimize surface area for evaporation and keep the evaporation out of the measurement area of the calorimeter (Figure 1). An example of the data that can be collected in this way is visible in Figure 2 above.

Figure 3. Figure from J. Chem. Thermodynamics 38 (2006) 1260–1268 illustrating the efficacy of encapsulation in measurement of the heat capacity of molten salts.

Another option you can encapsulate the liquid in a sealed vessel of constant or near-constant volume and instead measure the Cv, or heat capacity at constant volume. If the liquid has a low enough vapor pressure to be treated as incompressible, you can make the following assumption:

Cv ~ Cp

Common methods of this strategy include drop calorimetry for high temperature studies, or specialized single-use pressure cells for testing in standard pan-style calorimeters. An example of the type of data that can be collected via this encapsulation method is available in Figure 3, where a SETARAM Multi HTC Calvet-style high temperature drop calorimeter was used to generate test data on a liquid. Because of the relatively low vapor pressure of the liquids, the assumption holds and the Cv measurement can be treated as a Cp measurement.


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