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Limits: Evaluating a term

  1. Jan 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Please take a look at this expression, where T is our variable (it represents temperature):

    [tex]
    C_v = 2\left( {\frac{{\hbar \omega }}{T}} \right)^2 \frac{{\exp \left( {\frac{{\hbar \omega }}{T}} \right)}}{{\left( {\exp \left( {\frac{{\hbar \omega }}{T}} \right) - 1} \right)^2 }}.
    [/tex]

    I have to evaluate this for [itex]T \rightarrow 0[/itex]. I would use L'Hopital, but isn't there an easier way? Because when I differentiate the nominator (the top), then I will end up with an expression like the original nominator, which wont help me.

    Thanks in advance.

    Sincerely,
    Niles.
     
  2. jcsd
  3. Jan 20, 2009 #2
    Thermal physics correct?

    I had some sort of this question, it goes like this:
    change variables, to dimensionless i.e x=hbar*w/T
    so you now evaluate:
    [tex]lim_{x\leftarrow \infty} 2x^2(\frac{e^x}{(e^x-1)^2})[/tex]
    Other than L'hopital twice there isn't any other approach.
     
  4. Jan 20, 2009 #3
    Yeah, thermal physics :smile:

    Thanks!
     
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