Cv as a function of temperature for ionic solid and metal

In summary, the conversation discusses the specific heat capacity per unit volume (CV) as a function of temperature (T) for an ionic solid and a metal. The individual is seeking an explanation for why the curves differ and has searched for an answer in the book of Kittel. A possible resource for finding these plots is suggested.
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Homework Statement


The specific heat capacity per unit volume is denoted CV.Sketch Cv/T as a function of temperature T,in the limit T goes to zero, for both an ionic solid ,and a metal.Why do curves differ ?

Homework Equations


The question is very specific ,and in these cases as you know google is not very powerful.
I have searched carefully in the book of Kittel but no comprehesive answer is possible to be obtained from there .At least a hint here would be appreciated.


The Attempt at a Solution


 
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  • #2
Would it be okay to bump this question? I have a similar question and I can't find these plots anywhere.
 
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1. What is the relationship between Cv and temperature for ionic solids and metals?

The specific heat capacity (Cv) is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius. For both ionic solids and metals, the Cv generally increases with temperature. However, for ionic solids, the increase is more gradual, while for metals, it is more steep. This is because the atoms in ionic solids are held together by strong electrostatic forces, making it more difficult to increase their temperature, while the atoms in metals are more loosely bound, allowing for easier temperature changes.

2. How does the electronic structure of a material affect its Cv as a function of temperature?

The electronic structure of a material, specifically the number of valence electrons, can greatly influence its specific heat capacity as a function of temperature. In ionic solids, where the valence electrons are tightly bound to the atoms, there is less freedom for the electrons to move and contribute to the heat capacity. On the other hand, in metals, where valence electrons are free to move, they can contribute significantly to the heat capacity, resulting in a higher Cv.

3. Why does the Cv for metals increase with temperature more rapidly than for ionic solids?

This is because metals have a higher number of free electrons that can contribute to the heat capacity as temperature increases. These electrons have a greater degree of freedom to move and respond to changes in temperature, resulting in a steeper increase in Cv compared to ionic solids.

4. How do defects and impurities in a material affect its Cv as a function of temperature?

Defects and impurities in a material can disrupt its regular structure and affect the movement of electrons and atoms. This can lead to changes in the heat capacity of the material as a function of temperature. For example, the presence of defects in a metal can hinder the movement of electrons, resulting in a lower Cv compared to a pure metal. In contrast, impurities in ionic solids can increase the number of free electrons, leading to a higher Cv.

5. Can the Cv of a material change with temperature in a non-linear manner?

Yes, the Cv of a material can change with temperature in a non-linear manner. This is especially true for materials that undergo phase transitions, such as melting or solidification. During these transitions, a significant amount of heat energy is required to change the temperature of the material, resulting in a sudden change in the Cv. Additionally, changes in the electronic structure of a material at certain temperatures can also lead to non-linear changes in its Cv.

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