A very simple assumption for the specific heat of a crystalline solid is that each vibrational mode of the solid acts independently and is fully excited and thus c_v = 3N_A k_B = 24.9 c v =3N A k B =24.9 kJ/(kmol\cdot⋅K). This is called the law of Dulong and Petit. Calculate the Debye specific heat (in units of kJ/(kmol\cdot⋅K) of diamond at room temperature, 298 K. Use a Debye temperature of 2219 K.
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diamond has the Specific Heat capacity of 4.7 kJ/kmol-K.
Explanation:
- The Debye model is a simple way which is used to find the specific heat capacity of a material when we know the avogadro number and the room temperature and the debye temperature.
- By the Debye Model, the formula that is used to find the Specific Heat Capacity in kJ/kmol-K is given by the equation
c = 12π⁴ N k (T / θ )³/5
Here the value of N is the avogadro number which is equal to 6.02 × 10²³ mol⁻¹, k
= 1.38 × 10⁻²³ JK⁻¹
T stands for the room temperature which is equal to 298 K
θ is the Debye Temperature which is equal to 2219 K
- if you use the above values to find the specific heat capacity then substituting each of the value in the equation which is given above
c = 12π⁴Nk(T/θ)³/5
= 12π⁴(6.02 × 10²³ mol⁻¹)(1.38 × 10⁻²³ JK⁻¹)(298 K/2219 K)³/5
= 4.7 J/mol-K
= 4.7 × 10⁻³ kJ/10⁻³ kmol-K
- As a result of this, diamond has the Specific Heat capacity of 4.7 kJ/kmol-K
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