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In physical chemistry and chemical engineering, extent of reaction is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached.
In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken , who introduced this method in 1926. [ 1 ]
Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
Equation (2) is the means to get from the measured quantities L, T, and θ to the derived quantity g. Note that an alternative approach would be to convert all the individual T measurements to estimates of g, using Eq(2), and then to average those g values to obtain the final result.
To calculate the pressure drop in a given reactor, the following equation may be deduced: = + | |. This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation, which describes laminar flow of fluids across packed beds via the first term on the right hand side.
It is generally a good practice to convert it to {} format, but coherency must be respected; that is, such a conversion must be done in a whole article, or at least in a whole section. Moreover, such a conversion must be identified as such in the edit summary, and making other changes in the same edit should be avoided.
Modern improvements on Brent's method include Chandrupatla's method, which is simpler and faster for functions that are flat around their roots; [3] [4] Ridders' method, which performs exponential interpolations instead of quadratic providing a simpler closed formula for the iterations; and the ITP method which is a hybrid between regula-falsi ...
Only one equation of state will not be sufficient to reconstitute the fundamental equation. All equations of state will be needed to fully characterize the thermodynamic system. Note that what is commonly called "the equation of state" is just the "mechanical" equation of state involving the Helmholtz potential and the volume: