Good Accuracy

Figure 1 compares data reduction using the modified UNIQUAC equation with that using the original UNIQUAC equation. The data are those of Boublikova and Lu (1969) for ethanol and n-octane. The dashed line indicates results obtained with the original equation (q = q for ethanol) and the continuous line shows results obtained with the modified equation. The original equation predicts a liquid-liquid miscibility gap, contrary to experiment. The modified UNIQUAC equation, however, represents the alcohol/n-octane system with good accuracy. 

The average error is around 30%. This formula applies to pure substances and mixtures. For pure hydrocarbons, it is preferable to refer to solubility charts published by the API if good accuracy is required. 

An experimental activity on the stress measurement of a pressure vessel using the SPATE technique was carried out. It was demontrated that this approach allows to define the distribution of stress level on the vessel surface with a quite good accuracy. The most significant advantage in using this technique rather than others is to provide a true fine map of stresses in a short time even if a preliminary meticolous calibration of the equipment has to be performed. 

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

The preferable theoretical tools for the description of dynamical processes in systems of a few atoms are certainly quantum mechanical calculations. There is a large arsenal of powerful, well established methods for quantum mechanical computations of processes such as photoexcitation, photodissociation, inelastic scattering and reactive collisions for systems having, in the present state-of-the-art, up to three or four atoms, typically. " Both time-dependent and time-independent numerically exact algorithms are available for many of the processes, so in cases where potential surfaces of good accuracy are available, excellent quantitative agreement with experiment is generally obtained. In addition to the full quantum-mechanical methods, sophisticated semiclassical approximations have been developed that for many cases are essentially of near-quantitative accuracy and certainly at a level sufficient for the interpretation of most experiments.These methods also are com-... 

Organic molecule calculations can be done routinely to good accuracy on workstation-class hardware. It is advisable to examine tabulations of results in order to choose a method with acceptable accuracy and computational time for the property of interest. The trend toward having microcomputer versions of computational chemistry codes is making calculations on small organic molecules even more readily accessible. 

A titration method for primary and secondary nitroparaftins uskig hypochlorite gives good accuracy ( 0.1%) (84). It is based on the foUowkig equation ... 

The form of the equations here is given to provide good accuracy when many terms are used and to provide the variances of the parameters. Another form of the equations for a and b is simpler, but is sometimes inaccurate unless many significant digits are kept in the calculations. The minimization ofx" when Gj is the same for all i gives the following equations for a and b... 

Physically the cutting-corner trajectory implies that the particle crosses the barrier suddenly on the time scale of the slow -vibration period. In the literature this approximation is usually called sudden , frozen bath and fast flip approximation, or large curvature case. In the opposite case of small curvature (also called adiabatic and slow flip approximation), coj/coo < sin tp, which is relevant for transfer of fairly heavy masses, the MEP may be taken to a good accuracy to be the reaction path. 

Interestingly, the correction factor is to a good accuracy approximated by the Wigner formula (2.15) and it is practically independent of friction [Hanggi 1986], by contrast with the relatively strong dependence of on r. ... 

Now we make the usual assumption in nonadiabatic transition theory that non-adiabaticity is essential only in the vicinity of the crossing point where e(Qc) = 0- Therefore, if the trajectory does not cross the dividing surface Q = Qc, its contribution to the path integral is to a good accuracy described by adiabatic approximation, i.e., e = ad Hence the real part of partition function, Zq is the same as in the adiabatic approximation. Then the rate constant may be written as... 

Figure 8 Quantitaftive high depth resolution profile of O and N in a Ti metal film on Si, using electron-gas SNMS in the direct bombardment mode. Both O and N are measured with reasonably good sensitivity and with good accuracy both at the heavily oxidized surface and at the Ti/Si interface.

This shows that the presence of air in the gas phase has a very small influence on the vapor pressure of water. Repeating the same calculation procedure for other temperatures, we can show that the vapor pressure of water can with good accuracy be taken from the vapor pressure tables for saturated water (water has the same pressure as water vapor when they are in equilibrium), as though there were no air in the gas phase. So the vapor pressure of water is with good accuracy also in this case just a function of temperature, and Eq. (4.97) is valid. New vapor pressure tables will not be needed for calculations with humid air. 

First we note that with fairly good accuracy it is valid that... 

The measurement range for platinum is -200 to +800 °C, for nickel -50 to +250 °C, and for copper -50 to +200 °C. The advantages are good accuracy, almost linear characteristics, and stability. A disadvantage is the small change of resistance with temperature, which requires a high sensitivity from the rest of the measurement equipment. 

It must be noted that LCA is a fairly new approach, at least for use in design contexts. There is a comparatively long tradition of compiling site-specific LCI data with reasonably good accuracy however, these LCA methods are expensive and time-consuming. 

The equation proposed by Churchill [8] is also a direct solution with good accuracy [7]. 

To properly handle the changing composition relationships it is almost essential to utilize some electronic computer techniques if good accuracy is to be achieved. Even three component systems become tedious using desk size electronic calculators without significant internal memory. Computers can be well programmed to handle the complexities of trial and check for convergence to a preset acceptable limit. 

This applies with good accuracy for single wheels and for the overall multistage compressor. This is extremely useful in determining polytropic efficiency Values of n may be read from Figure 12-63 for approximate actual inlet flow capacity cfm, to the suction of the... 

One of the major advantages of plastics optical elements is that they can me made by different processes such as injection molding, casting, or extrusion to good accuracy at low cost. Some glass lenses are pressed from hot glass but the majority of the lenses... 

Near room temperature, Ea is roughly 2.5 kJ mol-1 (or 0.6 kcal mol-1) larger than AW. These treatments assume that both AW and Ea are temperature-independent. That is, the temperature profiles according to Eqs. (7-3) and (7-5) are both linear. Most data (but not all, see Sections 7.2 and 7.3) conform to that model, although Eq. (7-8) says that, literally, AW and Ea cannot both be temperature-independent constants. In fact, the RT term in Eq. (7-8) is usually much smaller than the others. Thus, the temperature independence of both Ea and AW can in practice be sustained with good accuracy. The choice of the T to use in Eq. (7-8) is not crucial—a midpoint value of the experimental range does the job. In the same vein, the value of AS and A are related by (see Problem 7.4)... 

Equation (7.17) introduces a number of new parameters, although physical properties such as AHj( should be available. If aU the parameters are all known with good accuracy, then the introduction of a heat balance merely requires that the two parameters ko nd EjRg=Tact be used in place of each rate constant. Unfortunately, parameters such as have 20% error... 

If kiAi is known with good accuracy, it may be possible to back out the intrinsic kinetics using the methods of Section 7.1. Knowing the intrinsic kinetics may enable a scaleup where kiAj(af — ai) is dilferent in the large and small units. However, it is better to adjust conditions in the pilot reactor so that they are identical to those expected in the larger reactor. Good pilot plants have this versatility. The new conditions may give suboptimal performance in the pilot unit but achievable performance in the full-scale reactor. 

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