Does Quantum Molar Internal Energy Converge to Classical at High Temperatures?

[plonker]

Homework Statement

I'm so confused please help :\

Show that the contribution to the total energy from molar internal energy Um reverts to the classical expression at high T.

Homework Equations

Classical: Um = 3NakT Quantum Um = 3NAhv/e^(hv/kT)-1

The Attempt at a Solution

Manipulating variables- E=hv
Quantum rearranging: hv/kT= ln(3Nahv)-ln(Um)
Very confused on what is meant by total energy though. Is that supposed to be E+Um?

 

[Bryson]

Pardon my ignorance (I have never heard of this in all my years in physics), but what is Um?

 

[plonker]

My teacher said it was "internal energy, U" but while in the context of the failures of classical physics in terms of heat capacities. Apparently Einstein calculated the contribution of the oscillation of the atoms to the total molar energy of metal and obtained the quantum equation above in place of the classical one? I'm so nervous for this course now :\

 

[Bryson]

I am assuming that for high T you can manipulate e^{\frac{h \nu}{k T}}. Try this.