# 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 Option 1)   $\frac{m\overline{v}^{2}}{6k_{B}}$ Option 2)   $\frac{m\overline v^{2}}{3k_{B}}$    Option 3) $\frac{m\overline v^{2}}{7k_{B}}$ Option 4)   $\frac{m\overline v^{2}}{5k_{B}}$

HCl has 3 translational , 2 rotational and 1 vibratonal degree of freedom

$E _{internal}$ = No. of degrees of freedom $\inline \times \frac{1}{2}K_{B}T$

$\inline =\; \; 6\times \frac{1}{2}\; K_{B}T$

$\frac{1}{2}\; m\overline{v}^{2}=6\times \frac{1}{2}\; K_{B}T$

$T=\frac{m\overline{v^{2}}}{6k_{B}}$

Option 1)

$\frac{m\overline{v}^{2}}{6k_{B}}$

Option 2)

$\frac{m\overline v^{2}}{3k_{B}}$

Option 3)

$\frac{m\overline v^{2}}{7k_{B}}$

Option 4)

$\frac{m\overline v^{2}}{5k_{B}}$

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