Substituting equation

The efficiency factor of 0.8 is already included in the equation. Substitution of the remaining values gives... 

Equation 6-74 is a first order differential equation substituting Equations 6-70 and 6-78 for the temperature, it is possible to simulate the temperature and time for various eonversions at AX = 0.05. Table 6-4 gives the eomputer results of the program BATCH63, and Eig-ure 6-7 shows profiles of both fraetional eonversion and temperature against time. The results show that for the endodiermie reaetion of (-i-AH[ /a) = 15.0 keal/gmol, die reaetor temperature deereases as eonversion inereases with time. 

Because the feed tray is essentially non-effective it is suggested that an additional theoretical tray be added to allow for this. This can be conveniently solved by the nomographs [21] of Figures 8-16 and 17. If the minimum number of trays in the rectifying section are needed, the)t can be calculated by the Fenske equation substituting the limits of xpi for x jj and x i, and the stripping section can be calculated by difference. 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

Downcomer Pressure Drop. When the downcomer is less than minimally fluidized, the pressure drop can be estimated with a modified Ergun equation substituting gas-solid slip velocities for gas velocities (Yoon and Kunii, 1970), as shown in Eq. (9). 

Rewriting this equation, substituting the quantum term hv, the equation becomes... 

Equation Method Write the equation, substituting in an equal sign for is, the multiplication sign for of, and change the percent to a decimal. 

In equations 9.6 and 9.7, /n/Pi and Q1/Q2 are determined by the properties and composition of the mixture to be separated, and R is fixed for a given bowl r, and r, are governed by the settings of the weirs. The radius rs of the interface between the two liquids is then the only unknown and this may be eliminated between the two equations. Substitution of the value r, from equation 9.10 then permits calculation of the required radius rw of the weir for the heavy liquid. 

Multiply each AHf value by its molar coefficient from the balanced chemical equation. Substitute into the following equation, and then solve. AH° = l,(nAHf products) - X(nAH°t reactants)... 

Using this new form for the equation, substitute the m(x + 1) fory in the equation of the circle. 

The force increases linearly from zero of the centre of the quadrupoie. The force in the x direction is independent of the position, that means the x and motions are independent and can be considered separately. The ion motion in a quadrupoie can be described in the form of the Mathieu equation. Substituting Equation (3.16) in to Equation (3.19) and considering that the acceleration of ions in the x direction is given by ax = d2 x/dl2 then the differential equation of ion motion results in ... 

The second front in the pulse, moving with velocity c2, sees the conversion of B to C. Thus 0 must fall from 0+. to zero. There may also be a final decay in the reactant concentration from a+ to zero. However, a+ is already small, so we will make the approximation that a = a+ k2 throughout the whole of this front. Assuming constant a means that again the system is reduced to one governing equation. Substituting a = k2 into eqn (11.52) gives a quadratic wave equation... 

Figure 1-1 illustrates the relationships between the three scales. Converting one scale into another is by the equations below. The equation on the right is a rearrangement of the equation on the left. We suggest you know one equation, substitute values and solve for the unknown, rather than taking the time to memorize two equations for essentially the same calculation. 

The global structure of IET formalism is similar to that of DET. The integral kinetic equations substitute for their differential analogs. The kernels of these equations are defined by the transfer rates and pair distribution functions. The auxiliary equations for these functions are also similar but not identical to those in DET. In the next section we will see that the integral theory may sometimes be reduced to the differential one, albeit under rigid conditions and with some losses. 

Rearrange the Michaelis-Menten equation, substitute for U0/Um ix, and solve for Km. 

The ring interconversion of the 2-axial/ equator / /-substituted chair con-formers of 1,3-dimethyl-2-methoxy-1,3-diazacyclohexane was studied by low temperature and 13C NMR spectroscopy (94JA715) and found to be 8.6-9.1 keal/mol well above the barrier for the N-inversion (< 6.7 keal/mol), still fast on the NMR time scale. 

There are three unknown concentration terms and three independent equations. Substituting Equation (2.1) and Equation (2.3) into Equation (2.4) yields ... 

One may apply the analogous method described in Section 5.6 and Section 5.7 to solve for the above equations. Substituting k32 = 0 into Equation (5.81) and Equation (5.82) gives the exact solution as ... 

The final boundary condition is expressed by the Nernst equation. Substituting the Sand equation (10.39), together with (10.40) and (10.41) into the Nernst equation... 

Consider, next, the energy equation. Substituting the instantaneous values of the variables into the unsteady form of this equation gives ... 

One name often used to describe this technique is the isolation method. The method of solution relies on one reactant being isolated. The concentrations of all reactants but one are held constant, which will allow you to cancel them in the calculation. We can use the generic rate law equation, substituting the data in for the variables. By setting up a calculation, we can try to solve for m or n ... 

The other important thing to remember is to square the value of Pco because of the coefficient it has in the balanced equation. Substituting the value of K and the value of Pco2 into the equation, we find that ... 

Rearrange and use the molar concentration equation. Substitute in the amount of solute you calculated in step 1. 

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