Measurement of heat capacity

Measurements of heat capacity jumps at the glass-transition temperatures, Tg, in the matrix material and the composites, carried out from heat-capacity experiments, were intimately related to the extent of the mesophase thickness. Further accurate measurements of the overall longitudinal elastic modulus of the composites and the... 

Spin-state transitions have been studied by the application of numerous physical techniques such as the measurement of magnetic susceptibility, optical and vibrational spectroscopy, the Fe-Mbssbauer effect, EPR, NMR, and EXAFS spectroscopy, the measurement of heat capacity, and others. Most of these studies have been adequately reviewed. The somewhat older surveys [3, 19] cover the complete field of spin-state transitions. Several more recent review articles [20, 21, 22, 23, 24, 25] have been devoted exclusively to spin-state transitions in compounds of iron(II). Two reviews [26, 27] have considered inter alia the available theoretical models of spin-state transitions. Of particular interest is the determination of the X-ray crystal structures of spin transition compounds at two or more temperatures thus approaching the structures of the pure HS and LS electronic isomers. A recent survey [6] concentrates particularly on these studies. 

The importance of temperature-controlled scanning calorimetry for measurements of heat capacity and of scanning transitiometry for simultaneous caloric and pVT analysis has been demonstrated for polymorphic systems [9]. This approach was used to study an enantiotropic system characterized by multiphase (and hindered) transitions, the role of heat capacity as a means to understand homogeneous nucleation, and the creation of (p, T) phase diagrams. The methodology was shown to possess distinct advantages over the more commonly used combination of characterization techniques. 

A lock-in present in a bridge for cryogenics has usually a reference at frequencies between 10 and 1000 Hz. Electrical power delivered to the resistive sensors are between 10-16 -7-10-14 W. The maximum measuring rates are usually less than 10 readings for second. The latter fact poses severe limits in dynamic measurements as, e.g., the measurement of heat capacity (see Section 12.6.4). 

We saw in Section 3.2 that the knowledge of low-temperature specific heat is extremely important to understand the physical properties of a solid. The measurements of heat capacity are not, conceptually, more difficult than those of thermal conductivity. On the contrary, some problems such as the anisotropy of materials are not present, and the shape of the sample to be measured is usually unimportant. Nevertheless, from a technical... 

Fig. 12.1. Scheme of the main elements present in a measurement of heat capacity. 

We shall report hereafter three examples of measurement of heat capacity the first (of a crystal) with a negligible addendum the second (of a polymer) with a heavy addendum the third is the measurement of the carrier specific heat of a heavily doped semiconductor. 

In a classical low-temperature measurement of heat capacity, the sample is placed (usually glued) onto a low heat capacity support which is thermally linked to the thermal bath by a thermal conductance (see Fig. 12.1). 

Figure 12.4 shows an example of experimental set up for a classical measurement of heat capacity the sample is glued onto a thin Si support slab. The thermometer is a doped silicon chip and the heater is made by a ( 60 nm thick) gold deposition pattern. Electrical wiring to the connect terminals are of superconductor (NbTi). The thermal conductance to the thermal bath (i.e. mixing chamber of a dilution refrigerator) is made with thin nylon thread. The Si slab, the thermometer and the heater represent the addendum whose heat... 

Fig. 12.4. Example of experimental set up for a classical measurement of heat capacity.

Figure 12.6 The measurement of heat capacity by DSC, under dynamic operating conditions.

The isothermal and isoperibol calorimeters are well suited to measuring heat contents from which heat capacities may be subsequently derived, while the adiabatic and heat-flow calorimeters are best suited to the direct measurement of heat capacities and enthalpies of transformation. 

Diedrich, A. and Gmehling, J., Measurement of heat capacities of ionic liquids by differential scanning calorimetry. Fluid Phase Equilib., 244, 68, 2006. 

Frequently, the context of a particular problem requires us to consider the limiting behaviour of a function as the value of the independent variable approaches zero. For example, consider the physical measurement of heat capacity at absolute zero. Since it is impossible to achieve absolute zero in the laboratory, a natural way to approach the problem would be to obtain measurements of the property at increasingly lower temperatures. If, as the temperature is reduced, the corresponding measurements approach some value m, then it may be assumed that the measurement of the property (in this case, heat capacity) at absolute zero is also m, so long as the specific heat function is continuous in the region of study. We say in this case that the limiting value of the heat capacity,... 

Another claim for an apparent mean-field behavior of ionic fluids came from measurements of heat capacities. The weak Ising-like divergences of the heat capacities Cv of the pure solvent and CPtx of mixtures should vanish in the mean-field case (cf. Table I). The divergence of Cv is firmly established for pure water. Accurate experiments for aqueous solutions of NaCl... 

We won t describe how the entropy of a substance is determined, except to note that two approaches are available (1) calculations based on Boltzmann s formula and (2) experimental measurements of heat capacities (Section 8.8) down to very low temperatures. Suffice it to say that standard molar entropies, denoted by S°, are known for many substances. 

Thermal analysis techniques are designed to measure the above mentioned transitions both by measurements of heat capacity and mechanical modulus (stiffness). 

It should be noted that experimental measurements of heat capacity at T > T2, as a rule, give the values decreased in a gradual manner up to zero (Fig. 1), but not nonzero heat capacity, that is caused by the existence of short-range order in crystal or by correlation in substitution of lattice sites by < > i. [Pg.224]

Abstract. One more method of study of the short-range order kinetics of H-atoms over tetrahedral interstices in lutetium (Lu) is proposed. It can be realized by the using of available data of measurements of heat capacity for h.c.p.-Lu-H interstitial solid solutions during the isothermal annealing. Comparison of estimated-parameters data from heat capacity and residual electrical-resistivity measurements is performed. It is shown that kinetics of heat capacity and residual resistivity at low temperatures is caused by the unique nature (short-range order relaxation) and can be described by two relaxation times at least. 

Measurements of heat capacities at very low temperatures provide data for the calculation from Eq. (5.11) of entropy changes down to 0 K. When these calculations are made for different crystalline forms of the same chemical species, the entropy at 0 K appears to be the same for all forms. When the form is noncrystalline, e.g., amorphous or glassy, calculations show that the entropy of the more random form is greater than that of the crystalline form. Such calculations, which are summarized elsewhere,t lead to the postulate that the absolute entropy is zero for all perfect crystalline substances at absolute zero temperature. While the essential ideas were advanced by Nemst and Planck at the beginning of the twentieth century, more recent studies at very low temperatures have increased our confidence in this postulate, which is now accepted as the third law. 

It will be of interest to consider the thermal measurements since this area has been one of major activity in recent years. It is well known that the measurement of heat capacities at low temperatures provides a powerful tool for studying many solid-state phenomena, including the energy separation degeneracy of low lying energy levels in crystalline substances. The advantage of low temperature heat capacity measure-... 

Measurement of heat capacity and heat flow in a single experiment... 

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