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An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is v̄, m is its mass and kB is Boltzmann constant, then its temperature will be -
- m v̄² / 7kB
- m v̄² / 6kB
- m v̄² / 5kB
- m v̄² / 3kB
Correct answer: m v̄² / 3kB
Solution
The correct option is based on the equipartition theorem, which states that each degree of freedom contributes to the total energy. For a diatomic molecule like HCl, there are three translational and two rotational degrees of freedom, leading to a total of five degrees of freedom. However, the effective temperature relation for gases considers only the translational motion, which results in the factor of 3 in the denominator when relating rms velocity to temperature.
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