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Want to make sure I'm understanding equipartition and statistical mechanics correctly

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Part a: A monoatomic ideal gas is confined to move in two dimensions. What is Cv for this gas?

    Part b: Consider a system composed of N independent harmonic oscillators in two dimensions. What is Cv for the system?


    2. Relevant equations
    Cv = ∂U/∂T
    U = (number of degrees of freedom)(1/2 NAkBT = (number of degrees of freedom)(1/2)RT


    3. The attempt at a solution

    I'm not very confident about this:

    Part a: Since the gas is monatomic, it only has translational degrees of freedom, and it is given that these are restricted to two.

    (2)(1/2)RT = RT and Cv = R

    Part b: Since it's a harmonic oscillator, there's a degree of freedom for U and K for each dimension, so 4 degrees of freedom, and Cv = 2R? I'm not sure what to do with the N though, since it's an average, it shouldn't affect the Cv? Or am I misunderstanding?
     
  2. jcsd
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