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

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Homework Help Overview

The discussion revolves around the relationship between quantum molar internal energy and classical expressions at high temperatures, specifically examining how the quantum expression converges to the classical one as temperature increases.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to manipulate variables related to quantum and classical expressions for internal energy. Questions are raised about the definition of total energy and the specific meaning of molar internal energy (Um). There is also a suggestion to consider the behavior of the exponential term at high temperatures.

Discussion Status

The discussion is ongoing, with participants expressing confusion about the concepts and terminology involved. Some guidance has been offered regarding the manipulation of variables, but no consensus has been reached on the definitions or implications of the terms used.

Contextual Notes

There is a mention of the context of classical physics failures in terms of heat capacities and the historical perspective of Einstein's contributions to the topic, indicating a potential gap in foundational knowledge among participants.

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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?
 
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Pardon my ignorance (I have never heard of this in all my years in physics), but what is Um?
 
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 :\
 
I am assuming that for high T you can manipulate [itex]e^{\frac{h \nu}{k T}}[/itex]. Try this.
 

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