Q. If the rms speed of a gaseous molecule is $x\ {ms}^{- 1}$ at a pressure $p$ atm, then what will be the rms speed at a pressure $2p$ atm and constant temperature?
A) $x$
B) $2x$
C) $4x$
D) $x/4$
Explanation
(a)
rms speed of a gaseous molecule is $x$ m/s at a pressure $p$ atm.
We know that in kinetic theory of gas
rms speed $= \sqrt{\frac{3RT}{M}}$
We know, $pV = RT\$
then rms speed $= \sqrt{\frac{3pV}{M}}$
As temperature is constant so, $pV$ is constant. Hence, rms speed is also constant. If the pressure is doubled at constant temperature, there is no change in rms speed.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.