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