Lattice specific heat, help understanding a passage in Ziman's book

In summary, the author divides by ##1/V## when calculating the specific heat because it results in an intensive quantity that is independent of system size. This is similar to calculating mass or molar heat capacity. Similarly, when calculating the fraction of modes with frequency in a given range, the author divides by ##V## to find an intensive quantity. This concept is also used in determining the phonon density of states.
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dRic2
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Hi, I don't understand why the author in calculating the expression for the specific heat, divides by ##1/V## (the total volume).
12.jpg


Also, in calculating the fraction of modes with frequency in the range ##v##, ##v+dv## he divides by ##V## (eq. 2.65, 2.67)

11.jpg
Thanks,
Ric
 
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  • #2
Energy is extensive (varies with system size), and dividing by another extensive quantity (volume) gives an intensive quantity. In this case, it’s volumetric heat capacity. Mass or molar heat capacity (where you divide the derivative of heat wrt temperature by mass or amount of substance) are more familiar, but it’s the same idea: you’re looking for a property which is independent of the size of the system.
 
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dRic2 said:
Also, in calculating the fraction of modes with frequency in the range v, v+dv he divides by V (eq. 2.65, 2.67)
The same as indicated by @TeethWhitener: The phonon density of states gives the number of modes per unit frequency per unit volume of real space.
 
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Thank you very much. I had to be sure because it was not explicitly specified, although it might be intuitive.
 

Related to Lattice specific heat, help understanding a passage in Ziman's book

What is lattice specific heat?

Lattice specific heat refers to the amount of heat energy required to raise the temperature of a lattice structure by one unit. It is a measure of the thermal energy stored in the vibrations of the atoms within the lattice.

How is lattice specific heat measured?

Lattice specific heat is typically measured using calorimetry, which involves measuring the change in temperature of a substance as heat is added or removed. The specific heat can then be calculated by dividing the amount of heat energy by the mass and temperature change.

What factors affect lattice specific heat?

The specific heat of a lattice structure is influenced by several factors, including the type of material, its crystal structure, and the temperature at which it is measured. Additionally, the presence of impurities or defects within the lattice can also affect its specific heat.

How does lattice specific heat relate to thermal conductivity?

Lattice specific heat is directly related to thermal conductivity, as both properties are determined by the same factors such as crystal structure and temperature. A material with a higher specific heat will typically have a lower thermal conductivity, as it requires more energy to raise its temperature.

What is the significance of understanding lattice specific heat?

Understanding lattice specific heat is important in the study of materials and their thermal properties. It can help in the design and development of materials for specific applications, as well as in predicting their behavior under different temperature conditions. Additionally, it is a fundamental concept in thermodynamics and solid state physics.

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