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Related Concept Videos

Kinetic Energy - II00:56

Kinetic Energy - II

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The kinetic energy of a particle is one-half of the product of the particle’s mass and the square of its speed. Note that just as Newton’s second law can be expressed as either the rate of change of momentum or mass multiplied by the rate of change of velocity, so too can the kinetic energy of a particle be expressed in terms of its mass and momentum, instead of its mass and velocity.
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Kinetic Energy - I01:18

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It’s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the direction of the velocity, only its magnitude. At the end of the seventeenth century, a quantity was introduced into mechanics to explain collisions between two perfectly elastic bodies, in which one body makes a head-on collision with an identical body at rest. When they collide, the first body stops, and the second body moves off with the...
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Kinetic Energy for a Rigid Body01:13

Kinetic Energy for a Rigid Body

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Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.
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Energy Diagrams - I01:14

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The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
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Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy03:07

Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

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The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a more quantitative fashion to derive these individual laws.
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Molecular Kinetic Energy01:21

Molecular Kinetic Energy

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The word "gas" comes from the Flemish word meaning "chaos," first used to describe vapors by the chemist J. B. van Helmont. Consider a container filled with gas, with a continuous and random motion of molecules. During collisions, the velocity component parallel to the wall is unchanged, and the component perpendicular to the wall reverses direction but does not change in magnitude. If the molecule’s velocity changes in the x-direction, then its momentum is changed.
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Kinetic energy decomposition scheme based on information theory.

Yutaka Imamura1, Jun Suzuki, Hiromi Nakai

  • 1Research Institute for Science and Engineering, Waseda University, Tokyo, 169-8555, Japan.

Journal of Computational Chemistry
|October 18, 2013
PubMed
Summary

We developed a new method to analyze molecular kinetic energy using information theory. This approach offers insights into chemical bonding and atomic energies for various molecules.

Keywords:
Hirshfeld partitioning • Weizäcker partitioning • kinetic energy density • virial ratioenergy decomposition • Kullback-Leibler information deficiency

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Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Chemical Physics

Background:

  • Understanding molecular behavior requires accurate analysis of kinetic energy.
  • Existing methods for kinetic energy partitioning have limitations.

Purpose of the Study:

  • To propose a novel kinetic energy decomposition analysis (KEDA) grounded in information theory.
  • To establish a framework analogous to Hirshfeld partitioning for electron densities.

Main Methods:

  • Formulating kinetic energy partitioning using Kullback-Leibler information deficiency.
  • Developing a new partitioning scheme for kinetic energy densities.
  • Conducting numerical assessments on ionic and covalent molecules.

Main Results:

  • The proposed KEDA provides chemically intuitive descriptions for ionic and covalent bonding.
  • The method allows for the estimation of atomic energies.
  • A correction using viral ratios refines atomic energy estimations.

Conclusions:

  • The information theory-based KEDA offers a robust approach to analyzing molecular kinetic energy.
  • This method enhances the understanding of chemical interactions and atomic contributions.