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

The correct option is A $\frac{1}{\sqrt{d}}$

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 $u=\sqrt{\frac{3P}{d}}\{d=\frac{M}{V}\}$

If pressure is constant, then

$u\propto \sqrt{\frac{1}{d}}$

Hence, the correct option is $\text{A}$