Question 393: Thermodynamics & KTG

Question

An HCl molecule has rotational, translational
and vibrational motions. If the rms velocity of
HCl molecules in its gaseous phase is $$\overline v $$ , m is
its mass and k
B
is Boltzmann constant, then its
temperature will be :

Accepted Answer

An HCl molecule, being diatomic, has:
3 translational degrees of freedom
2 rotational degrees of freedom
2 vibrational degrees of freedom
The total number of degrees of freedom is $3 + 2 + 2 = 7$.
According to the equipartition theorem, each degree of freedom contributes $\frac{1}{2} k_B T$ to the total energy. So the total energy is given by:
$\frac{7}{2} k_B T$
The translational kinetic energy is related to the root-mean-square (rms) speed $\overline{v}$ by:
$\frac{1}{2} m \overline{v}^2 = \frac{7}{2} k_B T$
Rearranging to solve for the temperature, we find:
$T = \frac{m \overline{v}^2}{7k_B}$

Answer

$${{m{{\overline v }^2}} \over {5{k_B}}}$$

Answer

$${{m{{\overline v }^2}} \over {6{k_B}}}$$

Answer

$${{m{{\overline v }^2}} \over {7{k_B}}}$$

Answer

$${{m{{\overline v }^2}} \over {3{k_B}}}$$

Thermodynamics & KTG

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\overline v $ , m is its mass and k B is Boltzmann constant, then its temperature will be :

Choose the correct answer: