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Dulong Petit derivation.How do we get this formula?E=kT

  1. Dec 4, 2013 #1
    Dulong Petit use energy,E=$k_B$T and the probability distribution as f(E)=1.
    Internal energy,u=3N$k_B$T
    $$C_v=∂u/∂T=3NkT$$
    Three there because there is 3 modes in each atom.
    Then my question is why do we use E=kT?
    I understand 1 atom has 3 degree of freedom,and 1 freedom has kT/2.
    A molecule has 5 degree of freedom at room temperature. Then why E=kT? Comes from?
    Thanks
     
  2. jcsd
  3. Dec 4, 2013 #2

    DrDu

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    kT/2 holds for a translational degree of freedom. For a vibration, you have rather kT. As an atom in a solid will vibrate in the cage formed by its neighbours, we get 3kT.
     
  4. Jan 14, 2014 #3
    Is that because in an atom in a solid, there are 6 neighbors so, (6/2)${k_B}$ T
     
  5. Jan 14, 2014 #4
    No, this is not true in general and this is not the reason for the 3 in the formula even when it is true (simple cubic crystals). In most metals there are 8 or 12 nearest neighbors, for example.

    An atom in a crystal has both kinetic and potential energy. In a gas it has only kinetic.
    This is the reason for the different formulas.
     
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