Thermal Expansion Thermodynamic Properties

Thermal conductivity Thermal diffusivity Thermal expansion Thermodynamics properties Transport properties Viscoelasticity... 

Thermal and Thermodynamic Properties 6.1 Density and Thermal Expansion... 

The interface region in a composite is important in determining the ultimate properties of the composite. At the interface a discontinuity occurs in one or more material parameters such as elastic moduli, thermodynamic parameters such as chemical potential, and the coefficient of thermal expansion. The importance of the interface region in composites stems from two main reasons the interface occupies a large area in composites, and in general, the reinforcement and the matrix form a system that is not in thermodynamic equiUbhum. 

From Mercury—Density and Thermal Expansion at Atmospheric Pressure and Temperatures from 0 to. 350 C, Tables of Standard Handbook Data, Standartov, Moscow, 1978. The density values obtainable from those cited for the specific volume of the saturated liquid in the Thermodynamic Properties subsection show minor differences. No attempt was made to adjust either set. 

The experiments result in an explicit measure of the change in the shock-wave compressibility which occurs at 2.5 GPa. For the small compressions involved (2% at 2.5 GPa), the shock-wave compression is adiabatic to a very close approximation. Thus, the isothermal compressibility Akj- can be computed from the thermodynamic relation between adiabatic and isothermal compressibilities. Furthermore, from the pressure and temperature of the transition, the coefficient dO/dP can be computed. The evaluation of both Akj-and dO/dP allow the change in thermal expansion and specific heat to be computed from Eq. (5.8) and (5.9), and a complete description of the properties of the transition is then obtained. 

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

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... 

Physical and thermodynamic property data, such as thermal expansion coeffici t, are important in process engineering. The following brief discussion illustrates such importance. Liquids contained in process equipment will expand with an increase in temperature. To accommodate such expansion, it is necessary to design a relief system which will relieve (or vent) the thermally expanding liquid and prevent pressure build-up from the expansion. If provisions are not made for a relief system, the pressure will increase from die diermally expanding liquid. If the pressure increase is excessive, damage to the process equipment vtdll occur. 

Recent work has shown 103) that for alkali halides the Debye characteristic temperature is not very sensitive to volume changes produced by thermal expansion. This probably indicates that, in general, volume changes of an adsorbent will not markedly affect its bulk thermodynamic properties. 

In addition to the temperature dependence of the properties such as strength and modulus, which we will discuss individually for each material class, there are two fundamental topics that are often described in the context of heat transfer properties or thermodynamics of materials—for example, thermal conductivity or specific heat—but are related more to mechanical properties because they involve dimensional changes. These two properties, thermoelasticity and thermal expansion, are closely related, but will be described separately. 

TABLE 11.2 Measured Thermodynamic Properties (in SI Units) of Some Common Fluids at 20° C, 1 atm Molar Heat Capacity CP, Isothermal Compressibility jS7, Coefficient of Thermal Expansion otp, and Molar Volume V, with Monatomic Ideal Gas Values (cf. Sidebar 11.3) Shown for Comparison... 

As we have seen from our previous discussions of heat capacities, thermal expansion coefficients, and compressibilities, partial derivatives are the key to discussing changes in thermodynamic systems. In a single-component system of fixed size, the specification of two state variables completely determines the state of the system. Calling one of the molar energy quantities Z, we can write Z = Z(X, Y), where Xand Tare any two state variables, such as Tand I] or Tand V. Using the general mathematical properties of functions of two variables that are discussed in Appendix A,... 

Equations (54) and (56) suggest that measurements of the force required to keep a rubber at constant length as a function of temperature would determine the thermodynamic properties of the rubber. However, due to thermal expansion, very large changes in pressure would be required to keep the polymer volume constant as its temperature is varied. Thus, measurements of (df /dT)l are usually made at constant pressure. Extending Eq. (10) of Appendix A to an additional variable gives... 

The anomalous low-temperature behaviour is reflected in other thermodynamic properties as well. The thermal expansion, for instance, is unusually large at low temperature. At writing ... 

There are some density data for solid salts above ambient temperature which are given in the form of thermal expansion coefficients. These have been listed when they seemed reliable. Above the melting point, density data are scarce. Most are available for alkali halides but those available for salts are taken from the critically evaluated compilation Janz, G.J., Thermodynamics and transport properties for molten salts, correlation equations for critically evaluated density, surface tension, electrical conductance, and viscosity data,./. Phys. Chem. Reference Data, 17, Suppl. 2, 1988. 

---