Entropy Question: Calculating Entropy Change for a Diamond

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In summary, the conversation is about using Debye's law to calculate the entropy change of a diamond when heated at constant volume from 10.0 K to 350 K. The equation used is \Delta S = \int_{T_1}^{T_2} C_v \frac{dT}{T}, where C_v is the molar heat capacity at constant volume and TD is the characteristic Debye temperature. The molar mass of carbon is needed for the calculation.
  • #1
Jerzey2Atl
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Hi, this is my first time using this forum. I have a question dealing with entropy and thermodynamics.

Here goes:

According to Debye’s law, the molar heat capacity at constant volume of a
diamond varies with temperature according to the relation

Cv = (12*pi^4*R / 5) x (T / TD)^3

where TD = 2230 K. For a diamond of mass 1. 20 g, what is its entropy change when it is heatedat constant volume from 10. 0 K to 350 K? The molar mass of carbon is 12. 0 g/mol.

I know Ih ave to first find the molar mass, but I am not sure of which form of the entropy equation to use. Any help is appreciated.
 
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  • #2
To solve the problem you can use this equation to find the molar entropy

[tex]\Delta S = \int_{T_1}^{T_2} C_v \frac{dT}{T}[/tex]

Multiply this result by the numer of moles (1.2/12) to get entropy in terms of energy/time.
 
  • #3
Thanks a lot...imma try this.
 

Related to Entropy Question: Calculating Entropy Change for a Diamond

1. What is entropy?

Entropy is a measure of the disorder or randomness of a system. It is a thermodynamic quantity that describes the energy dispersal within a system.

2. How is entropy calculated?

The change in entropy (ΔS) for a system can be calculated using the formula ΔS = Q/T, where Q is the heat transferred and T is the temperature in Kelvin.

3. Why is entropy important in thermodynamics?

Entropy is an important concept in thermodynamics because it helps us understand the direction of spontaneous processes. In general, the entropy of a system increases over time, meaning that the disorder of the system increases.

4. How does a diamond relate to entropy?

A diamond has a low entropy because it has a highly ordered and structured arrangement of atoms. This means that there is little disorder within the system, resulting in a low entropy value.

5. Can entropy change for a diamond?

Yes, the entropy of a diamond can change. It can increase if the diamond is heated, causing the atoms to vibrate more and increase the disorder within the system. It can also decrease if the diamond is cooled, as the atoms will have less energy and be more ordered.

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