First slide

Rms speed

Question

Molecular hydrogen at one atmosphere and helium at two atmospheres occupy volume V each at the same temperature. The rms velocity of hydrogen molecules is x times the rms velocity of helium molecules. What is the value of x?

Easy

A

1
B

2
C

$\sqrt{2}$
D

$\sqrt{3}$

Solution

$C_{H_{2}} = {xC}_{He}$
As $c \propto \frac{1}{\sqrt{M}}$
$\sqrt{M_{He}} = x \sqrt{M_{H_{2}}}$
$\sqrt{4} = x \sqrt{2}$
or $x = \frac{2}{\sqrt{2}} or x = \sqrt{2}$

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