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Physics GRE Question

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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
G01
Homework Helper
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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:
  • #3
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I'm really not sure where to start. I guess I'll just post this in a different part of the forum then.
 
  • #4
88
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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
 
  • #5
nicksauce
Science Advisor
Homework Helper
1,272
5
Well the equipartition theorem says that each Degree Of Freedom = 1/2KT. Can you think of why there would be 6 DOF?
 
  • #6
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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...
 
  • #7
nicksauce
Science Advisor
Homework Helper
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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?
 
  • #8
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Total energy for a 1-dimensional harmonic oscillator is (1/2)kx^2, right? And wouldn't that just be one degree of freedom?
 
  • #9
nicksauce
Science Advisor
Homework Helper
1,272
5
Total energy of a 1D SHO is (1/2)kx^2 + (1/2)mv^2...
 
  • #11
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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
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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