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Homework Help: Degrees of Freedom

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data

    I want to know why the average kinetic energy FOR A SOLID is 3/2*RT.

    2. Relevant equations

    For every degree of freedom = 1/2*RT
    Possible Degrees of freedom are:
    Translation, rotation, vibration

    3. The attempt at a solution

    In a solid, I am certain there is vibrational energy because of the spring like forces from interacting particles in a lattice. This would only account for 1 degree of freedom so far.
    I am against saying there is any translation or rotation because the particles are fixed in their respective positions since it is a solid.

    So I am confused why the average kinetic energy is 3/2*RT when I see it as 1/2*RT.

    (1 degree of freedom) x 1/2*RT = 1/2*RT
  2. jcsd
  3. Mar 4, 2013 #2


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    2017 Award

    Staff: Mentor

    You can have vibrations in 3 dimensions.
    Every vibration dimension corresponds to 2 degrees of freedom (potential and kinetic energy), so the result is 3RT, for an appropriate temperature range and in a crystal.
  4. Mar 4, 2013 #3
    Thanks a lot!
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