KVPY Sample Paper KVPY Stream-SX Model Paper-26

The root mean square velocity of an ideal gas at constant pressure varies with density [d] is

A) \[{{d}^{2}}\]

B) d

C) \[\sqrt{d}\]

D) \[1/\sqrt{d}\]

Correct Answer: D

Solution :

\[{{\operatorname{U}}_{RMS}}=\sqrt{\frac{3RT}{M}}\]using ideal gas equation	\[PV=nRT=\frac{w}{M}RT;\frac{RT}{M}=\frac{PV}{w}=\frac{P}{d}\]where d is density of the gas
\[\therefore \]\[{{U}_{RMS}}=\sqrt{\frac{3P}{d}}\]at constant pressure	\[{{\operatorname{U}}_{RMS}}\propto \frac{1}{\sqrt{d}}\]