- #1

Amok

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So, I can't really find this limit:

[tex]\lim_{T \to \infty} \ 3Nk {(\epsilon/kT)}^2 \frac{e^{(\epsilon/kT)}}{{(e^{(\epsilon/kT)}-1)}^2} [/tex]

This is actually the formula for the specific heat of an Einstein solid, which is pretty easy to derive but I haven't been able to calculate the limit to show it becomes Dulong-Petit at hight temperatures. Maybe I've been missing something simple... I don't see how you could use l'Hopital's rule.

note: I wasn't sure whether I should post this in one of the physics forums, but I figured it's more of a calculus problem at this point.

[tex]\lim_{T \to \infty} \ 3Nk {(\epsilon/kT)}^2 \frac{e^{(\epsilon/kT)}}{{(e^{(\epsilon/kT)}-1)}^2} [/tex]

This is actually the formula for the specific heat of an Einstein solid, which is pretty easy to derive but I haven't been able to calculate the limit to show it becomes Dulong-Petit at hight temperatures. Maybe I've been missing something simple... I don't see how you could use l'Hopital's rule.

note: I wasn't sure whether I should post this in one of the physics forums, but I figured it's more of a calculus problem at this point.

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