Incompressible volume

Note 3 For an isotropic, incompressible material, // = 0.5. It should be noted that, in materials referred to as incompressible, volume changes do in fact occur in deformation, but they may be neglected. 

This equation predicts the behavior of gases very well except at relatively low temperatures and at relatively high pressures. Just how low the temperature must be or how high the pressure must be before serious deviations from this equation are observed will vary from one gas to another. Under extreme conditions, these equations cannot be used without correction for the volume occupied by the molecules themselves or for the attractive forces between neighboring molecules. For every gas, conditions exist under which the molecules condense to a liquid that occupies a fairly incompressible volume. A hypothetical gas, called an ideal gas, would obey Equation II-2 under all conditions, and would possess zero volume at a temperature ofO K. Most gases obey this equation at normal temperatures and pressures. 

The Units for the van der Waals Constants The units for the van der Waals constants a and b depend upon the units in which Pand Vare expressed. It is evident that the constant a is expressed by the factor pV2/n2, i.e., pressure (volume)1 /mol2. If pressure is expressed in atm and volume in dm3, the value of a will be in dm6 atm mol-2. As regards b, it is incompressible volume per mole of a gas. Hence, it must have the same units as volume per mole, e.g., dm3 mob1. 

Adding new equations of state to the framework is an easy and straightforward process. Two things tend to define most modern cubic equations of state the mixing rules used to estimate incompressible volume b) and attraction parameter (a), and the form of the attractive (second) term of the equation (see equation... 

Here v is the total specific volume and v is the characteristic (hard-core, incompressible) volume. The last two names are based on the concept of squeezing out the whole free volume by applying a very high pressure so that only v remains. Instead of free volume, some people work with the reduced volume... 

Hard-core volume—also known as incompressible volume corresponding to extremely high pressure or zero thermodynamic temperature conditions. See Section 4.2.2 and Eq. (4.5). 

Note that the lower hmit of the integration of equation [7.76] is 0 when the distance between molecules tends towards zero, all known expressions of potential, particularly those of Lennard-Jones, leads to an integral that diverges. To overcome this issue, we will only count the potentials from distance D. This distance forms an impenetrable wall to a neighboring molecule. The volume of the corresponding sphere will be considered as an incompressible volume of the molecule, i.e. ... 

As compared to the incompressible volume, there exists an excess of free volume which makes the motion of chains all the more easy as the free volume increases. 

The parameters B and Vq resulting from linear plots of 0 of molten salts against V are shown in Table 3.18 too. These parameters are independent of the temperature and the Vq values are in good agreement with those derived by Chhabra and Hunter [253] as seen in the Table. They correspond to the volume of the virtual molten salt that has no free volume, but in which the ions are free to rotate. Such a volume should be close to that of the crystalline salt at the melting point, but there are no accurate data for this quantity for comparison. Bockris and Richards [137] reported values of for alkali metal halides and nitrates, where vq is the incompressible volume per ion. These values for the salts, shown in italics in Table 3.18 are comparable with the Vq values reported there. The Vq values of molten salts are on the average 87 6 % of the molar volumes of the liquid salts at the corresponding temperature of l.lTm (Tables 3.13 and 3.14). 

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