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vb.net barcode freeware Molecular Theory of Fluids in Software
161 Molecular Theory of Fluids QR Code Encoder In None Using Barcode creation for Software Control to generate, create QRCode image in Software applications. Recognize QRCode In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. The hardcore diameter d is a measure of the centertocenter separation for which U, and hence F, becomes infinite It is not subject to precise determination, but plays the role of a modeling parameter in some expressions for U The collision diameter o is defined as the separation for which U = 0 The equilibrium separation ro is the separation for which U attains its minimum value of  E At r = ro, the net intermolecular force is zero Quantity E is called the well depth For a particular class of chemical species (eg, noble gases, or cyclic alkanes), each of these special quantities increases with increasing molecular size Typical J Commonly, ranges of values for o and E are 0 x 3 to 8 x 10lo m and E x 01 to 10 x ro is about 10 to 15% greater than o Scores of expressions have been proposed for U' All are essentially empirical, although their functional forms often have some basis in theory The most widely used is the LennardJones (LJ) 12/6pairpotential function: Create Denso QR Bar Code In Visual C#.NET Using Barcode maker for VS .NET Control to generate, create Denso QR Bar Code image in VS .NET applications. Quick Response Code Drawer In .NET Using Barcode drawer for ASP.NET Control to generate, create QR Code image in ASP.NET applications. Equation (161) provides semiquantitative representations of thermodynamic and transport properties for nonpolar substances of relatively simple molecular structure In Eq (161), the rl2 term is supposed to represent bimolecular repulsions, and the r p 6term bimolecular attractions Although the attraction term has significant theoretical justification, the rl2 dependence for repulsions is chosen primarily for mathematical convenience Table 161 shows some values of the dimensionless potential energy U / r as a function of the dimensionless separation r l o , as implied by Eq (161) Clearly, the effects of intermolecular forces are significant only over a modest range of separations Although they operate over an infinite range (U and F together approach zero only in the limit as r + oo), both U and F for neutral molecular pairs are numerically negligible for separations greater than about 10 molecular diameters Print Denso QR Bar Code In Visual Studio .NET Using Barcode generator for Visual Studio .NET Control to generate, create QRCode image in Visual Studio .NET applications. Painting QR In VB.NET Using Barcode printer for VS .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications. Contributions to the Intermolecular Potential Energy
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The origins of intermolecular forces stem from the essential concept that a molecule is a distribution of charges: a collection of positively charged nuclei, surrounded by a cloud of negatively charged electrons Intermolecular repulsions at sufficiently small separations therefore result from the overlap of electron clouds of interacting molecules, giving rise to a Coulombic repulsion At still smaller separations the positively charged nuclei "see" each other, again promoting repulsion The origins of intermolecular attractions are less obvious, and several mechanisms can contribute First, consider the electrostatic interaction of two rigid charge distributions A and B By Coulomb's law, the electrostatic potential energy of interaction U(e1) is: UPCA Supplement 2 Creator In None Using Barcode drawer for Software Control to generate, create GS1  12 image in Software applications. Bar Code Generator In None Using Barcode generator for Software Control to generate, create barcode image in Software applications. a compilation of expressions for U see G C Maitland, M Rigby, E B Smith, and W A Wakeham, Intermolecular Forces: Their Origin and Determination, app 1, Clarendon Press, Oxford, 1981 Barcode Encoder In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. EAN 128 Printer In None Using Barcode maker for Software Control to generate, create UCC128 image in Software applications. 'A comprehensive discussion of these contributions to U ( r ) is given by J 0 Hirschfelder, C F Curtiss, and R B Bird, Molecular Theory of Gases and Liquids, pp 2530, 209, 9831020, John Wiley and Sons, New York, 1954 Bookland EAN Drawer In None Using Barcode drawer for Software Control to generate, create Bookland EAN image in Software applications. Encode Barcode In ObjectiveC Using Barcode printer for iPad Control to generate, create bar code image in iPad applications. CHAPTER 16 Introduction to Molecular Thermodynamics Table 161 Bimolecular Potential Energy as a Function of Separation for the LennardJones 1216 Potential Make UPC Symbol In Java Using Barcode generation for BIRT Control to generate, create UPC Symbol image in Eclipse BIRT applications. GTIN  13 Printer In .NET Using Barcode generation for ASP.NET Control to generate, create GTIN  13 image in ASP.NET applications. Here, qi is a charge in distribution A, qj is a charge in distribution B, and rij is the separation between charges qi and qj Quantity 0 is the electric permittivity of vacuum, a physical constant3 equal to 8854 19 x lo'' C V' m' (The unit of electric charge is the coulomb C, and the unit of electric potential difference is the volt V) The sums are taken over all charges in the distributions Equation (162) is exact, but awkward to use as it stands Application is facilitated when the charge separation rij is replaced by the centerofmass separation r of the two distributions Statistical averaging of contributions from all orientations of charge distribution yields the following approximate expression for U(e1) for two neutral rigid charge distribution^:^ GTIN  128 Generation In None Using Barcode creator for Word Control to generate, create GS1 128 image in Office Word applications. Bar Code Encoder In ObjectiveC Using Barcode drawer for iPhone Control to generate, create barcode image in iPhone applications. J Kl ; p~ and p~ are the permanent Quantity k is Boltzmann's constant, equal to 1381 x dipole moments for charge distributions A and B associated with the molecules This contribution to the pairpotential function vanishes only when one of the permanent dipole moments is zero The averaging procedure which leads to Eq (163) produces several remarkable results: Creating Bar Code In Visual Studio .NET Using Barcode creator for ASP.NET Control to generate, create bar code image in ASP.NET applications. Barcode Creator In None Using Barcode printer for Microsoft Excel Control to generate, create barcode image in Office Excel applications. Even though the distributions are electrically neutral, there is a net attraction between them The dependence of U(e1) on chargedistributionorientation becomes on averaging an rP6 dependence As given by Eq (163) U(e1) varies with T' Hence the magnitude of the permanentdipole interaction decreases with increasing temperature Equation (163) is the simplest example of a direct electrostatic potential for two neutral molecules; here, the dipole moment emerges as an important physical property Dipole moments are measures of the net separation of charge within a molecule For a spherically symmetric neutral charge distribution (eg, an atom of argon), p is zero For a molecule in which charge Iq 1 is separated from charge  Iq 1 by distance 1, the dipole moment is p = Iq 1 1 Hence p 3~nrelated the well depth E of Fig 161 to 4 ~ h iresult is only valid for modest dipole moments For a discussion, see T M Reed and K E Gubbins, Applied s Statistical Mechanics, sec 57, McGrawHill, New York, 1973

