States of Matter - Result Question 20
####20. The root mean square velocity of an ideal gas at constant pressure varies with density $(d)$ as
(a) $d^{2}$
(b) $d$
(c) $\sqrt{d}$
(d) $1 / \sqrt{d}$
$(2001, S, 1 M)$
Show Answer
Solution:
- Root mean square velocity $\left(u _{rms}\right)=\sqrt{\frac{3 R T}{M}}$
Also,
$$ p \cdot M=d R T $$
Substituting for $R T / M$ in $u _{rms}$ expression gives,
$$ u _{rms}=\sqrt{\frac{3 p}{d}} \Rightarrow u _{rms} \propto \frac{1}{\sqrt{d}} $$
