Which statement defines the heat capacity of a sample?

1.3.1 Calorimetry and calorimetric coefficients

3.4.4 Specific heat capacities

Specific heat capacity of solids and liquids (kJ kg−1 K−1)

Aluminium0.897Oil, machine1.676Aluminium bronze0.897Paraffin2.100Brass0.377Paraffin wax2.140Bronze0.343Petroleum2.140Cadmium0.235Phosphorus0.796Constantan0.410Platinum0.133Copper0.384Rubber2.010Ethanol2.940Salt, common0.880(ethyl alcohol)Sand0.796Glass: crown0.670Seawater3.940flint0.503Silica0.800Pyrex0.753Silicon0.737Gold0.129Silver0.236Graphite0.838Tin0.220Ice2.100Titanium0.523Iron: cast0.420Tungsten0.142pure0.447Turpentine1.760Kerosene2.100Uranium0.116Lead0.130Vanadium0.482Magnesia0.930Water4.196Magnesium1.030Water, heavy4.221Mercury0.138Wood (typical)2.0 toMolybdenum0.2723.0Nickel0.457Zinc0.388

Specific heat capacity of gases, gas constant and molecular weight (at normal pressure and temperature)

GasSpecific heats cp(kJ kg−1 K−1) cvγ=cpcvGas constant, R (kJ kg−1K−1)Molecular weight, MAir1.0050.7181.40.287128.96Ammonia2.1911.6631.320.52815.75Argon0.52340.31361.6680.208140Butane1.681.511.110.1758Carbon dioxide0.84570.65731.290.188944Carbon monoxide1.0410.74491.3980.296828Chlorine0.5110.3831.330.12865Ethane1.76681.49471.180.276530Helium5.2343.15681.6592.0774Hydrogen14.32310.19651.4054.1242Hydrogen chloride0.8130.5831.400.23036.15Methane2.23161.71241.300.518316Nitrogen1.0400.74361.400.296828Nitrous oxide0.9280.7081.310.22037.8Oxygen0.91820.65861.3940.259832Propane1.69151.5071.120.188644Sulphur dioxide0.64480.51501.250.129864

2.31.2.2.1 Linear scan

The most common mode of operation in DSC is heating or cooling at constant rates. The primary outcome of such an experiment is a plot of the heat flow rate versus time. If the temperature of the sample position is known, then data can also be represented as the heat flow rate versus temperature. (One should know that generally a temperature near the sample is measured and not the sample temperature itself.) Figure 2 shows a typical example.

From the heat flow rate curves shown in Figure 2, specific heat capacity cp(T) can be obtained as follows

[8]cp(T)=cp,sapphire(T)msapphireβmsampleβΦsample(T)−Φempty(T)Φsapphire(T)−Φempty(T)=K(T)Φsample(T)−Φempty(T)msampleβ

with

K(T)=cp,sapphire(T)msapphireβΦsapphire(T)−Φempty(T)

where K(T) is a temperature-dependent calibration factor, which can be stored for future use. Here, all measurements are collected at the same scanning rate. The isotherms at the beginning and the end of the scan are used to correct for small changes in heat losses between empty, sapphire, and sample measurements by aligning these parts of the curves. Small changes in losses are unavoidable, because the thermal properties, such as thermal conductivity, of the samples are different. On the other hand, inspection of the heat flow rate at the isotherms allows us to check the correct placement and thermal contacts of all the parts of the measuring system moved during sample changes. Especially the high temperature isotherm should not vary too much between successive measurements.

Specific heat capacity is the most useful quantity available from DSC because it is directly related to sample properties and, according to eqns [1]–[5], directly linked to stability and order. Nevertheless, often only heat flow rate, as obtained from a single sample measurement, is presented. There are several reasons why this should not be presented:

Each heat flow rate graph needs indication of endothermic or exothermic direction because plot direction is not standardized.

Curves measured at different scanning rates are not easy to compare.

If not divided by the sample mass, curves for different samples cannot be compared.

If empty pan measurements are not subtracted, traces may be curved and baseline construction for peak integration may be difficult.

If the heat flow rate calibration factor K(T) is temperature dependent, the obtained heat of fusions and other such parameters may be erroneous.

