Heat Capacity / Debye Temperature

[UNSWnano]

Homework Statement

We are looking at the molar heat capacity, Cv, of copper over temperatures from 1-300K
After plotting the numbers and looking at T from 1-15K, then fitting that to a curve. We have to find what the constants $$\beta$$ and $$\gamma$$ are in ...
Cv=$$\gamma$$T + $$\beta$$T$$_{3}$$

Where Cv= molar heat capacity
T = temperature
$$\gamma$$ and beta are constants.

Using CurveFit I found
$$\gamma$$ = 7.11E-04
$$\beta$$ = 4.78E-05

The question asks to find the limiting value of $$\Theta$$D which is the Debyne temperature.

It also asks what important information is contained in $$\gamma$$ (I think its electron concentration but wanted to confirm).

And what is the dominant contribution to Cv at low temperature (I would $$\beta$$ as it is obviously dominant).

ADVthanksANCE

 

[BigJDubs]

omework Equations Cv=\gammaT + \betaT_{3}The Attempt at a Solution For the Debye temperature, the limiting value is given by the equation \ThetaD=\left(\frac{12\pi^{4}nR}{5\beta}\right)^{\frac{1}{3}}Where n is the number of atoms per mole and R is the molar gas constant. Therefore, in this case, \ThetaD=187K.The important information contained in \gamma is the number of electrons per atom. This is because \gamma is related to the specific heat capacity at constant volume, which is proportional to the number of electrons in the metal. The dominant contribution to Cv at low temperatures is \beta, as it is the term that dominates the equation at lower temperatures.