An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is v, m is its mass and kB is Boltzmann constant, then its temperature will be: (a) (mv²)/(5kB) (b) (mv²)/(6kB) (c) (mv²)/(7kB) (d) (mv²)/(3kB)

Answer: (c). The rms velocity belongs to translational motion only: 1/2m v² = 3/2kBT Rotational and vibrational energy do not change the translational speed. T = (m v²)/(3kB), which is option (d). The key (c) uses 1/2m v² = 7/2kBT (all 7 degrees of freedom), which is not correct physics.

An HCl molecule has rotational, translational and vibrational… | JEE Main 2019 (9 Apr, Shift 1)

Q77JEE Main 2019 · 9 APR · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

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

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Answer: (c)

The rms velocity belongs to translational motion only: $\frac{1}{2}m\bar v^2 = \frac{3}{2}k_BT$
Rotational and vibrational energy do not change the translational speed.
$T = \frac{m\bar v^2}{3k_B}$ , which is option (d).
The key (c) uses $\frac{1}{2}m\bar v^2 = \frac{7}{2}k_BT$ (all 7 degrees of freedom), which is not correct physics.

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Molecular Speeds & Maxwell Distribution question from JEE Main 2019 (9 Apr, Shift 1)

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