Difference between revisions of "Equipartition"

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(New page: {{stub-general}} '''Equipartition''' usually refers to the fact that in classical statistical mechanics each degree of freedom that appears quadratically in the energy (Hamiltonian) has ...)
 
 
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'''Equipartition''' usually refers to the fact that
 
'''Equipartition''' usually refers to the fact that
in classical statistical mechanics each degree of freedom that appears
+
:in classical statistical mechanics each degree of freedom that appears quadratically in the energy (Hamiltonian) has an average value of <math>\frac{1}{2}k_B T</math>, where <math>k_B T</math> is the  [[thermal energy]].
quadratically in the energy (Hamiltonian) has an average value of <math>\frac{1}{2}k_B T</math>,
 
where <math>k_B T</math> is the  [[thermal energy]].
 
 
Thus, the thermal energy is shared equally ("equipartitioned") by all these degrees of freedom.
 
Thus, the thermal energy is shared equally ("equipartitioned") by all these degrees of freedom.
 
This is a consequence of the ''equipartition theorem'', which is very simple mathematically. As an
 
This is a consequence of the ''equipartition theorem'', which is very simple mathematically. As an
 
immediate corollary, the translational energy of a molecule must equal <math>\frac{3}{2}k_B T</math>,
 
immediate corollary, the translational energy of a molecule must equal <math>\frac{3}{2}k_B T</math>,
 
since translations are described by three degrees of freedom.
 
since translations are described by three degrees of freedom.
 +
 +
For elastic waves, '''equipartition''' refers to the fact that the average potential and kinetic energies are equal (and therefore equal to half the total energy, which is thereby "equipartitioned".)
 
[[category: classical thermodynamics]]
 
[[category: classical thermodynamics]]
 
[[category: statistical mechanics]]
 
[[category: statistical mechanics]]

Latest revision as of 13:51, 7 May 2008

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Equipartition usually refers to the fact that

in classical statistical mechanics each degree of freedom that appears quadratically in the energy (Hamiltonian) has an average value of \frac{1}{2}k_B T, where k_B T is the thermal energy.

Thus, the thermal energy is shared equally ("equipartitioned") by all these degrees of freedom. This is a consequence of the equipartition theorem, which is very simple mathematically. As an immediate corollary, the translational energy of a molecule must equal \frac{3}{2}k_B T, since translations are described by three degrees of freedom.

For elastic waves, equipartition refers to the fact that the average potential and kinetic energies are equal (and therefore equal to half the total energy, which is thereby "equipartitioned".)