First slide

Rms speed

Question

The temperature of an ideal gas is increased from 120K to 480K.The rms Velocity of the gas molecules is v at 120K.At 480k ,it becomes

Moderate

A

4v
B

6v
C

8v
D

2v

Solution

Since we know that
$_{V_{rms} = \sqrt{\frac{3 RT}{M_{w}}}}$
We have, $V_{rms} \propto \sqrt{T .} \Rightarrow {(V_{r m s})}_{T_{2}} = {(V_{r m s})}_{T_{1}} \sqrt{\frac{T_{2}}{T_{1}}}$
Hence ${(V_{rms})}_{T_{2}} = v \times \sqrt{\frac{480}{120}} = 2 v$

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