Q. The rms velocity of an ideal gas at constant pressure varies with density $(d)$ as
A) $\frac{1}{\sqrt{d}}$
B) $d$
C) $\sqrt{d}$
D) $d^{2}$
Explanation
(a)
Kinetic gas equation, for one mole gas is
$pV = \frac{1}{3}\ Mu^{2}$
Where, $p =$ pressure of gas
$V =$ volume of gas
$M =$ molecular mass of gas
$u =$ root mean square velocity
$\Rightarrow \ \ \frac{Mu^{2}}{3} = pV$
or $u = \sqrt{\frac{3pV}{M}}$
or $u = \sqrt{\frac{3p}{d}}$
If pressure is constant, then
$u \propto \sqrt{\frac{1}{d}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.