Question

The average velocity of a gas is $400m{s}^{-1}$.Find the rms velocity of the gas.

• A. $634m{s}^{-1}$
• B. $534m{s}^{-1}$
• C. $334m{s}^{-1}$
• D. $434m{s}^{-1}$

Answer 1

The correct option is D

$434m{s}^{-1}$

The rms and average velocities are given by

$u_{rms}={\left(\frac{3RT}{M}\right)}^{\frac{1}{2}}{u}_{avg}={\left(\frac{8RT}{\pi M}\right)}^{\frac{1}{2}}$

Finding $\frac{u_{rms}}{u_{avg}}$ , we get

$\frac{u_{rms}}{u_{avg}}=\frac{{\left(\frac{3RT}{M}\right)}^{\frac{1}{2}}}{{\left(\frac{8RT}{\pi M}\right)}^{\frac{1}{2}}}={\left(\frac{3\pi }{8}\right)}^{\frac{1}{2}}=1.085$

Thus , $u_{rms}=1.085\times u_{avg}=1.085\times 400=434m{s}^{-1}$