Expectation error

Computer Project 5-2, The result for hydrogenation of cyclopentene differs from that foi ethene by an amount that is well outside the expected error foi MM calculations. Suggest a reason for this. 

Expected errors for this method are 4-5 percent. At higher pressures, a pressure correction using Eq. (2-130) may be used. The mixture is treated as a hypothetical pure component with mixture critical properties obtained via Eqs. (2-5), (2-8), and (2-17) and with the molecular weight being mole-averaged. 

Expected errors are less than 10 percent when q is less than 5 and within 20 percent when q is greater than 5. 

Would you expect errors of the same magnitude when sampling anisokinetically at 80% of stack velocity as when sampling anisokinetically at 120% of stack velocity Explain. 

Our objective is to minimize the expected error, E, between the true coefficients and our estimates. 

A reaction rate constant can be calculated from the integrated form of a kinetic expression if one has data on the state of the system at two or more different times. This statement assumes that sufficient measurements have been made to establish the functional form of the reaction rate expression. Once the equation for the reaction rate constant has been determined, standard techniques for error analysis may be used to evaluate the expected error in the reaction rate constant. 

We can clearly see on this figure a spread of the [Sr/Ba] ratio. This spread is larger than the expected errors, confirming the results found by previous authors (see Honda et al. 2004 [2] and reference therein). Such a large scatter found in the [Sr/Ba] ratio can be explained by inhomogeneous models of chemical evolution which predict the existence of such a large variation (see for example Ishimaru et al. 2004). 

The nonzero spectral residuals in step (d) indicate a problem (no noise was added to the data and therefore zero residuals are expected). Tlie concentration residuals are also larger than the expected errors (again zero noise), further indicating a problem. In summary, the classical approach has failed to produce the correct concentration values, but the diagnostic tools flagged a problem. 

The difference between the two means is a factor of 2.2. This value is larger than the expected error of equation (9.7). Thus, a channel with a variation in slope and cross section along its length will have a higher K2 value computed from arithmetic means than an otherwise equivalent channel that does not have variation in slope and cross section. It may not be a coincidence that Moog and Jirka s calibration of Thackston and Krenkel s equation for flumes is an adjustment by a factor of 0.69 to represent held measurements. We need to pay attention to the impact that these variations in natural rivers and streams have on our predictive equations for K2. 

An evaluation of the expected errors in estimated hourly deposition was made from radiochemical data for three rainstorms. The results showed that the calculated values agreed with the measured values to within a factor of two, and the estimated and actual depositions rapidly approached the same value as the time period considered was increased. In general, for intervals of 6 hours, the errors do not exceed 30%. 

Figure 9. The ratio of the expected error in a first-order rate constant to the expected error with no background for various ratios of the background to the initial decay rate.

The focus of the previous section was to estimate the expected error from assuming the zonal invariance of mean values of moist static energy. This expected error contributes to the total expected error of a paleoaltitude estimate. Before proceeding to the next section (inferring paleoclimate from plant fossils), we examine the zonal invariance assumption as applied in the mean annual temperature approach to paleoaltimetry. Based on the initial method of Axelrod (1966), paleoaltitudes can be estimated by comparing mean annual temperature differences using the formula... 

Before estimating the total expected error in paleoaltitude, we estimate the contribution, 560 m, from the uncertainty, aH=5.5 kJ/kg, in predicting mean annual enthalpy. We estimate a comparable error, 390 m with y, = 5.9 K/km, for the mean annual temperature approach. Clearly, this latter error is an underestimate, because it is dependent on the choice of yt whereas the former error will remain constant. 

We obtain an expected error for the paleoaltitude by combining the expected errors from the zonal asymmetry, ah = 4.5 kJ/kg, and from the botanical inferences of enthalpy, [Pg.188]

We believe that this lower error estimate results partially from the use of altitude to estimate enthalpy at plant sites for which we have no humidity data. For such sites, we relied on meteorological estimates of h and heights of sites to infer H causing an unavoidable dependence of the value of H on altitude. The lower error estimate of 620 m implies that the error estimate of 910 m calculated from expected errors in the components is robust. 

The surface distribution for mean annual h results from two properties of atmospheric flow conservation of h following the large-scale flow and the maintenance of the vertical profile of h by convective processes. These features of the climate system allow one to quantify the expected errors for assuming that mean annual h is invariant with longitude and altitude for the present-day distribution. Forest et al. (1999) examined the distribution and calculated the expected error from assuming zonal invariance to be 4.5 kJ/kg for the mean annual climate. This error translates to an altitude error of 460 m and is compared with an equivalent error of 540 m from the mean annual temperature approach. Moreover, the uncertainty of the terrestrial lapse rate, y(, increases the expected error in elevation as elevations increase, particularly when small lapse rates are assumed. 

All the estimations of vapor pressure of liquids discussed above depend on the accuracy of the enthalpy of vaporization. Use of the Fishtine expression gives results that are not expected to be more accurate that 3% for AH ,. That implies that, even if the equation used to describe the temperature dependence of vapor pressure were exact, we still would expect no better than 3% accuracy in the estimated value of log (P /Pfc) the lower the vapor pressure the greater the expected error. For a vapor pressure of 10 kPa, the expected error is 7% for 100 Pa, 23% for 1 Pa, 41% and for 10 mPa, 62%. 

In the case of 1,2-diazetidines, in which two nitrogens are bonded to each other, there was a marked difference in the enthalpy of formation between the as- and /ram-isomer. As expected, the more sterically hindered f/r-isomer had a slightly higher enthalpy of formation, about 20-30 kj mol-1. Similarly, for 1,3-diazetidines, although the f/r-isomer had a slightly higher enthalpy of formation than the tram-isomer, the difference (1-3 kj mol-1) is probably within the expected error limits of the method. 

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