Question

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. $d^2$

Answer 1

Answer: (A)

Kinetic gas equation, for one mole gas is
$pV=\frac{1}{3}M{u}^2$
where, $p=$ pressure of gas
$V=$ volume of gas
$M=$ molecular mass of gas
$u=$ root mean square velocity
$\Rightarrow \frac{M{u}^2}{3}=pV$
or $u=\sqrt{\frac{3pV}{M}}$
or $u=\sqrt{\frac{3p}{d}}\left\{d=\frac{M}{V}\right\}$
If pressure is constant, then
$u\propto \sqrt{\frac{1}{d}}$