Debye's T^3 Law: Specific heat, Latice and Electronic terms

In summary, the conversation discusses the specific heat of KCl and how it is affected by temperature. It is mentioned that the specific heat is dependent on temperature, with an expression given for T<<θD and T>>θD. The discussion also mentions the extraction of lattice and electronic terms in the specific heat, with the electronic contribution being represented by γ. Part b of the question is about finding the y-intercept of the graph and rearranging the electronic contribution formula for EF. The lattice term is also discussed, with a reminder that the term given for C is only for high temperatures.
  • #1
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Homework Statement



QUESTION ADDED AS ATTACHMENT AS NEED TO SEE GRAPH.
Screen Shot 2015-05-06 at 11.59.52.png

Homework Equations


C = (12NkBπ4/5)(T/θD)3 for T<<θD
C = 3NkB for T>>θD

The Attempt at a Solution


a.)[/B] So I assume the expression for the specific heat as a function of temperature that the question must want:
C = (12NkBπ4/5)(T/θD)3
otherwise I thought that the specific heat wasn't dependent on temperature?

The second part of this question really stumped me. I have looked though all of the books in my university library that aren't currently on loan, of which few relevant ones are left for some reason, and can't find anything that helps me extract lattice and electronic terms in the specific heat. Does anyone have any Ideas?

EDIT: Just found something that shows the electronic contribution:
Ce = (π2/3)g(EFkb2T = γT

Therefore the electronic contribution = γ = (π2/3)(3NA/2EF)kB2

Still not sure on the lattice part.
\EDITb.) I think I can do.

c.) The low temperature heat capacity for KCl plotted as to demonstrate the T3 law at low temperatures. The fact that the graph of C/T vs T2 goes through the origin indicates the absence of a term linear in T. I.e there is no contribution to the energy via conduction electrons.

Am I along the right lines here?
 
Last edited:
  • #3
how did you do part b?
 
  • #4
γ is taken as the y intercept on the graph. Then rearrange the electronic contribution formula for EF.
 
  • #5
also the lattice term is just C for low temperature, so the term you have written for C
 

1. What is Debye's T^3 Law?

Debye's T^3 Law is a physical law that describes the temperature dependence of the specific heat capacity of a solid material. It states that at low temperatures, the specific heat capacity of a solid is proportional to T^3, where T is the temperature. This law was developed by physicist Peter Debye in the early 20th century.

2. How does Debye's T^3 Law relate to specific heat?

Debye's T^3 Law states that the specific heat capacity of a solid material is directly proportional to the temperature cubed. This means that as the temperature increases, the specific heat capacity also increases. This relationship helps scientists understand and predict the behavior of solids at different temperatures.

3. What is the significance of the lattice and electronic terms in Debye's T^3 Law?

The lattice and electronic terms in Debye's T^3 Law refer to the two main contributions to the specific heat of a solid. The lattice term describes the vibrations of the atoms in the solid's crystal lattice, while the electronic term accounts for the energy carried by the electrons in the solid. Both terms are important in understanding the specific heat of a solid material.

4. Are there any limitations to Debye's T^3 Law?

Yes, Debye's T^3 Law has some limitations. It is only applicable to solids at low temperatures, typically below 10 K. It also assumes that the solid has a perfect crystal lattice, which is not always the case in real materials. Additionally, it does not take into account other factors that may affect the specific heat of a solid, such as impurities or defects in the crystal structure.

5. How is Debye's T^3 Law used in scientific research?

Debye's T^3 Law is an important tool in studying the behavior of solids at low temperatures. It is used in various fields of science, such as physics, chemistry, and materials science, to understand the properties of different materials. It has also been used to develop new theories and models for specific heat in solids and to make predictions about the behavior of materials in extreme conditions, such as in high-pressure environments.

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