Heat capacity thermodynamic analysis

The heat capacity of a substance is extremely important in thermodynamic analysis involving both the first and second laws. 

The determination of the heat capacity of a substance as a function of the temperature is by itself a very important application of DSC, because it may lead to values of the thermodynamic functions S%, //-" — //q, and Gy, mentioned in chapter 2. An example is the study of C6o carried out by Wunderlich and co-workers [271], The application of DSC in the area of molecular thermochemistry has been particularly important to investigate trends in transition metal-ligand bond dissociation enthalpies. The typical approach used in these studies, and its limitations, can be illustrated through the analysis of the reaction 12.27, carried out by Mortimer and co-workers [272] ... 

The glass transition temperature can be measured in a variety of ways (DSC, dynamic mechanical analysis, thermal mechanical analysis), not all of which yield the same value [3,8,9,24,29], This results from the kinetic, rather than thermodynamic, nature of the transition [40,41], Tg depends on the heating rate of the experiment and the thermal history of the specimen [3,8,9], Also, any molecular parameter affecting chain mobility effects the T% [3,8], Table 16.2 provides a summary of molecular parameters that influence the T. From the point of view of DSC measurements, an increase in heat capacity occurs at Tg due to the onset of these additional molecular motions, which shows up as an endothermic response with a shift in the baseline [9,24]. 

Hen egg-white lysozyme, lyophilized from aqueous solutions of different pH from pH 2.5 to 10.0 and then dissolved in water and in anhydrous glycerol, exhibits a cooperative conformational transition in both solvents occurring between 10 and 100°C (Burova, 2000). The thermal transition in glycerol is reversible and equilibrium follows the classical two-state mechanism. The transition enthalpies AHm in glycerol are substantially lower than in water, while transition temperatures Tm are similar to values in water, but follow similar pH dependences. The transition heat capacity increment ACp in glycerol does not depend on the pH and is 1.25 0.31 kj (mol K) 1 compared to 6.72 0.23 kj (mol K)-1 in water. Thermodynamic analysis of the calorimetric data reveals that the stability of the folded conformation of lysozyme in glycerol is similar to that in water at 20-80°C but exceeds it at lower and higher temperatures. 

Aside from the original assumption of a lumped analysis, thus far there have been no other assumptions or approximations to the model. The model relies completely on basic thermodynamic principles, a known cell performance R(I), and rigorous mathematical operations. To solve the model, we need to know the bulk mass and heat capacity of the cell, M and C, respectively the reactant supply flow rate (m = fuel flow + air flow) the inlet temperature and pressure and the change in stream composition due to the electrochemical reaction, AX, so that the change in enthalpy can be calculated the electrical load current, / and the inlet and exit temperatures, Tm and rout. 

Varna-Nair M and Wunderlich B, "Heat Capacity and other Thermodynamic Properties of Linear Macromolecules", X-Update of the ATHAS (i.e. Advanced Thermal Analysis) Data Bank, a computerized version of the data bank of heat capacities. 

An interesting aspect of the photoreaction of PYP is the similarity to the protein folding/unfolding reaction. Hellingwerf and his coworkers applied the transition state theory to the photoreaction of PYP and estimated the thermodynamic parameters, the entropy, enthalpy, and heat capacity changes of activation [29]. They also carried out thermodynamic analysis on the thermal denaturation of PYP. Consequently, they found that the heat capacity changes in the photoreaction are comparable to those in the unfolding... 

Finally, once E and H are determined by integration of (1.18.13) or via heat capacities, F and G may be found by the Gibbs-Helmholtz relation (1.18.33), thus closing the loop. The reader is well advised to ponder the methodology of thermodynamics, because it is through this general approach that the theory is particularly powerful in the analysis of phenomena. Other aspects of this structure will be pointed out in later sections. 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

Thermodynamic properties of imidazolium-based ionic liquids, such as densities, heat capacities, and enthalpies of fusion of [bmim] [PFg] and [bmim] [NTf2] have been determined and a critical analysis of the effect of impurities on the measured thermodynamic properties has been carried out <2006CED1856>. 

Roberts ( 1 1) surveyed the superconductive properties of the elements and recommended a critical temperature of 1.175 0.002 K for Al(cr). Since this temperature is so low, the effects of superconductivity on the thermodynamic functions are not considered. The entropy contribution due to superconductivity will be less than 0.002 J X mol . The data of Giauque and Meads (j ) and Downie and Martin (3) agree at temperatures up to 150 K but drift apart by 0.2 J X mol at 200 X and 0.17 J X mol at 300 K, with the Downie and Martin study being lower. The Takahashi (4, 5) study is even lower at 298 X. The high temperature heat capacity values are derived from the enthalpy study of Ditmars et al. (9). Their curve is intermediate between those derived from previous studies (4, 5, 6, 7, 8) and implies a flatter Cp curve near the melting point (in comparison to previous interpretations). Numerous other heat capacity and enthalpy studies are available but were omitted in this analysis. A detailed discussion of the Group IIIA metals (B, Al, and Ga) is in preparation by the JANAF staff. 

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