Solveeit Logo

Question

Question: The rms velocity of an ideal gas at \(27^{o}C\) is 0.3 \(ms^{- 1}\). Its rms velocity at \(927^{o}C\...

The rms velocity of an ideal gas at 27oC27^{o}C is 0.3 ms1ms^{- 1}. Its rms velocity at 927oC927^{o}C (in ms1ms^{- 1}) is

A

3.0

B

2.4

C

0.9

D

0.6

Answer

0.6

Explanation

Solution

u=3RTMu = \sqrt{\frac{3RT}{M}}

For the same gas at two different temperatures,

u1u2=T1T2\frac{u_{1}}{u_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}; 0.3u2=3001200=12\frac{0.3}{u_{2}} = \sqrt{\frac{300}{1200}} = \frac{1}{2}, u2=0.6ms1u_{2} = 0.6ms^{- 1}