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Integral from solid state

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Trying to solve this integral

    [tex]\int_0^T \frac{dT'}{T'}\frac{d}{dT'}U(T',V)[/tex]

    where the temperature dependent part of U is

    [tex]\Sigma \frac{h\omega}{\exp(\beta\omega)-1}[/tex]

    3. The attempt at a solution

    using x = hw/T I find that I need to integrate

    [tex]\frac{x^3 \exp(x/k)}{(\exp(x/k)-1)^2 h\omega k}[/tex]

    with limits going to 0 -> inf and T -> hw/T

    I just don't see how with these limits it will work out nicely (the result is used to get the pressure in the harmonic approximation) but I can't find my mistake.
     
  2. jcsd
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