1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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):

    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 }}.

    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.

  2. jcsd
  3. Jan 20, 2009 #2


    User Avatar
    Gold Member

    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:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook