Question

the debye temperature of a solid element is 2000k.the specific heat per kmol for this element at 50k will be approximately equal to​

Answer 1

Given:

(i) The Debye temperature (Td) of a solid is 2000K.

To find:

(i) The specific heat per kmol of this element at 50K.

Solution:

We know that, according to the Debye's Theory of Specific Heat, the specific heat per kmol is given as:

$S = \frac{12\pi ^{4} * Na * Kb * T^{3} }{5 * (Td)^{3} }$

Here,

Na is Avogadro's constant = 6.023*10²³.

Kb is Boltzmann's constant = 1.38*10⁻²³JK⁻¹.

T is the temperature at which the element is kept = 50K,

Td is Debye's temperature = 2000K.

Substituting the values, we get,

$S = \frac{12\pi ^{4} * (6.023*10^{23}) * (1.38*10^{-23}) * 50^{3} }{5 * (2000)^{3} }$

$= 0.030 Jkmol^{-1} K^{-1}$

This is the value of specific heat per mol.

So, the specific heat per kmol is = S*10³

= (0.030)*10³

= 30 Jkmol⁻¹K⁻¹.

The specific heat per kmol of the element is 30 Jkmol⁻¹K⁻¹.