An HCl molecule has rotational,


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

  1. (1) $\frac{m \bar{v}^{2}}{6 k_{B}}$

  2. (2) $\frac{m \bar{v}^{2}}{3 k_{B}}$

  3. (3) $\frac{m \bar{v}^{2}}{7 k_{B}}$

  4. (4) $\frac{m \bar{v}^{2}}{5 k_{B}}$

Correct Option: 1


(1) In this case the total degree of freedom is 6 .

According to law of equipartition of energy,

$\frac{1}{2} m v^{-2}=6\left(\frac{1}{2} k_{B} T\right)$

$\therefore \frac{1}{2} m v^{-2}=3 k_{B} T$

or, $T=\frac{m v^{-2}}{6 k_{B}}$

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