What is the significance of heat capacity at extreme temperatures?

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Discussion Overview

The discussion revolves around the significance of heat capacity at extreme temperatures, particularly focusing on the behavior of heat capacity as temperature approaches zero and infinity. Participants seek to develop a deeper intuition about heat capacity in relation to internal energy, entropy, and microstates, as well as its implications for solid materials at absolute zero.

Discussion Character

  • Exploratory, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant defines heat capacity as the change in internal energy with temperature and seeks a more intuitive understanding of its significance, particularly in terms of disorder and microstates.
  • Another participant suggests expressing heat capacity in terms of entropy and temperature, hinting at a relationship that could provide further insight.
  • A different participant derives a relationship involving heat capacity, temperature, and entropy but expresses uncertainty about its usefulness in gaining new insights.
  • One participant questions why solid materials exhibit a heat capacity of zero at absolute zero, indicating a desire for intuitive explanations related to material properties.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the intuitive understanding of heat capacity at extreme temperatures, and multiple viewpoints and questions remain unresolved.

Contextual Notes

Participants express uncertainty about the implications of heat capacity being zero at extreme temperatures and the relationship between heat capacity, entropy, and internal energy. There are also unresolved aspects regarding the derivation of equations and their interpretations.

Who May Find This Useful

This discussion may be useful for students and researchers interested in thermodynamics, particularly those exploring the concepts of heat capacity, entropy, and the behavior of materials at extreme temperatures.

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So heat capacity is the change in the mean value of the internal energy when the temperature is changed: C = d<E>/dt
But I would like a little more intuition than that. T^(-1) = dS/d<E>, so going back to the intuition that the inverse of the temperature is a measure of how disordered the system becomes when we change the energy, what does this tell us that heat capacity is a measure for?
The reason I am asking is I got an exercise, where the heat capacity goes from 0 to a max and then back to sorry for T=[0,∞). I am asked to interpret the meaning that C=0 for T=0 or T=∞, but I can't get the right intuition in terms of microstates etc.
 
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Look for an equation where you are expressing C in terms of S and T rather than anything to do with E. (Hint: Multiply your two equations together)
 
well all I could get from that is:

dU = TdS
dU=CdT
so
C=T dS/dT which is just the chain rule for dU/dT=C

Was this what you were looking for? This doesn't for me give a lot of new insight.
 
I could also ask another way. Why is it intuitively that solid materials have C=0 at T=0?
 

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