Incompressible substance

When the two phases in contact are condensed phases and the entire volume is taken up by incompressible substances, positive adsorption of one component must be attended by negative adsorption (desorption) of other components. This phenomenon is called adsorptive displacement. 

A substance whose specific volume (or density) does not change with temperature or pressure is called an incompressible substance. The specific volumes of solids and liquids essentially remain constant during a process, and thus they can be approximated as incompressible substances without sacrificing much in accuracy. 

The constant-volume and constant-pressure specific heats are identical for incompressible substances (Fig. 1-10). Therefore, for solids and liquids the subscripts on c and Cp can be dropped and both. specific heals can be represented by a single symbol, c. That is, Cp = tv = c- This result could also be deduced from the physical definitions of constant-volume and constant-pressure specific heats. Specific heats of several common gases, liquids, and solids are given in the Appendix. 

The specific heats of incompressible substances depend on temperature only. Therefore, the change hi the internal energy of solids and liquids can be expressed as... 

The densities of liquids are essentially constant, and thus the flow of liquids is typically incompressible. Therefore, liquids are usually referred to as incompressible substances. A pressure of 210 atm, for example, causes the density of liquid water at 1 atm to change by just 1 percent. Gases, on the other hand, arc highly compressible. A pressure change of Just 0.01 atm, for example, causes a change of 1 percent in the density of atmospheric air. 

Assumptions 1 Steady operating conditions exist. 2 Oil is an incompressible substance with constant properties. 3 Body forces such as gravity are negligible. 4 The plates are large so that there is no variation in the i direction. Properties The properties of oil at 20°C are (Table A-13) ... 

Bridgman PW (1949) Linear compressions to 30,000 kg/cm, including relatively incompressible substances. Proc Am Acad Arts Sci 77 189-234... 

An easily compressible substance has a larger value of k, so larger volume fluctuations occur at a given pressure than in a more incompressible substance. Conversely, in a constant volume simulation a less compressible substance shows larger fluctuations in the pressure. The isothermal compressibility is the pressure analogue of the heat capacity, which is related to the energy fluctuations. 

The isothermal compressibility of an ideal gas is approximately 1 atm. So for a simulation in a box of side 20 A (volume 8000 A ) at 300 K, the root mean square change in the volume is approximately ISIOOA. This is larger than the initial size of the box For a relatively incompressible substance such as water (k, = 44 75 x 10 atm ) the fluctuation is 121A, which corresponds to the box only changing by about 01A in each direction. These values have clear implications for the appropriate size of the simulation system. 

Solution The two states are at different pressure. Since, however, pressure has negligible effect on the entropy of incompressible substances, eg. r4.iol may be used ... 

Solids and liquid have no distinction between constant-pressure or constant-volume specific heats, and a single specific heat value is appropriate. The specific heat of most incompressible substances varies only slightly with temperature and can generally be considered constant over a limited temperature range of interest to fuel cell studies. For example, the mass specific heat of liquid water at 25°C is 4.179 kJ/kg K, while at 1(X)°C, the specific heat of the liquid phase is 4.218 kJ/kg K, only about 1% higher. 

If fluidity, the physical property of a substance that enables it to flow and incompressibility were the only properties required, any liquid that is not too thick might be used in a hydraulic system. However, a satisfactory liquid for a particular system must possess a number of other properties. The most important properties and some characteristics are discussed in the following paragraphs. 

Incompressible inertialess flow of these substances is described by the following equations of continuity ... 

Solids are usually not used in cycles. Liquids can be approximated as incompressible (dv = 0) substances since their specific volumes remain near constant during a process. 

This section summarizes results of the phenomenological theory of viscoelasticity as they apply to homogeneous polymer liquids. The theory of incompressible simple fluids (76, 77) is based on a very general set of ideas about the nature of mechanical response. According to this theory the flow-induced stress at any point in a substance at time t depends only on the deformations experienced by material in an arbitrarily small neighborhood of that point in all times prior to t. The relationship between stress at the current time and deformation history is the constitutive equation for the substance. 

Consider a process starting at point 1 with a substance in the liquid phase. Temperature is held-eonstant,-and volume-is-inereased by removal of the mercury. This causes a reduction in pressure from p, to p . A relatively large change in pressure results from a small change in volume. This is because liquids are relatively incompressible. 

Standard values p° and p° depend on the total pressure, p, in the system. In particular, for an incompressible condense substance... 

When you heat a liquid or a solid it normally expands (i.e., its density decreases). In most process applications, however, it can be assumed with little error that solid and liquid densities are independent of temperature. Similarly, changes in pressure do not cause significant changes in liquid or solid densities these substances are therefore termed incompressible. 

Most constitutive equations have been developed for incompressible fluids owing to the fact that the treatment of these substances is easier than that of compressible fluids. In what follows, the constitutive equations of different kinds of fluids are briefly summarized (22) ... 

Liquids and solids are almost incompressible. Therefore, changes of atmospheric pressure have little effect on the entropy of substances in liquid or solid states. Ordinary changes in pressure have essentially no effect on melting and freezing. Although the elevation is high and atmospheric pressure is very low, water on Pike s Peak still freezes at 273.15 K. You will learn more about pressure effects on state changes in the next section. 

A substance is viscous, nearly incompressible, and not elastic. Is it most likely to be a solid, a liquid, or a gas ... 

Any substances that can enhance the filtration efficiency are termed a filter aid. Diatomaceous earth is the most common filter aid for the precoat filtration system. An efficient, economical filter aid must (a) have rigid, intricately shaped, porous, individual particles (b) form a highly permeable, stable, incompressible filter cake (c) remove even the finest solids at high rates of flow and (d) he as chemically inert and essentially insoluble in the Uquid being filtered. Commercial diatomaceous earth, such as Celite diatomite, meets these requirements due to the wide variety of intricately shaped particles and inert composition that makes it practically insoluble in all hut a few liquids. 

It is known that incompressible fluids represent a useful model for real fluids in fluid mechanics and heat and mass transfer. Their thermal equation of state is v = v0 = const. For pure substances and also for mixtures, isobaric and isochoric specific heat capacities agree with each other, cp = cv = c. 

The temperature form of the energy equation for incompressible pure substances is yielded from (3.85) under the assumption of constant thermal conductivity... 

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