Equipartition theorem: Difference between revisions
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The Theorem of the Equipartition of [[energy]] is a construct of [[classical mechanics]] and was first introduced by [[James Clerk Maxwell]] (1831-1879). It | The Theorem of the Equipartition of [[energy]] is a construct of [[classical mechanics]] and was first introduced by [[James Clerk Maxwell]] (1831-1879). It states: | ||
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'''"Every kind of [[molecule]] has a particular number of [[degrees of freedom]] ''f'' which are independent ways in which it can store energy. Each such degree of freedom has associated with it, on [[average]], an energy of <math> \frac{1}{2}\ kT</math> per molecule or <math> \frac{1}{2}\ RT</math> per [[mole]], where ''k'' is the [[Boltzmann constant]], ''R'' is the [[molar gas constant]] and ''T'' is [[temperature]] in [[kelvin]]."'''<ref>Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p591</ref>. | '''"Every kind of [[molecule]] has a particular number of [[degrees of freedom]] ''f'' which are independent ways in which it can store energy. Each such degree of freedom has associated with it, on [[average]], an energy of <math> \frac{1}{2}\ kT</math> per molecule or <math> \frac{1}{2}\ RT</math> per [[mole]], where ''k'' is the [[Boltzmann constant]], ''R'' is the [[molar gas constant]] and ''T'' is [[temperature]] in [[kelvin]]."'''<ref>Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p591</ref>. | ||
Revision as of 09:42, 5 May 2009
The Theorem of the Equipartition of energy is a construct of classical mechanics and was first introduced by James Clerk Maxwell (1831-1879). It states:
"Every kind of molecule has a particular number of degrees of freedom f which are independent ways in which it can store energy. Each such degree of freedom has associated with it, on average, an energy of per molecule or per mole, where k is the Boltzmann constant, R is the molar gas constant and T is temperature in kelvin."[1].
Degrees of freedom can be translational, rotational, or oscillatory.
Simple particles such as a monoatomic gas for instance will have three degrees of freedom, one for each dimension of potential movement. More complex molecules can have more degrees of freedom.
- ↑ Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p591