Solid idealized incompressible

Joule s experiments on the free expansion of an ideal gas showed that the internal energy of such a system is a function of temperature alone. For a real gas, this is only approximately true. For condensed phases, which are effectively incompressible, the volume dependence on the change in internal energy is negligible. As a result, the internal energies of liquids and solids are also considered a function of temperature alone. For this reason, the internal energy of a system may loosely be referred to as the thermal energy . 

The behavior of a flowing fluid depends strongly on whether or not the fluid is under the influence of solid boundaries. In the region where the influence of the wall is small, the shear stress may be negligible and the fluid behavior may approach that of an ideal fluid, one that is incompressible and has zero viscosity. The flow of such an ideal fluid is called potential flow and is completely described by the principles of newtonian mechanics and conservation of mass. The mathematical theory of potential flow is highly developed but is outside the scope of this book. Potential flow has two important characteristics (1) neither circulations nor eddies can form within the stream, so that potential flow is also called irrotational flow, and (2) friction cannot develop, so that there is no dissipation of mechanical energy into heat. 

To use the energy balances, we will need to relate the energy to more easily measurable properties, such as temperature and pressure (and in later chapters, when we consider mixtures, to composition as well). The interrelationships between energy, temperature, pressure, and composition can be complicated, and we will develop this in stages. In this chapter and in Chapters 4,5, and 6 we will consider only pure fluids, so composition is not a variable. Then, in Chapters 8 to 15, mixtures will be considered. Also, here and in Chapters 4 and 5 we will consider only the simple ideal gas and incompressible liquids and solids for which the equations relating the energy, temperature, and pressure are simple, or fluids for which charts and tables interrelating these properties are available. Then, in Chapter 6, we will discuss how such tables and charts are prepared. 

Equation 4.2-13b provides the basis for computing entropy changes for real fluids, and it will be used in that manner in Chapter 6. However, to illustrate the use of the entropy balance here in a simple way, we consider the calculation of the entropy change accompanying a change of state for 1 mol of an ideal gas, and for incompressible liquids and solids. 

For incompressible fiuids Cp = Cy. Tables B3 to B5 in Appendix B list the temperature-dependent heat capacity data for ideal gas, liquids, and solids at 298.15 K. 

Having found such a simple description for ideal rubbers, enabling us to make predictions of the stress for all kinds of deformations in a straightforward way, one might presume that the modifications in behavior, as they are observed for real rubbers, can be accounted for by suitable alterations performed in the framework of the general equation for incompressible solids Eq. (7.75). In a first step one may consider the effects of an inclusion of the... 

These expressions are idealized. Equations (3.13) and (3.14) assume that the atomic-scale entities are weakly (or non-)interacting, while Equations (3.14) to (3.16) assume the solvent, liquid, and solid to be incompressible. Real gas molecules and ions, of... 

Exponentiation of both sides of this equation results in an expression that is called the law of mass action (due to the assumptions made earlier that it is not really a law, but rather a rule of thumb, which holds well for ideal gases, ideal solutions, and incompressible solutions, liquids, and solids) ... 

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