The temperature of an ideal gas is increased from 200 K to 800 K. If the r.m.s. speed of the gas at 200 K is , then the r.m.s. speed of the gas at 800 K will be [2023]

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Solution

Q.
The temperature of an ideal gas is increased from 200 K to 800 K. If the r.m.s. speed of the gas at 200 K is $v_{0}$ , then the r.m.s. speed of the gas at 800 K will be [2023]

1 $v_{0}$

2 $4 v_{0}$

3 $\frac{v_{0}}{4}$

4 $2 v_{0}$

Ans.
(4)

$V_{rms} = \sqrt{\frac{3 R T}{M}} \Rightarrow V_{rms} \propto \sqrt{T}$

Increasing the temperature 4 times, the rms speed gets doubled.

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