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Kinetic energy
About: Kinetic energy is a research topic. Over the lifetime, 14569 publications have been published within this topic receiving 312206 citations.
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TL;DR: In this paper, a mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex, and a quantitative theory of the rates of oxidation reduction reactions involving electron transfer in solution is presented.
Abstract: A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation‐reduction reactions involving electron transfer in solution is presented. The assumption of "slight‐overlap" is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction.
This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over‐all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.
5,265 citations
TL;DR: In this paper, it was shown that two-dimensional turbulence has both kinetic energy and mean square vorticity as inviscid constants of motion, and two formal inertial ranges, E(k)∼e2/3k−5/3/3, where e is the rate of cascade of kinetic energy per unit mass, η is the time taken to reach a cascade of mean square velocity, and k is the kinetic energy of the entire mass.
Abstract: Two‐dimensional turbulence has both kinetic energy and mean‐square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k)∼e2/3k−5/3 and E(k)∼η2/3k−3, where e is the rate of cascade of kinetic energy per unit mass, η is the rate of cascade of mean‐square vorticity, and the kinetic energy per unit mass is ∫0∞E(k) dk. The −53 range is found to entail backward energy cascade, from higher to lower wavenumbers k, together with zero‐vorticity flow. The −3 range gives an upward vorticity flow and zero‐energy flow. The paradox in these results is resolved by the irreducibly triangular nature of the elementary wavenumber interactions. The formal −3 range gives a nonlocal cascade and consequently must be modified by logarithmic factors. If energy is fed in at a constant rate to a band of wavenumbers ∼ki and the Reynolds number is large, it is conjectured that a quasi‐steady‐state results with a −53 range for k « ki and a −3 range for k » ki, up to the viscous cutoff. The t...
2,950 citations
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01 Jan 1978
TL;DR: In this paper, the authors present an overview of the physical properties of Grains and their properties in terms of elastic collisions, grain alignment, and overall equilibrium in a stellar environment.
Abstract: Interstellar Matter-- An Overview. Elastic Collisions and Kinetic Equilibrium. Radiative Processes. Excitation. Ionization and Dissociation. Kinetic Temperature. Optical Properties of Grains. Polarization and Grain Alignment. Physical Properties of Grains. Dynamical Principles. Overall Equilibrium. Explosive Motions. Gravitational Motion. Symbols. Index.
2,462 citations
TL;DR: In this article, two methods of obtaining kinetic parameters from derivative thermoanalytical curves are proposed based on the general form of kinetic formulae and are applicable to general types of reactions governed by a single activation energy.
Abstract: Two methods of obtaining kinetic parameters from derivative thermoanalytical curves are proposed The methods are based on the general form of kinetic formulae and are applicable to general types of reactions governed by a single activation energy One method utilizes the linear relation between peak temperature and heating rate in order to estimate the activation energy, and only the information of the rate of conversion versus the temperature is necessary The other method needs the information of both the conversion and the rate of conversion versus the temperature, and the Arrhenius plot is made for an assumed kinetic mechanism
1,974 citations
TL;DR: In this paper, a non-equilibrium discharge in nitrogen-oxygen mixtures is developed, which almost wholly describes chemical transformations of particles in the cold (200 K
Abstract: A kinetic scheme for non-equilibrium discharge in nitrogen-oxygen mixtures is developed, which almost wholly describes chemical transformations of particles in the cold (200 K
1,558 citations