Cube root relationship

If the solute molecule is considered to be spherical, as is the case for globular proteins, r, is proportional to the cube root of the molecular weight, M, The linear relationship between (—In Kav)m and rs here implies that (—In Kav)112 will also vary linearly with M 13, and this has been observed for proteins on Sagarose gels.61... 

Figure 5 The value of //r is plotted against the cube root of rotation rate, showing a linear relationship.

For glutamic acid (18) and glycine (10) the yield of ammonia varies approximately as the cube root of the concentration. This variation agrees with the diffusion of the spur model which derives from the hypothesis that at higher solute concentrations, water radicals are scavenged which would react with each other in more dilute solution. However, for the effect of cathode rays on the aromatic amino acids phenylalanine, tryptophan, and tyrosine and for cystine, this relationship is inverted, and amino acid destruction decreased with an increase in concentration (29). 

Figure 2.22 Different fits for the relationship between reflectance and lightness. Note that the axes have been switched, compared with Figure 2.21. Logarithmic (excluding zero), cube root and square root fits are shown for Land s experimental data. The data is best approximated by the function Y = 9.033/J0 4296 — 0.0151, which is also shown.

In their study of the fluoride ion affinities of various fluoroacids Mallouk et al. (Mallouk, T. E. Rosenthal, G. L. Muller, G. Brusasco, R. Bartlett, N. Inorg. Chem. 1984, 23, 3167-3173) employed the linear dependence of lattice energy upon the inverse of the cube root of the formula unit volume to determine the lattice energies of salts of unknown structure. From that empirical relationship which is (kcal mol" ) = 556.3 (molar volume in A )- / + 26.3, l/UCfiFfiAsPs) =115 kcal mol" and C/L(C,oFgAsF6) 108 kcal mol". ... 

You have been given the K p for Mg(OH)2. The moles of Mg + ions in solution equal the moles of Mg(OH)2 that dissolved, but the moles of OH ions in solution are two times the moles of Mg(OH)2 that dissolved. You can use these relationships to write the solubility product constant expression in terms of one unknown. Because the equilibrium expression is a third power equation, you can predict that [OH ] will be approximately the cube root of 10 or approximately 10 . 

Although Newton had measured the black spot at the contact of glass spheres, and also seen the black spot expand and contract reversibly as the spheres were pressed together, he did not pursue the relationship between the spot size and load. Almost 200 years were to elapse before Hertz defined the connection published in 1882. Hertz was a 23-year-old assistant to Helmholtz in Berlin when he was stimulated by Newton s rings and derived the elastic theory of sphere contact in his Christmas vacation in 1880." He found that the spot diameter increased with the cube root of load F, showed that the elastic modulus E, Poisson s ratio v and sphere diameter D were also important, and verified his equation... 

The emissivity and resistivity may not be known precisely for a particular rare metal, but it is still possible to make use of the relationship between E and 7 if AT is first evaluated empirically in experimental equipment where the temperature can be measured. Once the constant, AT, has been determined, control equipment can be designed which will maintain the product of voltage and cube root of current at a constant value, and so ensure a stable temperature. ... 

BLEVE models arc a blend of empirical correlations (for size, duration, and radiant fraction) and more fundamental relationships (for view factor and transmissivity). Baker et al. (1983) have undertaken a dimensional analysis for diameter and duration which approximates a cube root correlation. Fragmentation correlations are empirical. 

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