The Thermal Properties of Solids

When a solid is heated, the heat is transferred throughout its mass by conduction. the heat energy passes from one part of the solid to another without the solid undergoing any mass changes. Heat conduction is the flow of energy from a spot of higher temperature to one of lower 

Temperature changes also cause dimensional changes in materials. When a material is heated or cooled, its length changes by an amount pro- 

TABLE 101a Thermal Properties of Some Archaeological Materials 

Chemical Effects of Temperature. Changes in temperature also affect the chemical properties of materials. The rate at which most chemical reactions take place, for example, is roughly doubled when the temperature of the reactants increases by 10°C. Consequently, any increase in temperature intensifies the rate at which most materials react with substances in the environment such as oxygen, water, and atmospheric and soil pollutants, and hastens their chemical degradation. 

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The theory of Debye is certainly the most complete and successful attempt to represent the thermal properties of solids which has yet been made by the aid of the theory of ergon ic distribution. 

The concept of quantization enabled physicists to solve problems that nineteenth-century physics could not. One of these involved the thermal properties of solids when they are heated to incandescence. The other involved the induction of electrical current in metals when they are exposed to only specific frequencies of electromagnetic radiation. 

The Thermal Properties of Solids, H. J. Goldsmid. 1.35 Microwave Spectroscopy, Walter Gordy, William V. Smith, and Ralph F. Trambarulo. 3.00... 

For the thermal properties of solids, Einstein developed an equation that could predict the heat capacity of solids in 1907. This model was then refined by Debye in 1912. Both models predict a temperature dependence of the heat capacity. At... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

PET, PTT, and PBT have similar molecular structure and general properties and find similar applications as engineering thermoplastic polymers in fibers, films, and solid-state molding resins. PEN is significantly superior in terms of thermal and mechanical resistance and barrier properties. The thermal properties of aromatic-aliphatic polyesters are summarized in Table 2.6 and are discussed above (Section 2.2.1.1). 

In contrast to the strong effect of gas properties, it has been found that the thermal properties of the solid particles have relatively small effect on the heat transfer coefficient in bubbling fluidized beds. This appears to be counter-intuitive since much of the thermal transport process at the submerged heat transfer surface is presumed to be associated with contact between solid particles and the heat transfer surface. Nevertheless, experimental measurements such as those of Ziegler et al. (1964) indicate that the heat transfer coefficient was essentially independent of particle thermal conductivity and varied only mildly with particle heat capacity. These investigators measured heat transfer coefficients in bubbling fluidized beds of different metallic particles which had essentially the same solid density but varied in thermal conductivity by a factor of nine and in heat capacity by a factor of two. 

A large number of techniques have been used to investigate the thermodynamic properties of solids, and in this section an overview is given that covers all the major experimental methods. Most of these techniques have been treated in specialized reviews and references to these are given. This section will focus on the main principles of the different techniques, the main precautions to be taken and the main sources of possible systematic errors. The experimental methods are rather well developed and the main problem is to apply the different techniques to systems with various chemical and physical properties. For example, the thermal stability of the material to be studied may restrict the experimental approach to be used. 

The forward search starts from the name of a chemical compound, proceeds to finding its molecular structure, and then its physical and chemical properties, such as the boiling point, melting point, density, etcetera, in a handbook. Many databases for single compounds are also organized by classes and families of similar structures. Fluid solutions represent the next level of complexity. For the most important fluids, such as water, air, and some refrigerants, we can find extensive tables for the thermal properties of mixtures. For complex fluids, such as paint and emulsion, which are difficult to characterize and to reproduce, specialized books and journals should be consulted. The properties of some crystalline solids can be found, but usually not for multicrystal composite and amorphous solids. 

The thermal properties of polymers include their behavior during heating from the solid amorphous (glassy) or crystalline to the liquid (molten) state, but also their chemical and mechanical stability in the entire range of application. 

Of the three general categories of transport processes, heat transport gets the most attention for several reasons. First, unlike momentum transfer, it occurs in both the liquid and solid states of a material. Second, it is important not only in the processing and production of materials, but in their application and use. Ultimately, the thermal properties of a material may be the most influential design parameters in selecting a material for a specific application. In the description of heat transport properties, let us limit ourselves to conduction as the primary means of transfer, while recognizing that for some processes, convection or radiation may play a more important role. Finally, we will limit the discussion here to theoretical and empirical correlations and trends in heat transport properties. Tabulated values of thermal conductivities for a variety of materials can be found in Appendix 5. 

From these examples, it is clear that the amplitude of the thermal motion transverse to the bonds will affect the thermal properties of the solid, but in ways that depend on details of the particular structure. It is therefore impossible to provide a universal model for the effects of the transverse thermal motion, the combinations of thermal expansion and thermal contraction must be considered individually for each structure. For most materials the combination results in a net thermal expansion, but there are a few compounds that show a net thermal contraction in one or more directions (Evans 1999). 

Lightfoot (L5, L6) considered the solidification of a semi-infinite steel mass in contact with a semi-infinite steel mold, where the thermal properties of the phases were taken to be identical. In a later paper, (L7) different thermal constants for the liquid and solid metal and for the mold were assumed. With uniform initial phase temperatures, it is seen that all boundaries of the system are immobilized in jj-space. Yang (Y2) rederived this result and further extended the application of the similarity transformation to three-region problems with induced motion. An example is the condensation of vapor, as a result of sudden pressurization, in a tank with relatively thick walls. 

The material properties of solids are affected by a number of complex factors. In a gas-solid flow, the particles are subjected to adsorption, electrification, various types of deformation (elastic, plastic, elastoplastic, or fracture), thermal conduction and radiation, and stresses induced by gas-solid interactions and solid-solid collisions. In addition, the particles may also be subjected to various field forces such as magnetic, electrostatic, and gravitational forces, as well as short-range forces such as van der Waals forces, which may affect the motion of particles. 

The thermal properties of some solid materials are given in Table 1.8. 

DSC has been used in studies of the thermal properties of aspartame in solid state combination with several other substances with which it may be formulated, such as mannitol [50, 52], caffeine [53], ampicillin [54], and cephalexin [55]. 

However, it should not be necessary to make any heat capacity measurements at all, or any assumptions as to the thermal properties of the solid and liquid states in order to calculate the correct value for the entropy of hydrogen. Since hydrogen gas at low temperatures consists entirely of molecules in the zero rotational state, its entropy will be that of a monatomic gas of atomic weight 2.016. The entropy at 298°K. will be obtained by adding the integral f CPd In T over the proper temperature range. The heat capacity may be separated into a constant term 5/2R and the rotational term Cr. 

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