Specific Heat Capacity Measurement

Heat capacity is an intrinsic physical property that determines the level of heat required to change a substance’s temperature by a predetermined amount. Specific heat capacity refers to a material’s heat capacity divided by mass, which governs the amount of energy needed to raise the temperature of one gram by one degree Celsius (or one Kelvin). This is a useful physical quantity for a range of objectives, e.g. to optimize technical processes or assess thermal risk. Specific heat capacity units are usually joules per gram-kelvin, or J/gK.

To calculate a material's heat capacity, the following equation applies:

c_p  =  q / (m  ∙ ∆ T)

Where c_p  =  specific heat, m = mass in grams, q  =   the energy lost or gained, and ∆T = change in temperature

Topics overview:

• Specific Heat Capacity as a Function of Temperature
• Specific Heat Values of Common Substances
• Differential Scanning Calorimetry (DSC)
• Standards
• STARe Software – Six Methods for Determining Specific Heat Capacity
• Adjustment and Calibration
• Tips and Hints
• FAQs

A substance’s specific heat capacity is a function of temperature. As shown in the diagram, the specific heat capacity of sapphire increases with temperature, which is typical for most substances. Water has an exceptionally high specific heat capacity of about 4 J/gK and exhibits anomalous behavior with a minimum specific heat capacity of about 35 °C.

To learn more, view our Webinar on Specific Heat Capacity Determination by DSC:

Different substances respond to heat in different ways. A common real-world example of this would be metal objects left in direct sunlight compared to an equal amount of water in the same conditions. The metal becomes very hot rapidly, while the water does not. In other words, water has a high heat capacity.

The values for solids and liquids range from 0.1 to 5 J/gK. Most substances’ specific heat increases with increasing temperature; the measurement is therefore often performed over a relatively large temperature range. Some examples at 25 °C are shown in the table.

A detailed explanation of specific heat capacity can be found in our Thermal Analysis in Practice handbook.

Differential scanning calorimetry (DSC) is a versatile measurement technique deployed in many analytical, QC and R&D laboratories. It is used to measure the heat flow produced in a sample when it is either heated, cooled, or held isothermally at a constant temperature.

DSC is a popular route for determining specific heat capacity due to its ease of use, short measurement times, and an attainable accuracy of up to ± 2% (depending on the specific method used; see next section).

Conventional DSC typically covers measurements of up to 700 °C. But great results can also be obtained above 700 °C using a METTLER TOLEDO TGA/DSC.

In this example of polystyrene, the heat flow curve is directly proportional to the specific heat capacity in the measured temperature range.

A standard is used to provide a comparative norm that is both widely recognized and widely applied. This ensures that production or testing processes are uniformly comparable to other procedures. It is a good way to ensure reliability of test results. Standards can – where available – replace method validation in analysis, which is required for quality assurance, accreditation, or approval. Today, standardization in thermal analysis is carried out by many national and international organizations, such as ISO, ASTM, DIN and CEN. In DSC, the specific heat capacity can be calculated from the heat flow curve. The results are evaluated according to Standards such as ISO 11357-1, ISO 11357-4, DIN 53765, DIN 51007-1 or ASTM E1269.

Several different methods can be used to determine specific heat capacity from the DSC heat flow curve. METTLER TOLEDO's STAR^e software supports the following methods:

The so-called Direct and Sapphire methods are performed using a conventional DSC instrument and a linear temperature program. With traditional DSC, there is only one heat flow signal (Total). The heat capacity, however, consists of two components: the sensible heat capacity (reversing heat flow) and the latent heat capacity (non-reversing heat flow):

c_p = c_{p, sensible} + c_{p, latent}

The latent heat capacity is related to physical or chemical transitions such as melting, crystallization, or chemical reactions. Such thermal events are observed on a DSC curve as endothermic or exothermic peaks. Consequently, the latent heat capacity is positive for endothermic events and negative for exothermic events.

The sensible heat capacity is related to the amount of heat absorbed due to rearrangements and overall movement of the molecules. This component is positive. The DSC curve in the diagram shows that the sensible heat capacity is directly related to the measured heat flow provided no thermal events occur. In many transitions, the sensible heat capacity defines the baseline of the related peak.

Temperature-modulated DSC (TMDSC) differs from conventional DSC in that it allows the total heat flow to be separated into reversing and non-reversing components. This is important for providing accurate cp data where different thermal effects overlap, e.g. glass transition (reversing heat flow component) and enthalpy relaxation (non-reversing heat flow component).

The temperature programs used in temperature-modulated DSC are more complex compared with those employed in conventional DSC experiments. METTLER TOLEDO offers three different techniques for performing temperature-modulated DSC measurements. Their most important features are summarized below.

The temperature should be calibrated (checked) in the usable measurement range as the specific heat is a function of temperature. Adjustments should be made if necessary. In DSC, the most important sources of non-reproducibility are the heat transfer between the sensor and crucible, and between the crucible and the sample. The resulting isothermal drift can be corrected by applying the method proposed in the DIN 51007 standard.

Accurate heat capacity data is achievable when the DSC is properly adjusted using certified reference substances, for example from LGC (UK), NIST (USA) or PTB (Germany). If the direct method is used, the heat flow must be properly adjusted for the desired temperature range and crucibles.

Thermal analysis calibration and the adjustment of heat flow and temperature is further explained in the following resources from METTLER TOLEDO:

The measurement of good quality quantitative heat capacity data is a challenging task for DSC. Nevertheless, it is a common and useful technique because of the availability of DSC instruments, simple sample preparation, relatively short measurement time, good accuracy, and easy evaluation using commercial software.

Tips and hints for obtaining good data include:

• Stabilize the instrument before the measurement.
• Never use the first measurement after switching on the instrument.
• Check the reproducibility using repeated measurements.
• Averaging different measurements improves the accuracy.
• Use blank-curve subtraction in the method (exception is TOPEM).
• Place the crucibles accurately on the sensor.
• Use the same crucibles for all three measurements. If this is not possible, use crucibles with only a small difference in mass, <10 µg, as proposed in the ASTM standard.
• For crucibles with larger differences, use crucible mass correction.
• Recommended: 40 µL crucible; sample mass: 10 to 20 mg for organic materials.
• Apply heating rates in the range of 5 to 10 K/min.
• Weigh the sample after the measurement. A significant mass loss reduces the reliability of your c_p data. Mass loss is automatically recorded in a TGA/DSC.
• For higher accuracy, especially when using non-modulated methods:
  • Use a larger sample mass, C_p (sample) » C_p (standard)
  • Ensure good thermal contact between the sample and the crucible