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The equation was derived by Kozeny (1927) [1] and Carman (1937, 1956) [2] [3] [4] from a starting point of (a) modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and (b) Poiseuille's law describing laminar fluid flow in straight, circular section pipes.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
The binding constant, or affinity constant/association constant, is a special case of the equilibrium constant K, [1] and is the inverse of the dissociation constant. [2] It is associated with the binding and unbinding reaction of receptor (R) and ligand (L) molecules, which is formalized as:
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
The value of the equilibrium constant for the formation of a 1:1 complex, such as a host-guest species, may be calculated with a dedicated spreadsheet application, Bindfit: [4] In this case step 2 can be performed with a non-iterative procedure and the pre-programmed routine Solver can be used for step 3.
The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation: = ‡ where is the rate constant, ‡ is the Gibbs energy of activation, is the transmission coefficient, is the Boltzmann constant, is the temperature, and is the Planck constant.
Step is based on bodies and forces placed by the user: Bodies range from tiny particles to huge polygons, and each body has unique properties that influence the outcome of the simulation, such as mass and velocity, and their derivations such as kinetic energy.
Thermodynamic equilibrium is characterized by the free energy for the whole (closed) system being a minimum. For systems at constant temperature and pressure the Gibbs free energy is minimum. [9] The slope of the reaction free energy with respect to the extent of reaction, ξ, is zero when the free energy is at its minimum value.