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lekhnath acharya
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 « Embed this message on: November 16, 2004, 01:45:05 pm »

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important knoeledge
reissner
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 « Embed this message Reply #1 on: August 16, 2005, 06:35:47 pm »

As I write this, questions arise. Please correct me in responses.

Think of a "degree of freedom" as a coordinate. A point particle has three (x,y,z), two point particles have 6, etc. A finite rigid sphere has six, three coordinates of the center of mass and two angular coordinates (polar, azimuthal), pertaining to rotation of the sphere.

Nature is thought to tell us how many degrees of freedom there are. The equipartition theorem was frequently used in the nineteenth century-- 1/2 kT of kinetic energy with each degree of freedom associated with motion. When experiment suggested "the count was off" great discoveries (quantum mechanics!) were made.

Think about a diatomic molecule. Here the count is three degrees of freedom for translation, two for rotation. The bond vibration is "frozen out," and the spin parallel to the bond axis is "inactive", essentially becase the moment of inertia is no huge.

When we count 3N - 5 degrees of freedom for an N-nucleus molecule, the 5 omitted are three translations of the COM and two rigid body rotations.

John E. Reissner
The University of North Carolina at Pembroke
reissner@gmail.com
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John E. Reissner
Professur emeritus, Chamistry and Physics
UNCP
john.reissner@uncp.edu
reissner@gamail.com
Janus20
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 « Embed this message Reply #2 on: September 30, 2005, 04:16:53 pm »

A monotomic gas of say Argon has an adiabatic expansion index of 5/3 say 1.66.

This can be defined as .. (3 modes of spin ENERGY + 2 modes of straight line vibrational POWER) / 3 degrees of spin ENERGY.

In thermodynamic gas terms 1.66 = (Work Done + internal energy)/(internal energy).

..................................................(2+3)/(3)
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serhanmete
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 « Embed this message Reply #3 on: December 24, 2005, 01:23:52 am »

In addition to all these useful informations on equipartition theorem, it works well in high temperatures (or more correctly classical limit), but low temperatures need corrections. The picture in general is somewhat more complicated, for solids for example one should examine low temperatures, high temperatures and medium temperatures (i.e. via Debye's Model, namely "Debye's interpolation formula" as Landau says) seperately.
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Know the universe as yourself and you can live anywhere in comfort. ...Lao Tzu (570-490 BC)