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# The rms velocity can be calculated by

$(a)\;u=\sqrt{\large\frac{3P}{d}}\qquad(b)\;u = 1.58\sqrt{\large\frac{T}{M}}\times 10^4cm\;sec^{-1}\qquad(c)\;\large\frac{u_2}{u_1}=\sqrt{\large\frac{T_2}{T_1}}\qquad(d)\;Any\;of\;the\;above$

Can you answer this question?

$u = \sqrt{\large\frac{3RT}{M}}$
$\;\;\;=\sqrt{\large\frac{T}{M}}\times \sqrt{3R}$
$\;\;\;=\sqrt{3\times8.314\times10^7}\times \sqrt{\large\frac{T}{M}}$
$\;\;\;=1.58\times10^4\times \sqrt{\large\frac{T}{M}}$
$\;\;\;=\sqrt{\large\frac{3PV}{M}}$
$\;\;\;\;=\sqrt{\large\frac{3P}{d}}$
Hence answer is (d)
answered Mar 2, 2014