Question:
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:
Correct Option: 1
Solution:
(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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