Performing corrections (3)–(5) yields specific heat capacity as given by eqn [8]. Because most of the DSC software packages include determination of specific heat capacity according to eqn [8], it is strongly recommended to determine specific heat capacity and not to present heat flow rate curves. Even though presenting specific heat capacity data is preferable, there may be reasons not to do so. The normalization of the heat flow rate curve by the scan rate and the sample mass may result in ‘pseudo cp measurements’, which can be used to determine temperature-dependent crystallinity and other quantities as shown in Reference 8. But there is another very strong argument in favor of presenting specific heat capacity rather than ‘pseudo cp’ or heat flow rate. For more than 200 polymers, specific heat capacity data from 0 to 1000 K are available from the ATHAS Data Bank (ATHAS-DB).36 The data can be used for a comparison of measured data in the glassy or liquid state with the recommended values. This allows an easy check of the quality of the measured data, although one should keep in mind that the accuracy of the recommended data bank data is only about 6%. Figure 3 shows specific heat capacity (according to eqn [8]) calculated from the data shown in Figure 2.

A more detailed discussion of the evaluation of the curves shown in Figure 3 is given in Reference 35.

Besides scan measurements on heating, DSC allows cooling in a wide range of cooling rates. Depending on the instrument and the temperature range of interest, cooling rates up to 750 K min−1 may be reached (HyperDSC™ PerkinElmer, USA).20,37–39 But generally the temperature range for controlled cooling at the highest rates is limited. Measurements performed in a wide range of heating or cooling rates require an optimization of the experimental conditions. The sample mass should scale inversely with the scanning rate. At low rates when the thermal lag is not an issue, the sample mass should be high to have a good signal-to-noise ratio. At high rates when signals are large, the sample mass should be small to minimize the heat flow to the sample, which is proportional to the rate and causes the thermal lag. Problems related to thermal lag, temperature calibration, and reproducibility in fast scanning DSC experiments were intensively studied and adequate recommendations were made.37,40,41 Figure 4 shows cooling curves in the crystallization range of low-density polyethylene (PE). At rates higher than 200 K min−1, controlled cooling down to 100 °C was not possible because of the limited cooling power of the used mechanical intercooler. If higher cooling rates are needed, liquid nitrogen has to be used. For the lower scanning rates shown in Figure 4, the sample mass must be large enough to ensure a good signal-to-noise ratio. For higher rates, the large sample (4 mg) causes some thermal lag, as discussed in the textbooks and References 37, 40, and 42. It is also seen in the broadening of the crystallization peak at 20 K min−1 compared with the 0.4 mg sample at the same cooling rate. Data as shown in Figure 4 provide information about crystallization kinetics and can be analyzed by using different kinetic models.43–48

As shown in Figure 4, DSC has a broad dynamic range that can be extended at least by 1 order of magnitude toward lower rates; in this way it covers 3 orders of magnitude. An extension by several orders of magnitude toward higher rates is discussed in Section 2.31.3.2. The possibility of cooling a sample reasonably fast allows us to study the structure formation in far-from-equilibrium situations such as ‘quasi’-isothermal crystallization at deep undercooling.

5.2.3 Thermal Performance

When selecting materials for strip and contact wire, the thermal performance of the material will also be considered. The pantograph and overhead contact line system works in a strong current environment. Joule heat, arc heat, and friction heat caused by current flowing through the pantograph and overhead contact line contact point will lead to temperature rise of strip and contact wire. Excessive temperature rise will bring negative impact to performance of strip and contact wire material.

Specific heat capacity, thermal expansion, heat conduction, thermal radiation, and thermoelectric force are all aspects of thermal performance.

Specific Heat Capacity of Dry Virgin Wood

The specific heat capacity of dry virgin wood as a function of temperature has been determined by Atreya (1983) for a temperature range from 0°C to 140°C. Fredlund (1988) has assumed that the relationship is valid even for temperatures above 140°C. The expression for the specific heat capacity of dry virgin wood as a linear function of temperature is given by

(4.11.37)Cpw=Cpw,o+Cpw,mTs

where Cpw,o = 1.4 kJ kg−1 K−1 and Cpw,m = 3.0 × 10−4 kJ kg−1 K−2. It is nonetheless noted that a constant specific heat capacity for dry virgin wood independent of temperature has also been assumed by a number of investigators such as Kanury and Blackshear (1970a), Kung (1972), Kung and Kalelkar (1973), Chan et al. (1985), Alves and Figueiredo (1989), Bonnefoy et al. (1993), and Di Blasi (1994a). Values ranging from 1.386 kJ kg−1 K−1 to 2.52 kJ kg−1 K−1 with most of them larger than 2.0 kJ kg−1 K−1 have been typically employed.

What statement defines the heat capacity of sample?

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