Molecule Movement Explained
"Molecule movement" exists as a variety of components. The translational movement of molecules as complete units in three-dimensional space is one major component. Other components include rotations and vibrations of all or part of a molecule. This kind of molecular movement is explainable using classic thermodynamics theory.
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Total Energy
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Molecules can be visualized as very tiny, elastic billiard balls. If a person holds a billiard ball up at shoulder height, the billiard ball is not moving, yet it has the potential to move if let go. It thus has "potential" (stored) energy. Release the ball, and some of its potential energy becomes "kinetic energy" (energy related to motion). The ball moves. Potential energy will be disregarded in this discussion, however, its existence should be noted, as it is the other component that contributes to the total energy.
Kinetic energy is not merely a vague and descriptive term. Kinetic energy can be quantified. The formula that does that is,
1) E = ½ mv²,
where "E" is kinetic energy, m is the mass of the "billiard ball" or molecule, and "v" is the velocity at which it travels.
Total Kinetic Energy
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Molecules under most circumstances are found in very large numbers. Hence, the formula for kinetic energy for a bulk substance becomes,
2) E(tot) = N₁MV₁² + N₂MV₂² + N₃MV₃²+ ...
where molecules of velocity (1) exist in quantity (1), molecules of another velocity (2) exist in quantity (2), and so on. The E(tot) then represents the total kinetic energy of the complete collection of molecules.
From the above equation, it is obvious that if the kinetic energy of a collection of molecules is increased, its overall velocity increases.
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Average Kinetic Energy
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Even though the energies of the particles differ one from another, it is a simple thing to determine the average kinetic energy of the particles. The equation is,
E(av) = E(tot) / N(tot), or,
3) E(av) = (N₁MV₁² + N₂MV₂² + N₃MV₃²+ ... ) / (N₁ + N₂ + N₃ + ... ).
Relationship to Temperature
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In increasing the average kinetic energy of a collection of molecules (sometimes called a "system"), the temperature of the system also increases.
Although the principles apply to solids, liquids, gases, and plasmas of all sorts, only the example of an ideal, monatomic gas will be considered here.
Kinetic Theory of Gases
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The kinetic theory of gases incorporates the "Boltzmann-Maxwell distribution". This describes the probable number of molecules at any particular velocity in a system with a given average kinetic energy. Thus, it elucidates equation three, above.
The mathematics involved produces the relationship,
4) E(av) = 3/2 kT,
where k = R/n and R is the Ideal Gas Constant, and n is Avogadro's number.
Energy, Motion and Temperature
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Thus the relationship between energy, molecular movement and temperature, as well as the relevant mathematics involved is explained. Increasing energy, such as in the form of heat, increases molecular movements, which in turn raises the temperature of a system, measurable by a thermometer.
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References
Resources
- Photo Credit Maxwell-Boltzmann Distribution for Noble Gases; Pdbailey/Commons.wikimedia.org
