First slide

Rms speed

Question

The ratio of rms speed of an ideal gas molecules at pressure p to that at pressure 2p at const volume is

Easy

A

1 : 2
B

2 : 1
C

$1 : \sqrt{2}$
D

$\sqrt{2} : 1$

Solution

According to the question,
In the first condition, $p = \frac{1}{3} ρ v_{r m s}^{2}$ …(i)
In the second condition,
$2 p = \frac{1}{3} ρ v_{rms}^{'}$ …(ii)
On dividing Eq. (i) by Eq. (ii), we get
$\frac{v_{rms}^{2}}{v_{rms}^{' 2}} = \frac{1}{2} \Rightarrow \frac{v_{rms}}{v_{rms}^{'}} = \frac{1}{\sqrt{2}}$

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