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Q. If the temperature of an ideal gas increases three times, then its rms velocity will become

Kinetic Theory

Solution:

The rms velocity of an ideal gas is
$v_{r m s}=\sqrt{\frac{3 R T}{M}}$
Where $T$ is the absolute temperature and $M$ is the molar mass of an ideal gas Since $M$ remains the same
$\therefore v_{r m s} \propto \sqrt{T}$
$\frac{v_{r m s}^{\prime}}{v_{r m s}}=\sqrt{\frac{T^{\prime}}{T}}=\sqrt{\frac{3 T}{T}} $
$\Rightarrow v^{\prime} r m s=\sqrt{3} v_{r m s}$