Question

The rms speed of the molecules of a gas of density $4kg{m}^{-3}$ and pressure $1.2\times {10}^{5}Nm$

• A. $300m{s}^{-1}$
• B. $900m{s}^{-1}$
• C. $120m{s}^{-1}$
• D. $600m{s}^{-1}$

Answer 1

The correct option is A $300m{s}^{-1}$

$\begin{array}{c}Asweknow,\\ u_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3P}{d}}\\ u_{rms}=\sqrt{\frac{3P}{d}}=\sqrt{\frac{3\times 1.2\times {10}^5}{4}}\\ =3\times {10}^{2}m{s}^{-1}=300m/\sec \end{array}$