IGNOU PHE 13 2026 - Calculate the Debye specific heat of copper at , given that its D

Question

Calculate the Debye specific heat of copper at $300\text{ K}$ , given that its Debye frequency is $4.11 \times 10^{13}\text{ rad s}^{-1}$ .

29 Jan 2026

Answer :

Word Count : 271

The Debye temperature ( \Theta_D ) is related to the Debye frequency ( \omega_D ) by [ \Theta_D = \frac{\hbar \omega_D}{k_B} ] Given: (\omega_D = 4.11 \times 10^{13} , \text{rad/s}), (\hbar = 1.054 \times 10^{-34} , \text{J·s}), (k_B = 1.381 \times 10^{-23} , \text{J/K}). [ \Theta_D = \frac{(1.054 \times 10^{-34}) (4.11 \times 10^{13})}{1.381 \times 10^{-23}} ] Step by step: Numerator: (1.054 \times 4.11 = 4.332) (approx), so [ \hbar \omega_D \approx 4.332 \times 10^{-21} , \text{J} ] Denominator: (k_B = 1.381 \times 10^{-23}). [ \Theta_D = \frac{4.332 \times 10^{-21}}{1.381 \times 10^{-23}} \approx 313.7 , \text{K}

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