If the r.m.s. velocity of a gas at a given temperature (Kelvin scale) is 300 m/s

Question

If the r.m.s. velocity of a gas at a given temperature (Kelvin scale) is 300 m/s, whathat will be the r.m.s. velocity of a gas having twice the molecular weight and half the temperature on Kelvin scale =

Options:

A . 300 m/sec

B . 600 m/sec

C . 75 m/sec

D . 150 m/sec

Answer: Option D
:
D

v_{m a x}

\sqrt{\frac{3 R T}{M}} \Rightarrow V_{m a x} \infty \sqrt{\frac{T}{M}}

\frac{v_{2}}{v_{1}}

\sqrt{\frac{M_{1}}{M_{2}} \times \frac{T_{2}}{T_{1}}} \sqrt{\frac{1}{2} \times \frac{1}{2}}

\Rightarrow v_{2} = \frac{v_{1}}{2} = \frac{300}{2} = 150 m / s e c

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