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The steady state approximation, [1] occasionally called the stationary-state approximation or Bodenstein's quasi-steady state approximation, involves setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero so that the kinetic equations can be simplified by setting the rate of formation of the intermediate equal to the rate of its destruction.
Steady state is also used as an approximation in systems with on-going transient signals, such as audio systems, to allow simplified analysis of first order performance. Sinusoidal Steady State Analysis is a method for analyzing alternating current circuits using the same techniques as for solving DC circuits.
For the overall reaction, the rates of change of the concentration of the intermediates •CH 3 and CH 3 CO• are zero, according to the steady-state approximation, which is used to account for the rate laws of chain reactions. [6] d[•CH 3]/dt = k 1 [CH 3 CHO] – k 2 [•CH 3][CH 3 CHO] + k 3 [CH 3 CO•] - 2k 4 [•CH 3] 2 = 0
The rate equation for the rate of formation of product P may be obtained by using the steady-state approximation, in which the concentration of intermediate A* is assumed constant because its rates of production and consumption are (almost) equal. [8] This assumption simplifies the calculation of the rate equation.
The equation or its variable is said to be stable if from any set of initial conditions the variable's limit as time goes to infinity exists; this limit is called the steady state. Difference equations are used in a variety of contexts, such as in economics to model the evolution through time of variables such as gross domestic product, the ...
The steady-state heat equation for a volume that contains a heat source (the inhomogeneous case), is the Poisson's equation: − k ∇ 2 u = q {\displaystyle -k\nabla ^{2}u=q} where u is the temperature , k is the thermal conductivity and q is the rate of heat generation per unit volume.
Regardless of the approximation applied, multiple independent parameters (k 1, k −1, and k 2 in the case of steady-state; k 2 and K 1 in the case of pre-equilibrium) are required to define the system. While one could imagine constructing multiple equations to describe the unknowns at different concentrations, when the data is obtained from a ...
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