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Testing Physics GRE Question

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  1. Jun 7, 2008 #1
    I'm studying for the Physics GRE and I came across this question. The correct answer is D, but I'm not sure quite how to do it. Any help would be greatly appreciated!

    A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of the oscillator is

    (A) (1/2)kT
    (B) kT
    (C) (3/2)kT
    (D) 3kT
    (E) 6kT
     
  2. jcsd
  3. Jun 7, 2008 #2

    G01

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    You need to show work in order to get help here. What have you tried so far? What concepts, etc. apply? What are your thoughts?
     
    Last edited: Jun 7, 2008
  4. Jun 7, 2008 #3
    I'm really not sure where to start. I guess I'll just post this in a different part of the forum then.
     
  5. Jun 7, 2008 #4
    I'm studying for the Physics GRE and I came across this question. The correct answer is D, but I'm not sure quite how to do it. Any help would be greatly appreciated!

    A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of the oscillator is

    (A) (1/2)kT
    (B) kT
    (C) (3/2)kT
    (D) 3kT
    (E) 6kT
     
  6. Jun 7, 2008 #5

    nicksauce

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    Well the equipartition theorem says that each Degree Of Freedom = 1/2KT. Can you think of why there would be 6 DOF?
     
  7. Jun 7, 2008 #6
    That's exactly what I was thinking. It seems like the problem basically states that there are 3 degrees of freedom, which would yield an answer of (3/2)kT. However, the answer guide clearly says that the answer is 6kT (this is from an official GRE practice test).

    I can't think of why there would be 6 degrees of freedom...
     
  8. Jun 7, 2008 #7

    nicksauce

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    Ok let's go back to the 1 dimensional harmonic oscillator... How would you write its total energy? How many DOF is that?
     
  9. Jun 7, 2008 #8
    Total energy for a 1-dimensional harmonic oscillator is (1/2)kx^2, right? And wouldn't that just be one degree of freedom?
     
  10. Jun 7, 2008 #9

    nicksauce

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    Total energy of a 1D SHO is (1/2)kx^2 + (1/2)mv^2...
     
  11. Jun 8, 2008 #10
  12. Jun 9, 2008 #11
    Acording to the Equipartition Theorem, there is a [itex]kt/2[/itex] contribution to the energy from each degree of quadratic freedom in the Hamiltonian. In equation form, the average total energy is [itex]<E> = skT[/itex], where s is the degrees of freedom.

    What is the expression for the Hamiltonian for any n-dimensional 1-particle system?
     
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