What are the limitations to the equipartition theorem

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The equipartition theorem has limitations primarily due to the influence of quantum effects, which become significant at temperatures around 1000 K. It is not applicable when energy levels are quantized, as seen in molecular vibrations. Additionally, the theorem assumes that all degrees of freedom contribute equally to the system's energy, which may not hold true in real-world scenarios. The heat capacity of diatomic gases illustrates these limitations, as deviations occur at higher temperatures. Understanding these constraints is crucial for accurate thermodynamic predictions.
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Homework Statement



What are the limitations to the equipartition theorem



The Attempt at a Solution



I have got this gap in my notes i am trying to fill, done some research but couldn't find anything, are there any limitations?
 
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imagemania said:

Homework Statement



What are the limitations to the equipartition theorem

The Attempt at a Solution



I have got this gap in my notes i am trying to fill, done some research but couldn't find anything, are there any limitations?
The theorem only works if the allowable energies are not restricted by quantum effects. Quantum effects dominate for vibrational energies of molecules at temperatures up to about 1000 K. You will notice this in the heat capacity for a diatomic gas, for example.

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