Proportionality sign

R is the shear stress in the fluid and divelocity gradient or the rate of shear. It may be noted that R corresponds to r used by many authors to denote shear stress similarly, shear rate may be denoted by either dw,/dy or y. The proportionality sign may be replaced by the introduction of the proportionality factor n, which is the coefficient of viscosity, to give ... 

Mathematically, the proportionality sign (a) can be removed by introducing a proportionality constant (k). 

Mathematically, this means that the volume is directly proportional to the inverse pressure, or V -jL To remove the proportionality sign and replace it with an equal sign, V must be multiplied by a proportionality constant, k. 

As we saw in Section 3.7, a proportionality sign (oc) can be replaced by an equals sign and a proportionality constant. The proportionality constant, in this case k, is called the rate constant. The rate constant describes how difficult it is to overcome the energy barrier of the reaction—how hard it is to reach the transition state. The larger the rate constant, the easier it is to reach the transition state (see Figure 10.3 on p. 365). 

The calculation according to Eqs. (6.11) and (6.12) gave the following EJE values 4.60 and 6.65, respectively. Since the experimental value EJE = 6.10 is closer to the value, calculated according to Eq. (6.12), then both interfacial layers are the reinforcing elements for the studied nanocomposites. Therefore, the coefficient 2 should be introduced in the equations for value determination (e.g. in Eq. (6.1)) in case of nanocomposites with elastomeric matrix. Let us consider that Eq. (6.1) in its initial form was obtained as a relationship with proportionality sign, i.e., without fixed proportionality coefficient [21]. 

As earlier, r] value was considered as reciprocal value of MFI and constant rig in the Eq. (49) was accepted equal to (MFI )". At these conditions and replacement of proportionality sign in the Eq. (49) by equality sign and also using in connection with this the additional constant 6.8 one can calculate theoretical values of MFI, if magnitude is expressed in microns. In Fig. 14, the comparison of the received by the indicated mode values ri=MFr with the experimental dependence MFVjW ) is adduced, from which theory and experiment good correspondence follows (the mean discrepancy of these parameters makes up 8%). 

Since in the Eq. (1) of Chapter 1 proportionality sign is used, then the value is determined in relative units at the condition T = const [47] ... 

Let s now ccmvert the proportionality sign to an equal sign by expressing ii as the number of moles of gas we then insert a proportionality constant—R, the molar gas constant... 

The proportionality sign (a) can be replaced by an equals sign and a proportionality constant (k). This is a second-order reaction because its rate depends linearly on the concentration of each of the two reactants. 

In Eq. (6.19) we used the proportionality sign, simply because (in contrast to the fluxes) the reaction rate is volume related. Since = 0 in equilibrium, it follows that Kr = k/ic. Because of ArG = -1-RTlnQR/KR (cf. Section 4.2) we obtain... 

When the proportionality sign (oc) is replaced with an equal sign and a proportionality constant, the product of the pressure and volume of a fixed amount of gas at a given temperature is seen to be a constant a). The value of a depends on the amount of gas and the temperature. The graph in Figure 6-6 is that of PV = fl. It is called a hyperbola. 

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