Why does the heat capacity of solids drop exponentially at low temperatures?

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Discussion Overview

The discussion revolves around the phenomenon of heat capacity in solids, particularly focusing on why it drops exponentially at low temperatures. Participants explore theoretical explanations, referencing models such as the Einstein and Debye models, and seek a conceptual understanding without delving into mathematical derivations.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants reference the Einstein and Debye models to explain the exponential drop in heat capacity at low temperatures.
  • There is a suggestion that the concept of "frozen degrees of freedom" at low temperatures may provide insight into the observed behavior of heat capacity.
  • One participant expresses a desire for a non-mathematical explanation of why heat capacity is very low at low temperatures.
  • Another participant humorously suggests explaining the concept in simple terms, as if to a layperson, to clarify the idea of frozen degrees of freedom.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the explanation for the drop in heat capacity, with multiple viewpoints and interpretations presented regarding the role of degrees of freedom and the applicability of the Einstein and Debye models.

Contextual Notes

The discussion includes assumptions about prior knowledge of heat capacity and the models mentioned, which may limit the clarity of explanations for those unfamiliar with the concepts.

pangru
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According to Einstein (or Debay) model of solids, heat capacity drops exponentially at low temperatures:

300px-Escv.png


question is >> why it changes so dramatically at low temperature
that is physical explanation of this?
 
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Hi,
Don't understand your question -- in the sense that where you found the picture, there also is a derivation of the expression. With a link to Debye for lowest T
Or do you seek an answer like "degrees of freedom are frozen" at low T ?
 
BvU said:
Or do you seek an answer like "degrees of freedom are frozen" at low T ?
yes, something like that :smile:

at low T, heat capacity is very low >> how this could be explained?
without math :biggrin:
 
pangru said:
yes, something like that :smile:

at low T, heat capacity is very low >> how this could be explained?
without math :biggrin:

BvU just did!

Zz.
 
ZapperZ said:
BvU just did!

Zz.
do you mean this? >> degrees of freedom are frozen" at low T
OK. .. and that does frozen degrees of freedom means? :D

Imagine you are Einstein, How would explain this to your grandmother? :D
 
pangru said:
do you mean this? >> degrees of freedom are frozen" at low T
OK. .. and that does frozen degrees of freedom means? :D

Imagine you are Einstein, How would explain this to your grandmother? :D

1. If my grandmother asks me that question, then she would have had some basic knowledge to know the figure she showed me in Post #1. In other words, she would have had to know what "heat capacity" is, what "Debye model" is to describe such heat capacity, the statistical derivation of it, and to know what that figure is saying. This means that she is well-equipped to comprehend the answer.

2. My grandmother was also not a lazy woman. She would have used everything at her disposal to figure out what freezing of the degree of freedom have anything to do with the specific heat curve. She was also pretty sharp to know when an answer to her question was already given and not have missed it this badly.

3. https://www.physicsforums.com/threads/if-you-cant-explain-it-to-your-grandmother.765734/

Zz.
 
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