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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Solution:

  1. 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,

$$ u _{rms}=\sqrt{\frac{3 p}{d}} \Rightarrow u _{rms} \propto \frac{1}{\sqrt{d}} $$



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