Heat capacity volume

Several material properties exhibit a distinct change over the range of Tg. These properties can be classified into three major categories—thermodynamic quantities (i.e., enthalpy, heat capacity, volume, and thermal expansion coefficient), molecular dynamics quantities (i.e., rotational and translational mobility), and physicochemical properties (i.e., viscosity, viscoelastic proprieties, dielectric constant). Figure 34 schematically illustrates changes in selected material properties (free volume, thermal expansion coefficient, enthalpy, heat capacity, viscosity, and dielectric constant) as functions of temperature over the range of Tg. A number of analytical methods can be used to monitor these and other property changes and... 

Here Cp, a and are the heat capacity, volume thermal expansivity and compressibility respectively. First-order transitions involving discontinuous changes in entropy and volume are depicted in Fig. 4.1. In this figure curves G Gu represent variations in free energies of phases I and II respectively, while // Hu and F, represent variations in... 

The most common applications of DSC are to the melting process which, in principle, contains information on both the quality (temperature) and the quantity (peak area) of crystallinity in a polymer [3]. The property changes at Tm are often far more dramatic than those at Tg, particularly if the polymer is highly crystalline. These changes are characteristic of a thermodynamic first-order transition and include a heat of fusion and discontinuous changes in heat capacity, volume or density, refractive index, birefringence, and transparency [3,8], All of these may be used to determine Tm [8],... 

Activities of Electrolytes.—When the solute is an electrolyte, the standard states for the ions are chosen, in the manner previously indicated, as a hypothetical ideal solution of unit activity in this solution the thermodynamic properties of the solute, e.g., the partial molal heat content, heat capacity, volume, etc., will be those of a real solution at infinite dilution, i.e., when it behaves ideally. With this definition of the standard state the activity of an ion becomes equal to its concentration at infinite dilution. 

The scope of the present work remains essentially that of Special Publication 454, The general aim 1 to assist the reader in locating those publications which contain thermochemical data which can best serve his needs. Equilibrium data Is taken in its most general sense and includes equilibrium constants, enthalpies, entropies, heat capacities, volumes, and partial molar and excess property data. To a much lesser extent, transport and other properties have been included. Unfortunately, much of the data on biochemical systems is scattered throughout much of the literature and there is a need for... 

This series of papers contains an extensive array of correlated data on aqueous electrolyte solutions, much of It having been calculated using the system of equations given In paper I In this series. The contents of these papers have been summarized by Pitzer In a chapter in the book edited by Pytkowicz (see Item [123]). The data Include activity and osmotic coefficients, relative apparent molar enthalpies and heat capacities, excess Gibbs energies, entropies, heat capacities, volumes, and some equilibrium constants and enthalpies. Systems of Interest Include both binary solutions and multi-component mixtures. While most of the data pertain to 25 °C, the papers on sodium chloride, calcium chloride, and sodium carbonate cover the data at the temperatures for which experiments have been performed. Also see Items [48], [104], and [124]. 

The glass transition point is typically not sharp and may take place over a range of more than 10 C. You should think of the glass transition more as a change in physical properties (specific heat capacity, volume) than a thermodynamic phase transition. 7 can be determined by two main methods Differential scanning calorimetry (see Chapter 2 for more... 

Typical behavior of heat capacity, volume, and entropy of a pure substance as a function of temperature given that the system undergoes a first-order phase transition (left) versus a second-order phase transition (right) at the temperature T. ... 

Noyes AA, Kato Y, Sosman RB (1910) The hydrolysis of ammonium acetate and the ionization of water at high temperatures. J Am Chem Soc 32 159-178 Oscarson JL, Gillespie SE, Christensen JJ, Izatt RM, Brown PR (1988) Thermodynamic quantities for the interaction of H and Na with C2H3O2 and Cl in aqueous solution from 275 to 320 °C. J Solution Chem 17 865-885 Ostiguy C, Ahluwalia JC, Perron G, Desnoyers JE (1977) Heat capacities, volumes, and expansibilities of sodium phenyl carboxylates in water. Can J Chem 55 3368-3370 Palma M, Morel J-P (1976) Viscosite des solutions aqueuses d acides carboxyliques aliphatiques et des carboxylates de potassium a 25 °C. J Chim Phys 73 643-649 Palmer DA, Drummond SE (1986) Thermal decarboxylation of acetate. Part I. The kinetics and mechanism of reaction in aqueous solution. Geochim Cosmochim Acta 50 813-823... 

DeLisi, R., Milioto, S., Triolo, R. Heat capacities, volumes and solubilities of pentanol in aqueous alkyltrimethylammonium bromides. J. Solution Chem. 1988, 77(7), 673-696. 

As one raises the temperature of the system along a particular path, one may define a heat capacity C = D p th/dT. (The tenn heat capacity is almost as unfortunate a name as the obsolescent heat content for// alas, no alternative exists.) However several such paths define state functions, e.g. equation (A2.1.28) and equation (A2.1.29). Thus we can define the heat capacity at constant volume Cy and the heat capacity at constant pressure as... 

In typical metals, both electrons and phonons contribute to the heat capacity at constant volume. The temperaPire-dependent expression... 

Differentiating this with respect to J = - TJ yields a heat capacity at constant volume,... 

However, the discovery in 1962 by Voronel and coworkers [H] that the constant-volume heat capacity of argon showed a weak divergence at the critical point, had a major impact on uniting fluid criticality widi that of other systems. They thought the divergence was logaritlnnic, but it is not quite that weak, satisfying equation (A2.5.21) with an exponent a now known to be about 0.11. The equation applies both above and... 

The heat capacity at constant volume Cj is defined from the relations... 

Except for gases, it is very difficult to detennine Cy. For a solid or liquid the pressure developed in keeping the volume constant when the temperature is changed by a significant amount would require a vessel so massive that most of the total heat capacity would be that of the container. It is much easier to measure the difference... 

Magee J W, Blanco J C and Deal R J 1998 High-temperature adiabatic calorimeter for constant-volume heat capacity of compressed gases and liquids J. Res. Natl Inst. Stand. Technol. 103 63... 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

A number of properties can be computed from various chemical descriptors. These include physical properties, such as surface area, volume, molecular weight, ovality, and moments of inertia. Chemical properties available include boiling point, melting point, critical variables, Henry s law constant, heat capacity, log P, refractivity, and solubility. 

Note This method of temperature regulation does not give all properties of the canonical ensemble. In particular, you cannot calculate Cy, heat capacity at constant volume. 

Equations for vapor pressure, liquid volume, saturated liquid density, liquid viscosity, heat capacity, and saturated Hquid surface tension are described in Refs. 13, 15, and 16. 

Equations for Hadacher vapor pressure, vapor heat capacity, saturated Hquid volume, and Hquid viscosity can be found in Refs. 34 and 41. 

Fig. 5. Heat capacities at ( ) constant piessuie, and at (----) constant volume, on the 220-MPa (31,900-psi) isobai. To convert kj to kcal, divide...

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