Is Heat Capacity the Same for All Materials?

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Discussion Overview

The discussion centers around the concept of heat capacity, specifically whether it is the same for all materials, particularly in the context of Dulong and Petit's law, which states that the heat capacity at constant volume for most solids at high temperatures is 3R. Participants explore the implications of this law and its applicability to different materials.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the heat capacity is the same for all materials, referencing Dulong and Petit's law (Cv=3R) for solids at high temperatures.
  • Another participant clarifies that while Cv is 3R per mole for solids above the Debye temperature, long organic molecules can have a much larger heat capacity due to additional degrees of freedom.
  • A note is made that it is the specific heat capacity per mole that is nearly identical across certain materials.
  • A participant inquires if it is appropriate to use 3R for the specific heat of a classical solid when calculating heat transfer (Q) per mole.
  • Another participant responds that using 3R is an approximation and may not always be accurate, advising caution and the need to clarify when using this value.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Dulong and Petit's law, indicating that while it may work under certain conditions, it is not universally applicable to all materials. The discussion remains unresolved regarding the generalization of heat capacity across different materials.

Contextual Notes

Participants highlight the limitations of classical physics in accurately predicting heat capacity for all materials, suggesting that specific heat capacity can vary significantly depending on the material's properties.

thentangler
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Hi there,
I have a quick question. According to duLong and petit's law, the heat capacity at constant volume for most solids at high temperatures is 3R. (I.e) Cv=3R.
Where R is the gas constant. Does this mean that the heat capacity is the same for all materials?
I thought each material at a unique heat capacity. Can somebody explain?
Thank You
 
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Hello thentangler,
For solids in high enough temperatures above the Debye temperature, the heat capacaity is 3R per mole.

Check the table of temperatures here

http://en.wikipedia.org/wiki/Debye_model#Debye_versus_Einstein

For long organic molecules, the heat capacity can be much larger than 3R per mole, because they have many active degrees of freedom.
 
Note: it is specific heat capacity per mole that is (almost) identical.
 
So suppose I encounter a material that is a classical solid, would it be safe to substitute 3R for its specific heat when I am calculating its Q per mole?
 
Define "safe". Dulong–Petit law is an approximation. Sometimes it works, sometimes it doesn't. If you can't find specific heat capacity and you use 3R you should always spell it out, as it is possible you are way off.
 
Aahh, thank you Borek. The limitations of classical physics I suppose. :)
 

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