Physical significance

However, if the liquid solution contains a noncondensable component, the normalization shown in Equation (13) cannot be applied to that component since a pure, supercritical liquid is a physical impossibility. Sometimes it is convenient to introduce the concept of a pure, hypothetical supercritical liquid and to evaluate its properties by extrapolation provided that the component in question is not excessively above its critical temperature, this concept is useful, as discussed later. We refer to those hypothetical liquids as condensable components whenever they follow the convention of Equation (13). However, for a highly supercritical component (e.g., H2 or N2 at room temperature) the concept of a hypothetical liquid is of little use since the extrapolation of pure-liquid properties in this case is so excessive as to lose physical significance. 

The impulse can be due to sudden collision with particles or to exposure to electromagnetic radiation. The physical significance of tire fonn factoi n r transitions in atomic hydrogen,... 

As discussed in preceding sections, FI and have nuclear spin 5, which may have drastic consequences on the vibrational spectra of the corresponding trimeric species. In fact, the nuclear spin functions can only have A, (quartet state) and E (doublet) symmetries. Since the total wave function must be antisymmetric, Ai rovibronic states are therefore not allowed. Thus, for 7 = 0, only resonance states of A2 and E symmetries exist, with calculated states of Ai symmetry being purely mathematical states. Similarly, only -symmetric pseudobound states are allowed for 7 = 0. Indeed, even when vibronic coupling is taken into account, only A and E vibronic states have physical significance. Table XVII-XIX summarize the symmetry properties of the wave functions for H3 and its isotopomers. 

Eqs. (D.5)-(D.7). However, when perturbations occur due to anharmonicity, the wave functions in Eqs. (D.11)-(D.13) will provide the conect zeroth-order ones. The quantum numbers and v h are therefore not physically significant, while V2 arid or V2 and I2 = m, are. It should also be pointed out that the degeneracy in the vibrational levels will be split due to anharmonicity [28]. 

Finally we must draw attention to an Interesting and physically significant approximate relation between the numerical magnitudes of the parameters P and 9 in Table 11.1. Their ratio Is given by... 

To clarify the physical significance of mixing such configurations, it is useful to consider what are found to be the two most important such configurations for the ground state of the Be atom ... 

We shall presently examine the physical significance of the shift factors, since they quantitatively embody the time-temperature equivalence principle. For the present, however, we shall regard these as purely empirical parameters. The following Ust enumerates some pertinent properties of a ... 

Note that Eqs. (6.5) and (6.12) are both first-order rate laws, although the physical significance of the proportionality factors is quite different in the two cases. The rate constants shown in Eqs. (6.5) and (6.6) show a temperature dependence described by the Arrhenius equation ... 

As a device for describing the effect of temperature on solution nonideality, it is entirely suitable to think of Eq. (8.115) as offering an alternate notation which accomplishes the desired effect with p and as adjustable parameters. We note, however, that the left-hand side of Eq. (8.115) contains only one such parameter, x, while the right-hand side contains two p and . Does this additional parameter have any physical significance ... 

In developing these ideas quantitatively, we shall derive expressions for the light scattered by a volume element in the scattering medium. The symbol i is used to represent this quantity its physical significance is also shown in Fig. 10.1. [Our problem with notation in this chapter is too many i s ] Before actually deriving this, let us examine the relationship between i and 1 or, more exactly, between I /Iq and IJIq. 

Statistical mechanics provides physical significance to the virial coefficients (18). For the expansion in 1/ the term BjV arises because of interactions between pairs of molecules (eq. 11), the term C/ k, because of three-molecule interactions, etc. Because two-body interactions are much more common than higher order interactions, tmncated forms of the virial expansion are typically used. If no interactions existed, the virial coefficients would be 2ero and the virial expansion would reduce to the ideal gas law Z = 1). 

Although the Pitzer correlations are based on data for pure materials, they may also be used for the calculation of mixture properties. A set of recipes is required relating the parameters T, Pc, and (0 for a mixture to the pure-species values and to composition. One such set is given by Eqs. (2-80) through (2-82) in Sec. 2, which define pseudopa-rameters, so called because the defined values of T, Pc, and (0 have no physical significance for the mixture. 

In the event that three real roots obtain for these equations, only the largest 2 (smallest p) appropriate for the vapor phase has physical significance, because the viriaf equations are suitable only for vapors and gases. 

When i = J, all equations reduce to the appropriate values for a pure species. When i j, these equations define a set of interaction parameters having no physical significance. For a mixture, values of By and dBjj/dT from Eqs. (4-212) and (4-213) are substituted into Eqs. (4-183) and (4-185) to provide values of the mixture second virial coefficient B and its temperature derivative. Values of and for the mixture are then given by Eqs. (4-193) and (4-194), and values of In i for the component fugacity coefficients are given by Eq. (4-196). 

Numerous attempts have been made to develop hybrid methodologies along these lines. An obvious advantage of the method is its handiness, while its disadvantage is an artifact introduced at the boundary between the solute and solvent. You may obtain agreement between experiments and theory as close as you desire by introducing many adjustable parameters associated with the boundary conditions. However, the more adjustable parameters are introduced, the more the physical significance of the parameter is obscured. 

Equation 5-247 is a polynomial, and the roots (C ) are determined using a numerical method such as the Newton-Raphson as illustrated in Appendix D. For second order kinetics, the positive sign (-r) of the quadratic Equation 5-245 is chosen. Otherwise, the other root would give a negative concentration, which is physically impossible. This would also be the case for the nth order kinetics in an isothermal reactor. Therefore, for the nth order reaction in an isothermal CFSTR, there is only one physically significant root (0 < C < C g) for a given residence time f. 

Figure 2-5 Physical Significance of the Anisotropic Stress-Strain Relations...

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