Vectorial forces

Once again, these fluxes are not all independent and some care must be taken to rewrite everything so that syimnetry is preserved [12]. Wlien this is done, the Curie principle decouples the vectorial forces from the scalar fluxes and vice versa [9]. Nevertheless, the reaction temis lead to additional reciprocal relations because... 

When we look at the overall molecular structure of carbon tetrachloride, the net vectorial force in this molecule is zero as its shape is symmetrical so CC14 is a non-polar molecule. 

The two hydrogen atoms having the same electronegativity value cause the BeH2 molecule to be nonpolar. This is because the molecule is symmetrical and the net vectorial force applied on Be atom by the bond dipoles is zero. 

The geometry of the BH3 molecule is trigonal planar. The net vectorial force applied on the boron atom by the three polar bonds is zero due to the symmetrical shape, so the molecule is nonpolsur. 

In the CH4 molecule the net vectorial force applied on carbon atom by the four Figure 6 The shape of the CH4 molecule. 

For thermodynamic vectorial forces, such as a difference in chemical potential of component /, proper spatial characteristics must be assigned for the description of local processes. For this purpose, we consider all points of equal as the potential surface. For the two neighboring equipotential surfaces with chemical potentials p, and /z, + dp the change in p, with number of moles N is dpJdN, which is the measure of the local density of equipotential surfaces. At any point on the potential surface, we construct a perpendicular unit vector with the direction corresponding to the direction of maximal change in p,. With the unit vectors in the direction x, y, and z denoted by i, j, and k, respectively, the gradient of the field in Cartesian coordinates is... 

Surface tension. Assuming that a membrane stretches over each interface, the magnitudes of the interfacial tension between each pair of phases are the fluid-fluid interfacial tension Ogt, the wetting fluid-solid interfacial tension oft, and the nonwetting fluid-solid interfacial tension ogs. When in static equilibrium, the vectorial force balance at the line of contact (the law of Neumann triangle, Ref. 87) gives... 

Coupling can take place (i) amongst vectorial forces or (ii) amongst scalar forces, but no coupling can take place between vectorial and scalar forces (Curie-Prigogine principle). 

Vectorial effects. Where components of a vectorial force act Independently, the factor applied to any favourable component shall be... 

Equations (2.19) and (2.20) have exactly the same form, i.e., Newton s equation of motion is indeed covariant under Galilean transformations. These two equations describe the same physical situation with respect to two different inertial frames of reference. Although the physical vectorial force is of course the same in both frames of reference, F = F, its components F, and F- are in general different functions of their arguments. This relationship is given by the second equality of Eq. (2.20). 

At this point, as far as shaking forces go, the gas forces do not make a contribution. If the rod load or bearing loads are to be analyzed, the gas forces must be calculated and added vectorially to the inertia forces to... 

FIGURE 22.21 The mechanism of photophosphorylation. Photosynthetic electron transport establishes a proton gradient that is tapped by the CFiCFo ATP synthase to drive ATP synthesis. Critical to this mechanism is the fact that the membrane-bound components of light-induced electron transport and ATP synthesis are asymmetrical with respect to the thylakoid membrane so that vectorial discharge and uptake of ensue, generating the proton-motive force. 

We do not need an oriented driving force for the chemical reaction. The quantity L+r is a vectorial coefficient that reflects the structure of the system. 

For more complex vector-field potentials depending on the relative orientation as well as the separation of the two particles, the corresponding vector expression is F = — V V, where V = (d/dx, d/dy, d/dz) is the gradient operator. Such vectorial aspects of intermolecular forces are obviously important for real molecules of nonspherical shape.]... 

In the examples (2.62), (2.63), the force vector F was parallel to the displacement vector dr [i.e., 6 = 0 in (2.61b)]. In these cases, the vectorial aspects of the work expression (2.60) could be ignored, because the integration path from initial to final r has only a 1-dimensional character. More generally, the integration path may vary in 3-dimensional (nonlinear) manner from initial point A (at rA) to final point B (at rB), and the value of the integral is not uniquely determined until the exact A —> B path is specified. In this case, the work wa b must be evaluated as a line integral (or path integral cf. Sidebar 1.6),... 

The concept of the vectorial coupling of quasispin momenta was first applied to the nucleus to study the short-range pairing nucleonic interaction [117]. For interactions of that type the quasispin of the system is a sufficiently good quantum number. In atoms there is no such interaction - the electrons are acted upon by electrostatic repulsion forces, for which the quasispin quantum number is not conserved. Therefore, in general, the Hamiltonian matrix defined in the basis of wave functions (17.56) is essentially non-diagonal. 

Fig. 1.1. A magnetic moment can be seen as a magnetic dipole n characterized by north (N) and south (S) polarities. It gives rise to a magnetic field which is indicated by force lines. The dipolar nature provides the vectorial nature of this moment, whose intensity is indicated by H-...

A rule of thumb for the validity of linear relationships is that processes should be slow and the thermodynamic states near equilibrium. But even then, not all flows can be coupled. Coupling is limited to certain cases. Casimir shows that coupling is only possible between driving forces of the same tensorial character, such as scalar, vectorial, and so forth. For more details, see Ref. [2],... 

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