Heat capacity direct measurement

Calorimeters are instruments used for the direct measurement of heat quantities including heat production rates and heat capacities. Different measurement principles are employed and a very large number of calorimetric designs have been described since the first calorimetric experiments were reported more than 200 years ago. The amount of heat evolved in a chemical reaction is proportional to the amount of material taking part in the reaction and the heat production rate the thermal power, is proportional to the rate of the reaction. Calorimeters can therefore be employed as quantitative analytical instruments and in kinetic investigations, in addition to their use as thermodynamic instruments. Important uses of calorimeters in the medical field are at present in research on the biochemical level and in studies of living cellular systems. Such investigations are often linked to clinical applications but, so far, calorimetric techniques have hardly reached a state where one may call them clinical (analytical) instruments. ... 

The adiabatic expansion method is not the best method of determining the heat capacity ratio. Much better methods are based on measurements of the velocity of sound in gases. One such method, described in Part B of this experiment, consists of measuring the wavelength of sound of an accurately known frequency by measuring the distance between nodes in a sonic resonance set up in a Kundt s tube. Methods also exist for determining the heat capacities directly, although the measurements are not easy. 

Since DSC measures heat capacity directly, rapidly, and accurately, it is an ideal technique for the determination of Tg. The calorimeter accepts polymers in any form (powder, pellet, or fibre), and only a few milligrams of sample are required. Samples are placed in a standard aluminium sample pan, crimped by a crimping press to ensure good thermal contact, placed in the sample holder, and scanned at an appropriate rate over the temperature range of interest. 

Differential scanning calorimetry measures heat capacity directly, rapidly, and accurately, so it is an ideal technique for the determination of the glass transition temperature, 7. ... 

The heat capacity is, as shown in Section II.l.l defined as the increase in heat content if the tanperature of the sample is increased by one degree Celsius. In the following discussion, the heat capacity is measured under the condition of constant pressure. Heat capacities at constant volume, which are rntwe amenable to theoretical interpretation are not determined directly, but are calculated using the thermo-d5mamic relationship (see Eq. 11.25). 

Because a lot is known about the particular behavior of iso-thermally crystallized iPS, we can constmct baseline heat capacity as described and end up with reasonable data in Figure 30. Already for nonisothermally crystallized iPS, this procedure does not work, because we do not know at what temperature the RAF devitrifies. Obviously it would be best to measure baseline heat capacity directly. Temperature-modulated calorimetry may provide a tool for such measurements if reversing melting can be excluded. As discussed in Section 2.31.2.2.3, temperature modulation at sufifidendy high frequencies offers the possibility of a direct measurement of baseline heat capacity. A first attempt... 

Whereas heat capacity is a measure of energy, thermal diffusivity is a measure of the rate at which energy is transmitted through a given plastic. It relates directly to processability. In contrast, metals have values hundreds of times larger than those of plastics. Thermal diffusivity determines plastics rate of change with time. Although this function depends on thermal conductivity, specific heat at constant pressure, and density, all of which vary with temperature, thermal diffusivity is relatively constant. 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

Texturization is not measured directly but is inferred from the degree of denaturation or decrease of solubility of proteins. The quantities are determined by the difference in rates of moisture uptake between the native protein and the texturized protein (Kilara, 1984), or by a dyebinding assay (Bradford, 1976). Protein denaturation may be measured by determining changes in heat capacity, but it is more practical to measure the amount of insoluble fractions and differences in solubility after physical treatment (Kilara, 1984). The different rates of water absorption are presumed to relate to the degree of texturization as texturized proteins absorb water at different rates. The insolubility test for denaturation is therefore sometimes used as substitute for direct measurement of texturization. Protein solubility is affected by surface hydrophobicity, which is directly related to the extent of protein-protein interactions, an intrinsic property of the denatured state of the proteins (Damodaran, 1989 Vojdani, 1996). 

Although heat capacities have been reported for the butoxyethanol/ water system, excess enthalpies that could be compared directly with our results apparently have not been measured (12). 

Experimental Methods In Differential thermal analysis (DTA) the sample and an inert reference substance, undergoing no thermal transition in the temperature range under study are heated at the same rate. The temperature difference between sample and reference is measured and plotted as a function of sample temperature. The temperature difference is finite only when heat is being evolved or absorbed because of exothermic or endothermic activity in the sample, or when the heat capacity of the sample changes abruptly. As the temperature difference is directly proportional to the heat capacity so the curves are similar to specific heat curves, but are inverted because, by convention, heat evolution is registered as an upward peak and heat absorption as a downward peak. 

From classic thermodynamics alone, it is impossible to predict numeric values for heat capacities these quantities are determined experimentally from calorimetric measurements. With the aid of statistical thermodynamics, however, it is possible to calculate heat capacities from spectroscopic data instead of from direct calorimetric measurements. Even with spectroscopic information, however, it is convenient to replace the complex statistical thermodynamic equations that describe the dependence of heat capacity on temperature with empirical equations of simple form [15]. Many expressions have been used for the molar heat capacity, and they have been discussed in detail by Frenkel et al. [4]. We will use the expression... 

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. 

Heat contents can be measured accurately by a number of techniques based on a drop method. This involves heating the sample to a high temperature and dropping it directly into a calorimeter held at a lower temperature. The calorimeter then measures the heat evolved while the sample cools to the temperature of the calorimeter. The temperature at which the sample is initially heated is varied and a plot of Ht — 298.15 vs temperature is drawn (Fig. 4.1). Heat capacities can then be calculated using Eq. (3.9). A popular calorimeter for this is the diphenyl ether calorimeter (Hultgren et al. 1958, Davies and Pritchard 1972) but its temperature range is limited below about 1050 K. 

Flame temperatures can be measured directly, using special high-temperature optical methods. They can also be calculated (estimated) using heat of reaction data and thermochemical values for heat of fusion and vaporization, heat capacity, and transition temperatures. Calculated values tend to be higher than the actual experimental results, due to heat loss to the surroundings as well as the endothermic decomposition of some of the reaction products. Details regarding these calculations, with several examples, have been published [5]. 

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

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