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At very low temperatures, the heat capacity CV\text{C}_\text{V}CV​​ of a solid is:
Question

At very low temperatures, the heat capacity CV\text{C}_\text{V} of a solid is:

A.

(12π4/5)NkB(T/θ)3\left(12 \pi^4 / 5\right) N k_B(T / \theta)^3​​

B.

(12π4)NkB( T/θ)3\left(12 \pi^4\right) N k_B(\mathrm{~T} / \theta)^3​​

C.

(12π4)NkB(θT)3\left(12 \pi^4\right) N k B\left(\frac{\theta}{T}\right)^3​​

D.

(12π4/5)NkB(θT)3\left(12 \pi^4 / 5\right) N k B\left(\frac{\theta}{T}\right)^3​​

Correct option is A

CV=(12π45)NkB(Tθ)3Where:N is the number of atoms,kB is the Boltzmann constant,T is the temperature,θ is the Debye temperature.C_V = \left( \dfrac{12 \pi^4}{5} \right) N k_B \left( \dfrac{T}{\theta} \right)^3\\\text{Where:}\\\begin{aligned}N &\text{ is the number of atoms,} \\k_B &\text{ is the Boltzmann constant,} \\T &\text{ is the temperature,} \\\theta &\text{ is the Debye temperature.}\end{aligned}​​

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