Quantum Um vs Classical Um

1. Sep 18, 2013

plonker

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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?

Last edited: Sep 18, 2013
2. Sep 18, 2013

Bryson

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

3. Sep 18, 2013

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 :\

4. Sep 18, 2013

Bryson

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