Q. Deye Diamond: According to the Debye model, the molar heat capacity at consta

Question

Q. Deye Diamond:

According to the Debye model, the molar heat capacity at constant volume of a diamond varies with temperature according to:

        Equation : http://i40.tinypic.com/2ajpfy8.png

What is the entropy change, of a diamond of mass 1.2g when it is heated at constant volume from 10K to 350K? The molar mass of diamond is 12g/mol and O(symbol in equation under T) is 2230K.

According to the Debye model, the molar heat capacity at constant volume of a diamond varies with temperature according to: What is the entropy change, of a diamond of mass 1.2g when it is heated at constant volume from 10K to 350K? The molar mass of diamond is 12g/mol and O(symbol in equation under T) is 2230K.

Explanation / Answer

?S = (integral)dQ/T
dQ = cvdT (heat capacity at constant volume)
so: ?S = (integral from T1 to T2)(cvdT/T)


So before doing the integral I replaced cv with the Debye's law.

I then moved all the constants outside the integral so I had

?S = 3R(4(pi)4/5)(integral from T1 to T2)(T2/?3dT/T)

Then I integrated and replaced T1 with 10K and T2 with 350K. I also multiplied by .012kg since that's the molar mass.

?S= 0.00362R J/K

?S=0.03009668 J/K

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