Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmospheres respectively . If both samples are at the same temperature ,the rms velocity of hydrogen molecules is :

Question

Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmospheres respectively . If both samples are at the same temperature ,the rms velocity of hydrogen molecules is : (A) equal to that of helium (B) twice that of helium (C) half that of helium (D) √2 times that of helium

Tardigrade Admin · Accepted Answer

Given V RMS =√(3 RT / M ) i.e. Ratio of RMS velocities =√(T M text helim /T M text hydrogen ) Both the temperatures are equal. Ratio of RMS velocities =√(4/1)=2 Hence RMS velocity of hydrogen would be twice as much as the RMS for helium.

Q. Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmospheres respectively . If both samples are at the same temperature ,the rms velocity of hydrogen molecules is :

equal to that of helium

twice that of helium

half that of helium

$2$ times that of helium

Given $V_{RMS} = \frac{3 RT}{M}$
i.e. Ratio of RMS velocities $= \frac{T M _{helim}}{T M _{hydrogen}}$
Both the temperatures are equal.
Ratio of RMS velocities $= \frac{4}{1} = 2$
Hence RMS velocity of hydrogen would be twice as much as the RMS for helium.