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) $1 / \sqrt{d}$
$(2001, S, 1 M)$
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Answer:
Correct Answer: 20. (d)
Solution:
Root mean square velocity $\left(u _{rms}\right)=\sqrt{\dfrac{3 R T}{M}}$
Also,$\hspace{10mm} p \cdot M=d R T $
Substituting for $R T / M$ in $u _{rms}$ expression gives,
$ u _{rms}=\sqrt{\dfrac{3 p}{d}} \Rightarrow u _{rms} \propto \dfrac{1}{\sqrt{d}} $
BETA
