States of Matter 1 Question 20
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20. The root mean square velocity of an ideal gas at constant pressure varies with density $(d)$ as
======= ####20. The root mean square velocity of an ideal gas at constant pressure varies with density $(d)$ as
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (a) $d^{2}$
(b) $d$
(c) $\sqrt{d}$
(d) $1 / \sqrt{d}$
$(2001, \mathrm{~S}, 1 \mathrm{M})$
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Solution:
- Root mean square velocity $\left(u_{\mathrm{rms}}\right)=\sqrt{\frac{3 R T}{M}}$
Also,
$$ p \cdot M=d R T $$
Substituting for $R T / M$ in $u_{\mathrm{rms}}$ expression gives,
$$ u_{\mathrm{rms}}=\sqrt{\frac{3 p}{d}} \Rightarrow u_{\mathrm{rms}} \propto \frac{1}{\sqrt{d}} $$
